{"id":1027,"date":"2022-04-13T10:19:56","date_gmt":"2022-04-13T10:19:56","guid":{"rendered":"https:\/\/www.splashlearn.com\/article-test-new\/?page_id=1027"},"modified":"2024-04-02T09:32:23","modified_gmt":"2024-04-02T09:32:23","slug":"brackets-definition-with-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/brackets","title":{"rendered":"Brackets in Math &#8211; Definition, Types, Examples"},"content":{"rendered":"\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\"><div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-5307669e-7e67-445e-95b5-ed5a40eecdea\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/brackets#0-what-are-brackets>What are Brackets?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/brackets#1-different-kinds-of-brackets>Different kinds of Brackets<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/brackets#3-how-to-use-parentheses-in-math>How to Use Parentheses in Math?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/brackets#8-solved-examples-on-brackets>Solved Examples on Brackets<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/brackets#9-practice-problems-on-brackets>Practice Problems on Brackets<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/brackets#10-frequently-asked-questions-on-brackets>Frequently Asked Questions on Brackets<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-are-brackets\">What are Brackets?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>You must have seen different symbols like these: (, ), [, ], {, and } in your math books. These symbols are called brackets<\/strong>. Brackets in mathematics serve a very important purpose; these symbols help us group different expressions or numbers together. Brackets imply that the thing or expression enclosed by them is to be given higher precedence over other things.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"346\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/brackets-expressions.png\" alt=\"Brackets Expressions\" class=\"wp-image-41603\" title=\"Brackets Expressions\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/brackets-expressions.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/brackets-expressions-300x167.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/evaluate-algebraic-expressions-with-one-operation\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/algebra_evaluate_algebric_exp_1_pt.png\" alt=\"Evaluate Algebraic Expressions with One Operation Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Evaluate Algebraic Expressions with One Operation Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/evaluate-algebraic-expressions-with-two-operations\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/algebra_evaluate_algebric_exp_2_pt.png\" alt=\"Evaluate Algebraic Expressions with Two Operations Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Evaluate Algebraic Expressions with Two Operations Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/form-algebraic-expressions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/algebra_choose_exp_1_pt.png\" alt=\"Form Algebraic Expressions Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Form Algebraic Expressions Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    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     checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"1-different-kinds-of-brackets\">Different kinds of Brackets<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In math, you will often have to use brackets while creating or solving equations. They help in grouping numbers and defining the order of operations. Generally, three kinds of brackets are used in mathematics,<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Parentheses or Round Brackets, ( )<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Curly or Brace Brackets { }<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Square or Box Brackets [ ]<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"292\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/different-kinds-of-brackets-parentheses-braces-and-square-brackets.png\" alt=\"Different Kinds of Brackets : Parentheses , Braces and Square Brackets.\" class=\"wp-image-41604\" title=\"Different Kinds of Brackets : Parentheses , Braces and Square Brackets.\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/different-kinds-of-brackets-parentheses-braces-and-square-brackets.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/different-kinds-of-brackets-parentheses-braces-and-square-brackets-300x141.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Brackets always come in pairs, and if there is an opening bracket, there has to be a closing bracket. The opening brackets are (, [&nbsp; and {. Their corresponding closing brackets are ), ] and }.&nbsp;&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-parentheses-brackets\">Parentheses Brackets<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">These are also known as the round brackets and written as ( ). These are the most common types of brackets. They are used for grouping different values and equations together. Parentheses or \u201cround brackets\u201d are used to group terms together or specify the order of operations in an equation.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"643\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/parentheses.png\" alt=\"Parentheses\" class=\"wp-image-41605\" title=\"Parentheses\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/parentheses.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/parentheses-289x300.png 289w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-how-to-use-parentheses-in-math\">How to Use Parentheses in Math?<\/h2>\n\n\n\n<ol class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">In math, you can use parentheses in math to separate numbers. For instance, you can use them to mention negative numbers when writing an addition equation.<\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here is an example to understand this better:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$3 + ( \u22125) = \u22122$<\/p>\n\n\n\n<ol start=\"2\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The second use of parentheses in math is to multiply numbers. If there is no arithmetic operation present in an equation, the presence of parentheses means you have to apply <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/multiplication\" title=\"\">multiplication<\/a>.<\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let us understand this with an example:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$6 (4 + 2)$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">can be written as $6 \\times (4 + 2)$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Therefore, the answer is $6 \\times 6 = 36$.<\/p>\n\n\n\n<ol start=\"3\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The third and final use of parentheses in math is to group numbers and define the order of operations.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">When used simply around numbers, the round brackets denote multiplication.<\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example : $(3)(4) = 12$<\/p>\n\n\n\n<ol start=\"5\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">They can also be used to write negative integers in mathematical expressions.<\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example $5 + ( \u22124) = 1$<\/p>\n\n\n\n<ol start=\"6\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Parentheses can also be used to separate out numbers from their exponents. For example: $(2)^{-3}$<\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Examples: $(2 + 4), 5(111), 25 \u2212 (12 + 8)$, etc.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-curly-brackets\">Curly Brackets<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Braces in math are symbols that are used twice, once to open \u201c{\u201c and once to close \u201c}\u201d an argument, <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/expression\" title=\"\">expression<\/a>, or <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/equation\" title=\"\">equation<\/a>. These are commonly referred to as curly brackets and written as { }.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In general, we use braces in math for two purposes:<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">For grouping a large equation, in which the second-last bracket is braces or curly brackets. For example, $7[2 + \\left\\{3(1 + 1) + 1\\right\\}]$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">For denoting a set, such as {x, y, z,\u2026}<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Like Parentheses, curly brackets are also used to group various mathematical components; however, curly brackets are also used to depict sets or to write nested expressions.&nbsp; Examples:&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$[4+\\left\\{3\\times(-2)\\right\\}] \u2212 [\\left\\{(4 \\times 6)+(14 \\div 7)\\right\\} \u2212 ( \u22123)]$,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;$[\\left\\{12 \u2212 (12 \u2212 2)\\right\\} + (5 \u2212 7)] + 9$, etc.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>How Do We Use Braces in Math?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Braces in math are frequently used in mathematical expressions when we have two or more than two nested groups for calculations.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So, in the first nested group, we use parentheses. In the second nested group, we use braces, and in the third nested group, we use box brackets, which contain both parentheses and braces.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example: $3[2 \u2212 \\left\\{4(2 + 2) + 2\\right\\}]$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here, we have three nested groups with appropriate brackets.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So, the order of solving would be<em>:<\/em><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"310\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/order-of-using-brackets-in-math.png\" alt=\"Order of using Brackets in Math\" class=\"wp-image-41606\" title=\"Order of using Brackets in Math\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/order-of-using-brackets-in-math.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/order-of-using-brackets-in-math-300x150.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-fun-facts\">Fun Facts<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-4fc3f8e1 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>Some conventions differentiate the order of solving brackets, which is:<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"280\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/alternate-order-of-using-brackets-in-math.png\" alt=\"Alternate Order of Using Brackets in Math\" class=\"wp-image-41607\" title=\"Alternate Order of Using Brackets in Math\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/alternate-order-of-using-brackets-in-math.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/alternate-order-of-using-brackets-in-math-300x135.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><em>We will use the first convention with curly brackets in the second position throughout this article.<\/em><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">You need to know the BODMAS or order of operations to simplify and solve a problem.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-square-brackets\">Square Brackets<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Square brackets are generally used to distinguish between sub-expressions of a complex mathematical expression.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Examples: $[100 \u2212 (3 \u2212 1) + (7 \\times 8)], 10 \\times [(4 \u2212 2) \\times ( 4 \\times 2)]$, etc.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-order-of-operations-of-brackets\">Order of Operations of Brackets<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">When we evaluate a mathematical expression that is made up of different brackets, we have to follow certain rules. This is called the rules of operation or order of operation of brackets.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">When we have a long equation for multiplication, <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/division\/division\" title=\"\">division<\/a>, <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/addition\/addition\" title=\"\">addition<\/a>, and <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/subtraction\/subtract\" title=\"\">subtraction<\/a>, we solve each function in order to find the right answer. If the problem is solved without this order, then the chances of getting a wrong answer are high!<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The general order of operation of the bracket can be illustrated as $[ \\left\\{ ( ) \\right\\} ]$; this means that in a given problem, you would have to simplify the values in the innermost bracket first. This means that first $( )$ brackets will be solved, following which, $\\left\\{ \\right\\}$ brackets are solved and finally $[ ]$ brackets.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The second step in solving these problems is to look for an exponent; if there is any, solve it first.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">In the third step, we look for expressions with multiplication or division operators. If both the operators are present, we check the expression from left to right. Whichever operator comes first, we solve that operator first.<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example, in the expression, $10 \\times 6 \\div 5$, we check from left to right, since multiplication comes first so we solve multiplication first and then division.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$10 \\times 6 \\div 5$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$=60 \\div 5$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 12$<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">In the fourth and last step, we look for numbers that need to be added or subtracted. We follow the same instruction if both the operators are present, we look from left to right in the expression, and whichever operator comes first, we solve that expression first. But if the operations are in brackets, we always solve the brackets first since brackets have the utmost precedence.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"285\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/pemdas-meaning.png\" alt=\"PEMDAS meaning\" class=\"wp-image-41608\" title=\"PEMDAS meaning\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/pemdas-meaning.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/pemdas-meaning-300x138.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">To remember the above mention steps, we can use the acronym PEMDAS,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">P &#8211; Parentheses,(or brackets)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">E &#8211; <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/exponent\" title=\"\">Exponents<\/a>, (or order)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">M &#8211; Multiplication&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">D &#8211; Division<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A &#8211; Addition<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">S &#8211; Subtraction.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Example 1: Let&#8217;s use pemdas to evaluate the expression&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$100 \u2212 [(3 \u2212 1) + (7 \\times 8)]$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Step 1: Solve the brackets. Follow the order of solving round brackets $( )$ first, then curly brackets $\\left\\{ \\right\\}$, and then square brackets $[ ]$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 100 \u2212 [(2) + (56)]$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 100 \u2212 58$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Step 2: No exponent in the given expression.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Step 3: No multiplication or division in the given expression.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Step 4: Solve the subtraction.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 100 \u2212 58$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 42$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Example 2: While we write the order in the above form, division or multiplication and addition or subtraction hold equal importance. This means that you can either take up multiplication first or division first.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Similarly, you can take either addition first or subtraction first. The answer will be the same. So, we usually try to solve these two from left to right.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let\u2019s solve the above example:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$4[2 + \\left\\{3(1 + 1) + 2\\right\\}]$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">First, we start with the innermost bracket (the parentheses).<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 4[2 + \\left\\{3(2) + 2\\right\\}]$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Now, we solve the braces or curly brackets.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 4[2 + \\left\\{6 + 2\\right\\}]$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 4[2 + 8]$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Then, we solve the square brackets.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 4[10]$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 40$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In summary:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here is the order you can follow when multiple symbols are present in an equation:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"385\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/order-of-operations.png\" alt=\"Order of Operations\" class=\"wp-image-41609\" title=\"Order of Operations\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/order-of-operations.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/order-of-operations-300x186.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If you come across parentheses in an equation, you will first look at the terms present within them.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let us understand this better with an example.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Take the problem: $9 \u2212 10 \\div 5 \u2013 3 \\times 2 + 7$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let us solve this using the order of operations you have learned.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 9 \u2212 10 \\div 5 \u2013 3 \\times 2 + 7$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 9 \u2212 2 \u2212 3 \\times 2 + 7$ (First, you divide)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 9 \u2212 2 \u2212 6 + 7$ (Then, you multiply)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 7 \u2212 6 + 7$ (Then, you subtract)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 1 + 7$ (Then, you subtract)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 8$ (And finally, you add)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Now, let us look at the same problem with parentheses:&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$9 \u2212 10 \\div (5 \u2212 3) \\times 2 + 7$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">You need to calculate the numbers within the parentheses first.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 9 \u2212 10 \\div 2 \\times 2 + 7$ (Solve the expression inside the parentheses)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 9 \u2212 5 \\times 2 + 7$ (Divide)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 9 \u2212 10 + 7$ (Multiply)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= \u22121 + 7$ (Add)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 6$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Did you notice? The answer to the same equation changed because parentheses were present in the equation!<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Point to Remember: If there are parentheses inside other parentheses, you solve the inner expression first.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let us understand this with an example:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Simplify the expression $(2 + (3 \\times 4))$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here, we will solve the inner bracket first.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So, the expression will become $(2 + 12) = 14$<br><br>Note that it is highly recommended to write any mathematical equation or expression with proper use of parentheses, leaving no place for ambiguity. It is important to convey the intention behind writing the math operations and indicate which operations should be carried out first.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-solved-examples-on-brackets\">Solved Examples on Brackets<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Question 1: Find the value of the expression: <\/strong>$(5 + 4) \u2212 (3 \u2212 2)$<strong>.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Answer:<\/strong> The given expression is,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$(5 + 4) \u2212 (3 \u2212 2)$,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Step 1: Solving the values in the brackets,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$(9) \u2212 (1)$,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, the answer is $(9) \u2212 (1) = 8$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Question 2: Find the value of the expression: <\/strong>$\\left\\{(7 \u2212 2) \\times 3\\right\\}&nbsp; \\div 5$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Answer: The given equation is,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\left\\{(7 \u2212 2) \\times 3\\right\\}&nbsp; \\div 5$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Step 1: Solving the parentheses&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\left\\{(7 \u2212 2) \\times 3\\right\\}&nbsp; \\div 5$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= \\left\\{5 \\times 3\\right\\} \\div 5$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Solving the curly bracket<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= \\left\\{15\\right\\} \\div 5$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 15 \\div 5$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 3$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Question 3: Find the value of the expression: <\/strong>$(12 \\div 6) \\times (4 \u2212 2)$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Solution:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The given equation is,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$(12 \\div 6) \\times (4 \u2212 2)$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Solving the values in the brackets,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$(2) \\times (2)$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, the answer is $(2) \\times (2) = 4$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Question 4: Find the value of the expression: <\/strong>$[120 + \\left\\{ (3 \\times 4) + (4 \u2212 2) \u2212 1 \\right\\} + 20 ]$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Answer:<\/strong> Following the PEMDAS rule, first,&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Step 1: We solve the values in ( ) brackets,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$[120 + \\left\\{ (3 \\times 4) + (4 \u2212 2) \u2212 1 \\right\\} + 20 ]$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= [ 120 + \\left\\{ (12 ) + ( 2 ) \u2212 1 \\right\\} + 20 ]$,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Now we solve the values inside the { } brackets,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= [ 120 + \\left\\{ 13 \\right\\} + 20 ]$,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Finally, add all the values in the [ ] bracket,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The answer is 153.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example 5: Simplify the expression: <\/strong>$(2 + 4 \\times 6) \u2212 4 + (2 \\times 3)$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution<\/strong>: Start by solving the expressions inside the parentheses.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= (2 + 24) \u2212 4 + 6$ (Multiply inside the parentheses)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 26 \u2212 4 + 6$ (Solve the terms inside the parentheses)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 22 + 6$ (Add)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 28$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example 6: Simplify the expression: <\/strong>$( 2 \\times (7 \u2212 5)) \u2212 ((6 \\div 3) + 4)$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Start by solving the innermost parentheses<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= (2 \\times 2) \u2212 (2 + 4)$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 4 \u2212 6$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= \u2212 2$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example 7: Simplify the expression: <\/strong>$2 (3 + 5) + 8 (4 \u2212 1)$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">First, solve the expressions within the parentheses.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here, the parentheses also denote a multiplication sign.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 2 \\times 8 + 8 \\times 3$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 16 + 24$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 40$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example 8: If you have to solve the following equation, how will you proceed?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$2[1 \u2212 \\left\\{2(2 + 2) + 2\\right\\}]$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong> We solve the parentheses first:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 2[1 \u2212 \\left\\{2(4) + 2\\right\\}]$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 2[1 \u2212 \\left\\{8 + 2\\right\\}]$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Now, we solve the braces:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 2[1 \u2212 \\left\\{10\\right\\}]$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Finally, we solve the square brackets:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 2[ \u22129]$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= \u221218$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example 9: How would you solve the following equation?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$4\\left\\{5(4 + 2) + 1\\right\\}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong> First, we solve the parentheses:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 4\\left\\{5(6) + 1\\right\\}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Now, we need to solve the curly brackets. But within these brackets, we have to solve multiplication and addition.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So, we multiply first and then add:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 4 \\left\\{30 + 1\\right\\}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 4 \\left\\{31\\right\\}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Finally, we multiply 4 with the value inside the braces:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 124$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example 10: What is the process you will follow to solve an equation with more than one parentheses?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$20 \\div \\left\\{1(2 + 2) + (3 + 3)\\right\\}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong> We will start by solving the equations within the parentheses:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 20 \\div \\left\\{1(4) + (3 + 3)\\right\\}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 20 \\div \\left\\{1(4) + (6)\\right\\}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Now, we have to solve the equation within the braces, but we have multiplication within the curly brackets, so we will solve that first:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;$= 20 \\div \\left\\{4 + (6)\\right\\}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 20 \\div \\left\\{10\\right\\}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 2 \\div 1$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 2$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-practice-problems-on-brackets\">Practice Problems on Brackets<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Brackets<\/h2><p style=\"display:none;\">Attend this Quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">Solve: $[\\left\\{(2^{2} + 3^{3}) \\times 4^{2}\\right\\} \u2212 (20 \\div 5)]$<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">490<\/div><div class=\"spq_answer_block\" data-value=\"1\">492<\/div><div class=\"spq_answer_block\" data-value=\"2\">494<\/div><div class=\"spq_answer_block\" data-value=\"3\">500<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 492<br\/>Step 1: Solve all brackets keeping the precedence in mind.<br>\r\n$[\\left\\{(2^{2} + 3^{3}) \\times 42\\right\\} \u2212 (20 \\div 5)]$<br>\r\n$= [\\left\\{(4 + 27) \\times 16\\right\\} \u2212 (4)]$<br>\r\n$= [\\left\\{(31) \\times 16\\right\\} \u2212 (4)]$<br>\r\n$= [{31 \\times 16} \u2212 4]$<br>\r\n$= [496 \u2212 4]$<br>\r\n$= 492$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">What is the right representation of the order of operation in brackets?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$( \\left\\{ [ ] \\right\\} )$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$[ ( \\left\\{ \\right\\} ) ]$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\left\\{ [ ( ) ] \\right\\}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$[ \\left\\{ ( ) \\right\\} ]$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $[ \\left\\{ ( ) \\right\\} ]$<br\/>$[ \\left\\{ ( ) \\right\\} ]$ is the correct representation of order of operation in brackets.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">$\\Biggr [\\bigg\\{ \\bigg( \\frac{1}{2} \\bigg)^2 \\bigg\\}^{-3} \\Biggr]^2$<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">4,096<\/div><div class=\"spq_answer_block\" data-value=\"1\">64<\/div><div class=\"spq_answer_block\" data-value=\"2\">256<\/div><div class=\"spq_answer_block\" data-value=\"3\">1,024<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 4,096<br\/>$\\Biggr[\\bigg\\{ \\bigg(\\frac{1}{2}\\bigg)^{2}\\bigg\\}^{-3}\\Biggr]^{2} = \\Biggr[\\bigg\\{\\frac{1}{4}\\bigg\\}^{-3}\\Biggr]^{2} = \\Biggr[\\bigg\\{\\frac{4}{1}\\bigg\\}^{3}\\Biggr]^{2} = [64]^{2} = 4,096$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">Solve this expression, $12 + (5 + 3)$,<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">18<\/div><div class=\"spq_answer_block\" data-value=\"1\">20<\/div><div class=\"spq_answer_block\" data-value=\"2\">16<\/div><div class=\"spq_answer_block\" data-value=\"3\">8<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 20<br\/>$12 + (5 + 3) = 12 + 8 = 20$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">Simplify the expression: $(3 + 2 \\times 8) \u2013 4 + (5 \\times 7)$<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">45<\/div><div class=\"spq_answer_block\" data-value=\"1\">50<\/div><div class=\"spq_answer_block\" data-value=\"2\">24<\/div><div class=\"spq_answer_block\" data-value=\"3\">40<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 50<br\/>We know that the equation within the parentheses is solved first.<br>\r\nSo, $19 \u2013 4 + 35 = 50$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">6<\/span><h3 class=\"sqp_question_text\">Simplify the expression: $( 4 \\times (6 \u2013 2)) \u2013 ((8 \\div 2) + 5 )$<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">7<\/div><div class=\"spq_answer_block\" data-value=\"1\">2<\/div><div class=\"spq_answer_block\" data-value=\"2\">17<\/div><div class=\"spq_answer_block\" data-value=\"3\">10<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 7<br\/>We know that the equation within the parentheses is solved first.<br>\r\nSo, $( 4 \\times 4) \u2013 ( 4 + 5)$<br>\r\n$16 \u2013 9 = 7$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">7<\/span><h3 class=\"sqp_question_text\">Simplify the expression: $4 (3 + 2) + 4 (7 \u2013 2)$<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">10<\/div><div class=\"spq_answer_block\" data-value=\"1\">50<\/div><div class=\"spq_answer_block\" data-value=\"2\">20<\/div><div class=\"spq_answer_block\" data-value=\"3\">40<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 40<br\/>We know that parentheses also denote multiplication.<br>\r\nSo, $4 \\times 5 + 4 \\times 5$<br>\r\n$20 + 20 = 40$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">8<\/span><h3 class=\"sqp_question_text\">Solve the equation containing braces in math.<br> $57 \\div \\left\\{5 + (4 \\times 2) + (3 + 3)\\right\\}$<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">3<\/div><div class=\"spq_answer_block\" data-value=\"1\">4<\/div><div class=\"spq_answer_block\" data-value=\"2\">13<\/div><div class=\"spq_answer_block\" data-value=\"3\">4<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 3<br\/>After solving the $( )$, we perform addition within the $\\left\\{ \\right\\}$, and then divide.\r\n$57 \\div {5 + (4  2) + (3 + 3)} = 57  {5 + 8 + 6} = 57 19 = 3$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">9<\/span><h3 class=\"sqp_question_text\">Which of the following examples use braces, brackets, and parentheses correctly?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">60 $\\div$ [(2 $\\times$ 2) + (3 + 3)}<\/div><div class=\"spq_answer_block\" data-value=\"1\">60 $\\div$ {(2 $\\times$ 2) + (3 + 3)}<\/div><div class=\"spq_answer_block\" data-value=\"2\">60 $\\div$ {[2 $\\times$ 2] + (3 + 3)}<\/div><div class=\"spq_answer_block\" data-value=\"3\">(60 $\\div$ {[2 $\\times$ 2] + (3 + 3})<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 60 $\\div$ {(2 $\\times$ 2) + (3 + 3)}<br\/>It uses the braces, brackets, and parentheses correctly because the innermost brackets have parentheses and then braces.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">10<\/span><h3 class=\"sqp_question_text\">If we have the following expressions inside the curly brackets, which of the expressions would you solve first?<br> $10\\left\\{(\\frac{4}{2}) + (6 \\times 2) \u2013 (3 + 3) + (7 \u2013 2)\\right\\}$<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$(\\frac{4}{2})$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$(\\frac{4}{2}) \\text{or} (6 \\times 2)$<\/div><div class=\"spq_answer_block\" data-value=\"2\">Any parentheses inside the $\\left\\{ \\right\\}, (\\frac{4}{2}), (6 \\times 2), (3 + 3), (7 \u2013 2)$}<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of the above<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: Any parentheses inside the $\\left\\{ \\right\\}, (\\frac{4}{2}), (6 \\times 2), (3 + 3), (7 \u2013 2)$}<br\/>We can solve any of the parentheses inside the curly brackets first. Once these parentheses are solved, we have to simply add and subtract, which can be done in any order.<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this Quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Brackets\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Brackets\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Solve: $$[\\\\left\\\\{(2^{2} + 3^{3}) \\\\times 4^{2}\\\\right\\\\} \u2212 (20 \\\\div 5)]$$\",\n                    \"text\": \"Solve: $$[\\\\left\\\\{(2^{2} + 3^{3}) \\\\times 4^{2}\\\\right\\\\} \u2212 (20 \\\\div 5)]$$\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Step 1: Solve all brackets keeping the precedence in mind.<br>\r\n$$[\\\\left\\\\{(2^{2} + 3^{3}) \\\\times 42\\\\right\\\\} \u2212 (20 \\\\div 5)]$$<br>\r\n$$= [\\\\left\\\\{(4 + 27) \\\\times 16\\\\right\\\\} \u2212 (4)]$$<br>\r\n$$= [\\\\left\\\\{(31) \\\\times 16\\\\right\\\\} \u2212 (4)]$$<br>\r\n$$= [{31 \\\\times 16} \u2212 4]$$<br>\r\n$$= [496 \u2212 4]$$<br>\r\n$$= 492$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"490\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Step 1: Solve all brackets keeping the precedence in mind.<br>\r\n$$[\\\\left\\\\{(2^{2} + 3^{3}) \\\\times 42\\\\right\\\\} \u2212 (20 \\\\div 5)]$$<br>\r\n$$= [\\\\left\\\\{(4 + 27) \\\\times 16\\\\right\\\\} \u2212 (4)]$$<br>\r\n$$= [\\\\left\\\\{(31) \\\\times 16\\\\right\\\\} \u2212 (4)]$$<br>\r\n$$= [{31 \\\\times 16} \u2212 4]$$<br>\r\n$$= [496 \u2212 4]$$<br>\r\n$$= 492$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"494\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Step 1: Solve all brackets keeping the precedence in mind.<br>\r\n$$[\\\\left\\\\{(2^{2} + 3^{3}) \\\\times 42\\\\right\\\\} \u2212 (20 \\\\div 5)]$$<br>\r\n$$= [\\\\left\\\\{(4 + 27) \\\\times 16\\\\right\\\\} \u2212 (4)]$$<br>\r\n$$= [\\\\left\\\\{(31) \\\\times 16\\\\right\\\\} \u2212 (4)]$$<br>\r\n$$= [{31 \\\\times 16} \u2212 4]$$<br>\r\n$$= [496 \u2212 4]$$<br>\r\n$$= 492$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"500\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Step 1: Solve all brackets keeping the precedence in mind.<br>\r\n$$[\\\\left\\\\{(2^{2} + 3^{3}) \\\\times 42\\\\right\\\\} \u2212 (20 \\\\div 5)]$$<br>\r\n$$= [\\\\left\\\\{(4 + 27) \\\\times 16\\\\right\\\\} \u2212 (4)]$$<br>\r\n$$= [\\\\left\\\\{(31) \\\\times 16\\\\right\\\\} \u2212 (4)]$$<br>\r\n$$= [{31 \\\\times 16} \u2212 4]$$<br>\r\n$$= [496 \u2212 4]$$<br>\r\n$$= 492$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"492\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Step 1: Solve all brackets keeping the precedence in mind.<br>\r\n$$[\\\\left\\\\{(2^{2} + 3^{3}) \\\\times 42\\\\right\\\\} \u2212 (20 \\\\div 5)]$$<br>\r\n$$= [\\\\left\\\\{(4 + 27) \\\\times 16\\\\right\\\\} \u2212 (4)]$$<br>\r\n$$= [\\\\left\\\\{(31) \\\\times 16\\\\right\\\\} \u2212 (4)]$$<br>\r\n$$= [{31 \\\\times 16} \u2212 4]$$<br>\r\n$$= [496 \u2212 4]$$<br>\r\n$$= 492$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Step 1: Solve all brackets keeping the precedence in mind.<br>\r\n$$[\\\\left\\\\{(2^{2} + 3^{3}) \\\\times 42\\\\right\\\\} \u2212 (20 \\\\div 5)]$$<br>\r\n$$= [\\\\left\\\\{(4 + 27) \\\\times 16\\\\right\\\\} \u2212 (4)]$$<br>\r\n$$= [\\\\left\\\\{(31) \\\\times 16\\\\right\\\\} \u2212 (4)]$$<br>\r\n$$= [{31 \\\\times 16} \u2212 4]$$<br>\r\n$$= [496 \u2212 4]$$<br>\r\n$$= 492$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the right representation of the order of operation in brackets?\",\n                    \"text\": \"What is the right representation of the order of operation in brackets?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$[ \\\\left\\\\{ ( ) \\\\right\\\\} ]$$ is the correct representation of order of operation in brackets.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$( \\\\left\\\\{ [ ] \\\\right\\\\} )$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$[ \\\\left\\\\{ ( ) \\\\right\\\\} ]$$ is the correct representation of order of operation in brackets.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$[ ( \\\\left\\\\{ \\\\right\\\\} ) ]$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$[ \\\\left\\\\{ ( ) \\\\right\\\\} ]$$ is the correct representation of order of operation in brackets.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\left\\\\{ [ ( ) ] \\\\right\\\\}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$[ \\\\left\\\\{ ( ) \\\\right\\\\} ]$$ is the correct representation of order of operation in brackets.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$[ \\\\left\\\\{ ( ) \\\\right\\\\} ]$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$[ \\\\left\\\\{ ( ) \\\\right\\\\} ]$$ is the correct representation of order of operation in brackets.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$[ \\\\left\\\\{ ( ) \\\\right\\\\} ]$$ is the correct representation of order of operation in brackets.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"$$\\\\Biggr [\\\\bigg\\\\{ \\\\bigg( \\\\frac{1}{2} \\\\bigg)^2 \\\\bigg\\\\}^{-3} \\\\Biggr]^2$$\",\n                    \"text\": \"$$\\\\Biggr [\\\\bigg\\\\{ \\\\bigg( \\\\frac{1}{2} \\\\bigg)^2 \\\\bigg\\\\}^{-3} \\\\Biggr]^2$$\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$\\\\Biggr[\\\\bigg\\\\{ \\\\bigg(\\\\frac{1}{2}\\\\bigg)^{2}\\\\bigg\\\\}^{-3}\\\\Biggr]^{2} = \\\\Biggr[\\\\bigg\\\\{\\\\frac{1}{4}\\\\bigg\\\\}^{-3}\\\\Biggr]^{2} = \\\\Biggr[\\\\bigg\\\\{\\\\frac{4}{1}\\\\bigg\\\\}^{3}\\\\Biggr]^{2} = [64]^{2} = 4,096$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"64\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\Biggr[\\\\bigg\\\\{ \\\\bigg(\\\\frac{1}{2}\\\\bigg)^{2}\\\\bigg\\\\}^{-3}\\\\Biggr]^{2} = \\\\Biggr[\\\\bigg\\\\{\\\\frac{1}{4}\\\\bigg\\\\}^{-3}\\\\Biggr]^{2} = \\\\Biggr[\\\\bigg\\\\{\\\\frac{4}{1}\\\\bigg\\\\}^{3}\\\\Biggr]^{2} = [64]^{2} = 4,096$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"256\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\Biggr[\\\\bigg\\\\{ \\\\bigg(\\\\frac{1}{2}\\\\bigg)^{2}\\\\bigg\\\\}^{-3}\\\\Biggr]^{2} = \\\\Biggr[\\\\bigg\\\\{\\\\frac{1}{4}\\\\bigg\\\\}^{-3}\\\\Biggr]^{2} = \\\\Biggr[\\\\bigg\\\\{\\\\frac{4}{1}\\\\bigg\\\\}^{3}\\\\Biggr]^{2} = [64]^{2} = 4,096$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"1,024\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\Biggr[\\\\bigg\\\\{ \\\\bigg(\\\\frac{1}{2}\\\\bigg)^{2}\\\\bigg\\\\}^{-3}\\\\Biggr]^{2} = \\\\Biggr[\\\\bigg\\\\{\\\\frac{1}{4}\\\\bigg\\\\}^{-3}\\\\Biggr]^{2} = \\\\Biggr[\\\\bigg\\\\{\\\\frac{4}{1}\\\\bigg\\\\}^{3}\\\\Biggr]^{2} = [64]^{2} = 4,096$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"4,096\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$\\\\Biggr[\\\\bigg\\\\{ \\\\bigg(\\\\frac{1}{2}\\\\bigg)^{2}\\\\bigg\\\\}^{-3}\\\\Biggr]^{2} = \\\\Biggr[\\\\bigg\\\\{\\\\frac{1}{4}\\\\bigg\\\\}^{-3}\\\\Biggr]^{2} = \\\\Biggr[\\\\bigg\\\\{\\\\frac{4}{1}\\\\bigg\\\\}^{3}\\\\Biggr]^{2} = [64]^{2} = 4,096$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$\\\\Biggr[\\\\bigg\\\\{ \\\\bigg(\\\\frac{1}{2}\\\\bigg)^{2}\\\\bigg\\\\}^{-3}\\\\Biggr]^{2} = \\\\Biggr[\\\\bigg\\\\{\\\\frac{1}{4}\\\\bigg\\\\}^{-3}\\\\Biggr]^{2} = \\\\Biggr[\\\\bigg\\\\{\\\\frac{4}{1}\\\\bigg\\\\}^{3}\\\\Biggr]^{2} = [64]^{2} = 4,096$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Solve this expression, $$12 + (5 + 3)$$,\",\n                    \"text\": \"Solve this expression, $$12 + (5 + 3)$$,\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$12 + (5 + 3) = 12 + 8 = 20$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"18\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$12 + (5 + 3) = 12 + 8 = 20$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"16\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$12 + (5 + 3) = 12 + 8 = 20$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"8\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$12 + (5 + 3) = 12 + 8 = 20$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"20\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$12 + (5 + 3) = 12 + 8 = 20$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$12 + (5 + 3) = 12 + 8 = 20$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Simplify the expression: $$(3 + 2 \\\\times 8) \u2013 4 + (5 \\\\times 7)$$\",\n                    \"text\": \"Simplify the expression: $$(3 + 2 \\\\times 8) \u2013 4 + (5 \\\\times 7)$$\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"We know that the equation within the parentheses is solved first.<br>\r\nSo, $$19 \u2013 4 + 35 = 50$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"45\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We know that the equation within the parentheses is solved first.<br>\r\nSo, $$19 \u2013 4 + 35 = 50$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"24\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We know that the equation within the parentheses is solved first.<br>\r\nSo, $$19 \u2013 4 + 35 = 50$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"40\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We know that the equation within the parentheses is solved first.<br>\r\nSo, $$19 \u2013 4 + 35 = 50$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"50\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"We know that the equation within the parentheses is solved first.<br>\r\nSo, $$19 \u2013 4 + 35 = 50$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"We know that the equation within the parentheses is solved first.<br>\r\nSo, $$19 \u2013 4 + 35 = 50$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Simplify the expression: $$( 4 \\\\times (6 \u2013 2)) \u2013 ((8 \\\\div 2) + 5 )$$\",\n                    \"text\": \"Simplify the expression: $$( 4 \\\\times (6 \u2013 2)) \u2013 ((8 \\\\div 2) + 5 )$$\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"We know that the equation within the parentheses is solved first.<br>\r\nSo, $$( 4 \\\\times 4) \u2013 ( 4 + 5)$$<br>\r\n$$16 \u2013 9 = 7$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"2\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We know that the equation within the parentheses is solved first.<br>\r\nSo, $$( 4 \\\\times 4) \u2013 ( 4 + 5)$$<br>\r\n$$16 \u2013 9 = 7$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"17\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We know that the equation within the parentheses is solved first.<br>\r\nSo, $$( 4 \\\\times 4) \u2013 ( 4 + 5)$$<br>\r\n$$16 \u2013 9 = 7$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"10\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We know that the equation within the parentheses is solved first.<br>\r\nSo, $$( 4 \\\\times 4) \u2013 ( 4 + 5)$$<br>\r\n$$16 \u2013 9 = 7$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"7\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"We know that the equation within the parentheses is solved first.<br>\r\nSo, $$( 4 \\\\times 4) \u2013 ( 4 + 5)$$<br>\r\n$$16 \u2013 9 = 7$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"We know that the equation within the parentheses is solved first.<br>\r\nSo, $$( 4 \\\\times 4) \u2013 ( 4 + 5)$$<br>\r\n$$16 \u2013 9 = 7$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Simplify the expression: $$4 (3 + 2) + 4 (7 \u2013 2)$$\",\n                    \"text\": \"Simplify the expression: $$4 (3 + 2) + 4 (7 \u2013 2)$$\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"We know that parentheses also denote multiplication.<br>\r\nSo, $$4 \\\\times 5 + 4 \\\\times 5$$<br>\r\n$$20 + 20 = 40$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"10\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We know that parentheses also denote multiplication.<br>\r\nSo, $$4 \\\\times 5 + 4 \\\\times 5$$<br>\r\n$$20 + 20 = 40$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"50\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We know that parentheses also denote multiplication.<br>\r\nSo, $$4 \\\\times 5 + 4 \\\\times 5$$<br>\r\n$$20 + 20 = 40$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"20\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We know that parentheses also denote multiplication.<br>\r\nSo, $$4 \\\\times 5 + 4 \\\\times 5$$<br>\r\n$$20 + 20 = 40$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"40\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"We know that parentheses also denote multiplication.<br>\r\nSo, $$4 \\\\times 5 + 4 \\\\times 5$$<br>\r\n$$20 + 20 = 40$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"We know that parentheses also denote multiplication.<br>\r\nSo, $$4 \\\\times 5 + 4 \\\\times 5$$<br>\r\n$$20 + 20 = 40$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Solve the equation containing braces in math.<br> $$57 \\\\div \\\\left\\\\{5 + (4 \\\\times 2) + (3 + 3)\\\\right\\\\}$$\",\n                    \"text\": \"Solve the equation containing braces in math.<br> $$57 \\\\div \\\\left\\\\{5 + (4 \\\\times 2) + (3 + 3)\\\\right\\\\}$$\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"After solving the $$( )$$, we perform addition within the $$\\\\left\\\\{ \\\\right\\\\}$$, and then divide.\r\n$$57 \\\\div {5 + (4  2) + (3 + 3)} = 57  {5 + 8 + 6} = 57 19 = 3$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"4\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"After solving the $$( )$$, we perform addition within the $$\\\\left\\\\{ \\\\right\\\\}$$, and then divide.\r\n$$57 \\\\div {5 + (4  2) + (3 + 3)} = 57  {5 + 8 + 6} = 57 19 = 3$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"13\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"After solving the $$( )$$, we perform addition within the $$\\\\left\\\\{ \\\\right\\\\}$$, and then divide.\r\n$$57 \\\\div {5 + (4  2) + (3 + 3)} = 57  {5 + 8 + 6} = 57 19 = 3$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"4\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"After solving the $$( )$$, we perform addition within the $$\\\\left\\\\{ \\\\right\\\\}$$, and then divide.\r\n$$57 \\\\div {5 + (4  2) + (3 + 3)} = 57  {5 + 8 + 6} = 57 19 = 3$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"3\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"After solving the $$( )$$, we perform addition within the $$\\\\left\\\\{ \\\\right\\\\}$$, and then divide.\r\n$$57 \\\\div {5 + (4  2) + (3 + 3)} = 57  {5 + 8 + 6} = 57 19 = 3$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"After solving the $$( )$$, we perform addition within the $$\\\\left\\\\{ \\\\right\\\\}$$, and then divide.\r\n$$57 \\\\div {5 + (4  2) + (3 + 3)} = 57  {5 + 8 + 6} = 57 19 = 3$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following examples use braces, brackets, and parentheses correctly?\",\n                    \"text\": \"Which of the following examples use braces, brackets, and parentheses correctly?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"It uses the braces, brackets, and parentheses correctly because the innermost brackets have parentheses and then braces.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"60 $$\\\\div$$ [(2 $$\\\\times$$ 2) + (3 + 3)}\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"It uses the braces, brackets, and parentheses correctly because the innermost brackets have parentheses and then braces.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"60 $$\\\\div$$ {[2 $$\\\\times$$ 2] + (3 + 3)}\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"It uses the braces, brackets, and parentheses correctly because the innermost brackets have parentheses and then braces.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"(60 $$\\\\div$$ {[2 $$\\\\times$$ 2] + (3 + 3})\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"It uses the braces, brackets, and parentheses correctly because the innermost brackets have parentheses and then braces.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"60 $$\\\\div$$ {(2 $$\\\\times$$ 2) + (3 + 3)}\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"It uses the braces, brackets, and parentheses correctly because the innermost brackets have parentheses and then braces.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"It uses the braces, brackets, and parentheses correctly because the innermost brackets have parentheses and then braces.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If we have the following expressions inside the curly brackets, which of the expressions would you solve first?<br> $$10\\\\left\\\\{(\\\\frac{4}{2}) + (6 \\\\times 2) \u2013 (3 + 3) + (7 \u2013 2)\\\\right\\\\}$$\",\n                    \"text\": \"If we have the following expressions inside the curly brackets, which of the expressions would you solve first?<br> $$10\\\\left\\\\{(\\\\frac{4}{2}) + (6 \\\\times 2) \u2013 (3 + 3) + (7 \u2013 2)\\\\right\\\\}$$\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"We can solve any of the parentheses inside the curly brackets first. Once these parentheses are solved, we have to simply add and subtract, which can be done in any order.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$(\\\\frac{4}{2})$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We can solve any of the parentheses inside the curly brackets first. Once these parentheses are solved, we have to simply add and subtract, which can be done in any order.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$(\\\\frac{4}{2}) \\\\text{or} (6 \\\\times 2)$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We can solve any of the parentheses inside the curly brackets first. Once these parentheses are solved, we have to simply add and subtract, which can be done in any order.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of the above\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We can solve any of the parentheses inside the curly brackets first. Once these parentheses are solved, we have to simply add and subtract, which can be done in any order.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Any parentheses inside the $$\\\\left\\\\{ \\\\right\\\\}, (\\\\frac{4}{2}), (6 \\\\times 2), (3 + 3), (7 \u2013 2)$$}\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"We can solve any of the parentheses inside the curly brackets first. Once these parentheses are solved, we have to simply add and subtract, which can be done in any order.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"We can solve any of the parentheses inside the curly brackets first. Once these parentheses are solved, we have to simply add and subtract, which can be done in any order.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"10-frequently-asked-questions-on-brackets\">Frequently Asked Questions on Brackets<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-b7dc6d8b-9efb-4762-8135-edb1d77cbb18\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-b7dc6d8b-9efb-4762-8135-edb1d77cbb18\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b7dc6d8b-9efb-4762-8135-edb1d77cbb18\"><strong>Why are brackets important in mathematics?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-b7dc6d8b-9efb-4762-8135-edb1d77cbb18\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Brackets are very important parts of a mathematical equation; they separate different mathematical expressions from each other and help set the priority for expressions that need to be solved first.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-b7dc6d8b-9efb-4762-8135-edb1d77cbb18\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b7dc6d8b-9efb-4762-8135-edb1d77cbb18\"><strong>Is PEMDAS the only method to solve bracket problems?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-b7dc6d8b-9efb-4762-8135-edb1d77cbb18\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">BODMAS is a different acronym for PEMDAS, where B stands for Bracket, O for Of or Exponents, D for Division, M for Multiplication, A for Addition, and S for Subtraction. Any expression is considered correctly solved if they have followed the PEMDAS or BODMAS rule.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-b7dc6d8b-9efb-4762-8135-edb1d77cbb18\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b7dc6d8b-9efb-4762-8135-edb1d77cbb18\"><strong>Are there any more kinds of brackets?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-b7dc6d8b-9efb-4762-8135-edb1d77cbb18\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Angle Brackets are also used in various mathematical expressions; they are represented with\u3008 \u3009. The angle brackets are used to represent a list of numbers or a sequence of numbers.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-b7dc6d8b-9efb-4762-8135-edb1d77cbb18\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b7dc6d8b-9efb-4762-8135-edb1d77cbb18\"><strong>What are some other applications of brackets?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-b7dc6d8b-9efb-4762-8135-edb1d77cbb18\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Brackets are also used to define the coordinates of a point on a map or to describe the variable of a function.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-4-b7dc6d8b-9efb-4762-8135-edb1d77cbb18\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b7dc6d8b-9efb-4762-8135-edb1d77cbb18\"><strong>Are parentheses the same as braces?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-4-b7dc6d8b-9efb-4762-8135-edb1d77cbb18\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">No. Parentheses denoted by ( ) are different from braces { }. They have distinct uses in math. They are used in nesting expressions. You will learn more about them later.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-5-b7dc6d8b-9efb-4762-8135-edb1d77cbb18\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b7dc6d8b-9efb-4762-8135-edb1d77cbb18\"><strong>Is there another name for parentheses?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-5-b7dc6d8b-9efb-4762-8135-edb1d77cbb18\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Yes. Sometimes, parentheses are also called round brackets.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-6-b7dc6d8b-9efb-4762-8135-edb1d77cbb18\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b7dc6d8b-9efb-4762-8135-edb1d77cbb18\"><strong>What are { } called?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-6-b7dc6d8b-9efb-4762-8135-edb1d77cbb18\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">These are curly brackets, also known as braces in math. Braces are used in math equations when we are making at least two nested groups for calculation.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-7-b7dc6d8b-9efb-4762-8135-edb1d77cbb18\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b7dc6d8b-9efb-4762-8135-edb1d77cbb18\"><strong>In which other ways can we use braces besides in math equations?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-7-b7dc6d8b-9efb-4762-8135-edb1d77cbb18\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Braces are also used to define a set.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example, $\\left\\{3, 5, 7, 9, 10\\right\\}$ means a set containing the numbers 3, 5, 7, 9, 10.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-8-b7dc6d8b-9efb-4762-8135-edb1d77cbb18\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b7dc6d8b-9efb-4762-8135-edb1d77cbb18\"><strong>Do braces mean multiplication?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-8-b7dc6d8b-9efb-4762-8135-edb1d77cbb18\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Yes, braces can also mean multiplication. You need to multiply the value outside the braces by the value inside the braces.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Take this equation as an example: $2\\left\\{2(4 + 2) + 1\\right\\}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here, 2 will be multiplied by the answer inside the curly brackets or braces.<\/p>\n\n<\/div><\/div>\n<\/div><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>What are Brackets? You must have seen different symbols like these: (, ), [, ], {, and } in your math books. These symbols are called brackets. Brackets in mathematics serve a very important purpose; these symbols help us group different expressions or numbers together. Brackets imply that the thing or expression enclosed by them &#8230; <a title=\"Brackets in Math &#8211; Definition, Types, Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/brackets\" aria-label=\"More on Brackets in Math &#8211; Definition, Types, Examples\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-1027","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/1027","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=1027"}],"version-history":[{"count":71,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/1027\/revisions"}],"predecessor-version":[{"id":41610,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/1027\/revisions\/41610"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=1027"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=1027"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=1027"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}