{"id":13309,"date":"2022-11-10T07:37:58","date_gmt":"2022-11-10T07:37:58","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=13309"},"modified":"2024-03-06T09:43:26","modified_gmt":"2024-03-06T09:43:26","slug":"number-integers","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/integers","title":{"rendered":"Integers"},"content":{"rendered":"<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-94557c4d-a40c-48d1-b281-1673b07bb420\" 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\/integers#0-what-are-integers>What Are Integers?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/integers#1-integers-definition>Integers Definition<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/integers#2-types-of-integers>Types of Integers<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/integers#18-solved-examples-on-integers>Solved Examples on Integers<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/integers#19-practice-problems-on-integers>Practice Problems on Integers<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/integers#20-frequently-asked-questions>Frequently Asked Questions<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-are-integers\">What Are Integers?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">An integer is a Latin word that means \u201cwhole\u201d or \u201cintact.\u201d Hence, integers include all whole numbers and negative numbers without fractions and decimals.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"649\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/Integers.png\" alt=\"Integers\" class=\"wp-image-40821\" style=\"width:454px;height:475px\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/Integers.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/Integers-287x300.png 287w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let&#8217;s discuss the definition, types, and properties of integers and conduct arithmetic operations!<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"1-integers-definition\">Integers Definition<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We can define integers as numbers that can be written without a fractional component. They can be positive, negative, or zero.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Is -1 an integer? Yes!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Is -2 an integer? Yes!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Is $\\frac{-1}{6}$ an integer? No!<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Integer examples: $-7$, $-1$, 0, 2, 7, 15, etc.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Non-integer examples:&nbsp; $\\frac{8}{5}, 3.14,\\sqrt{7}$, etc.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Integer symbol: The set of integers is represented by the symbol <strong>\u2124<\/strong>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"314\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/What-are-integers-2.png\" alt=\"Set of Integers\" class=\"wp-image-13314\" title=\"Set of Integers\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/What-are-integers-2.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/What-are-integers-2-300x152.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-types-of-integers\">Types of Integers<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Integer numbers can be divided into three categories: zero, positive integers, and negative integers.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Zero:<\/strong> Zero is an integer that is neither positive nor negative. It is simply written as 0 without any positive or negative sign.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Positive Integers:<\/strong> Positive integers are natural counting numbers greater than zero. They are sometimes denoted by $Z+$. Examples of positive integers are 1, 2, 3, 4, 5, 6, 7, . . .<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Negative Integers: <\/strong>Negative integers are integers with a value less than zero. They are represented by $Z-$. Examples of negative integers are -1, -2, -3, -4, -5, -6, . . .<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-how-to-represent-integers-on-a-number-line\">How to Represent Integers on a Number Line?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">All three categories of integers can be visually represented on an integer number line.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Zero is placed at the center of the number line. All positive integers lie on the right side of zero, and all negative integers lie on the left side of zero.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"344\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/What-are-integers-3.png\" alt=\"Integers on a Number Line\" class=\"wp-image-13315\" title=\"Integers on a Number Line\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/What-are-integers-3.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/What-are-integers-3-300x166.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The numbers get bigger as we move from left to right on the number line. Therefore, the integer on the right-hand side is greater than the integer on the left-hand side. For example, $+6$ is greater than $-6$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The more the integer is positive, the greater it is. For example, $+15$ is greater than $+12$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The more the integer is negative, the smaller it is. For example, $-33$ is smaller than $-19$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">All positive integers are greater than all the negative integers. For example, $+17$ is greater than $-20$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-how-to-perform-arithmetic-operations-on-integers\">How to Perform Arithmetic Operations on Integers<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;The four basic mathematical operations are:<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Addition<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Subtraction<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Multiplication<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Division<\/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\/2022\/11\/What-are-integers-4.png\" alt=\"Arithmetic Operation Symbols\" class=\"wp-image-13316\" title=\"Arithmetic Operation Symbols\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/What-are-integers-4.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/What-are-integers-4-300x138.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"5-addition-of-integers\">Addition of Integers<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For adding integers with the same sign, we simply add the absolute values of the numbers. The absolute value of a number is the non-negative value of the number without regard to its sign. For instance, the absolute value of $\u20133$ is | $\u20133$ |$= 3$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The resultant integer will have the same sign as the given integers.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example:<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$7 + 3 = 10$<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here, 7 and 3 are positive. So, the answer is +10 or simply 10.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$(\u20137) + (\u20133) = \u201310$<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here, the absolute values are 7 and 3. Their sum is 10.&nbsp; Since both the numbers have a (\u2013) sign, the answer is&nbsp; \u201310.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For adding integers with different signs, we subtract the absolute value of the integers. The resultant integer should be given the sign of the number that has the largest absolute value.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example:<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$\u20134 + 8 = +4$<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here, the absolute values of integers are 4 and 8. On subtracting them, we get 4. Now eight has the largest absolute value, and its sign is $(+)$. So the answer is $+4$.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$\u20136 + 2 = \u2013$$4$<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here, the absolute values of integers are 6 and 2. On subtracting them, we get 4. Now six has the largest absolute value, and its sign is $(\u2013)$. So the answer is $\u20134$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The rules for addition are summarized in the table below:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"207\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/What-are-integers-5.png\" alt=\"Addition of Integers\" class=\"wp-image-13317\" title=\"Addition of Integers\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/What-are-integers-5.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/What-are-integers-5-300x100.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"6-subtraction-of-integers\">Subtraction of Integers<\/h3>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Convert the subtraction operation into an addition operation by changing the sign of the second number that is being subtracted.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Apply the rules for adding integers as discussed above to get the answer.<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example:<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$(\u2013$$6)$ $\u2013$ $(+7) = (\u2013$$6) + ($$\u2013$$7) = \u2013$$13$<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here, we first convert the problem into addition by changing the sign of 7. Then, we follow the rules for addition. The absolute value of the integers is 6 and 7, and their sum is 13. Since both of them have a (\u2013) sign, the answer is $\u201313$.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$(+5)$ $\u2013$ $(\u2013$$4) = (+5) + (+4) = +9$<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here, we first convert the problem into addition by changing the sign of 4. Then, we follow the rules for addition. The absolute value of the integers is 5 and 4, and their sum is 9. Since both of them have a (+) sign, the answer is +9.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"207\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/What-are-integers-6.png\" alt=\"Subtraction of Integers\" class=\"wp-image-13318\" title=\"Subtraction of Integers\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/What-are-integers-6.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/What-are-integers-6-300x100.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"7-multiplication-of-integers\">Multiplication of Integers<\/h3>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">If both integers have the same sign, the resultant product will have a positive (+) sign.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">If the integers have different signs, the resultant product will have a negative (\u2013) sign.<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The rules are summarized in the table below:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"448\" height=\"187\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/What-are-integers-7.png\" alt=\"Multiplication of Integers\" class=\"wp-image-13319\" title=\"Multiplication of Integers\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/What-are-integers-7.png 448w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/What-are-integers-7-300x125.png 300w\" sizes=\"auto, (max-width: 448px) 100vw, 448px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"8-division-of-integers\">Division of Integers<\/h3>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">If both integers have the same sign, the result will have a positive $(+)$ sign.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">If the integers have different signs, the result will have a negative $(\u2013)$ sign.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image eplus-wrapper\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/Hv7XlpUFFRVVUAthbsUhb5X709lexCrGMChhD5vUlukSlSC3vEBxlQTm1foWl6_Iskr1lAspUsHw9udo9mJOX-0EJrbfsCOz9g5qtKygWdIrc0wGSfrnCBx2LZ9pKUNHKGVzKknp10DSKj14ByCE-6SWS6NvPWTpLKGe-oALmQTFx4PK45daVsbKCYy5XA\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><em>Alt Tag: Division of Integers<\/em><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-properties-of-integers\">Properties of Integers<\/h2>\n\n\n\n<ol class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Closure Property<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Commutative Property<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Associative Property<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Distributive Property<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Additive Inverse Property<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Multiplicative Inverse Property<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Identity Property<\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let\u2019s learn more about them!<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"10-1-closure-property\">1. Closure Property<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The closure property states that the addition, subtraction, or multiplication of integers results in an integer. So, for any two integers <em>a<\/em> and <em>b<\/em>:<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$a + b =$ Integer<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$a$ $\u2013$ $b =$ Integer<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$a \\times b =$ Integer<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example:<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$\u20135 + 4 = \u20131$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$8$ $\u2013$ $5 = 3$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$2 \\times 3 = 6$<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">However, the closure property does not work for the division of integers because the division of two integers may result in a non-integer.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example:&nbsp; $15 \\div 2 = 7.5$<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"11-2-commutative-property-\">2. Commutative Property&nbsp;<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The commutative property states that changing the position of integers during addition and multiplication does not change the result of the operation.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Interestingly, this property is true only for addition and multiplication and not for division and subtraction.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So, for two integers<em> a<\/em> and<em> b<\/em>:<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$a + b = b + a$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$a \\times b = b \\times a$<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Example:<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$\u20135 + 2 = 2 + (\u2013$$5) = -$$3$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$3 \\times 6 = 6 \\times 3 = 18$<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"601\" height=\"187\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/What-are-integers-9.png\" alt=\"Commutative Property of Integers\" class=\"wp-image-13320\" title=\"Commutative Property of Integers\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/What-are-integers-9.png 601w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/What-are-integers-9-300x93.png 300w\" sizes=\"auto, (max-width: 601px) 100vw, 601px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"12-3-associative-property\">3. Associative Property<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">According to the associative property, changing the grouping of integers does not change the result of the operation. As above, this property is true for the addition and multiplication but not for division and subtraction.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So, for any three integers a, b, and c:<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$a + (b + c) = (a + b) + c$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$a \\times (b \\times c) = (a \\times b) \\times c$<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"239\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/What-are-integers-10.png\" alt=\"Associative Property of Integers\" class=\"wp-image-13321\" title=\"Associative Property of Integers\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/What-are-integers-10.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/What-are-integers-10-300x116.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"13-4-distributive-property-\">4. Distributive Property&nbsp;<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The distributive property states that the multiplication of integers can be distributed over addition and subtraction to make the calculation easier.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So, for three integers <em>a, b<\/em>, and <em>c<\/em>:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$a \\times (b + c) = (a \\times b) + (a \\times c)$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example:<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$5 \\times (4 + 3) = (5 \\times 4 + 5 \\times 3) = 35$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$\u20132 \\times (6 + 1) = \\left\\{(\u20132) \\times 6 + (\u20132) \\times 1\\right\\} = \u201314$<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"14-5-additive-inverse-property\">5. Additive Inverse Property<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">This property states that the addition of an integer and its negative value will always be zero. So, for any integer <em>a<\/em>:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$a + (\u2013$$a) = 0$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example:<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$6 + (\u2013$$6) = 0$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$15 + (\u2013$$15) = 0$<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"15-6-multiplicative-inverse-property\">6. Multiplicative Inverse Property<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">This property states that the multiplication of an integer and its reciprocal will give the answer 1.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So, for any integer<em> a<\/em>:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$a \\times \\frac{1}{a} = 1$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example:<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$3 \\times \\frac{1}{3} =1$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$\u201315 \\times \\frac{1-}{15} = 1$<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"16-7-identity-property-\">7. Identity Property&nbsp;<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The identity property of an integer states that any integer added to zero will result in the same integer. Similarly, any integer multiplied by one will give the same integer.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So, for any integer a:<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$a + 0 = 0 + a = a$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$a \\times 1 = 1 \\times a = a$<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Example:<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$10 + 0 = 0 + 10 = 10$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$10 \\times 1 = 1 \\times 10 = 10$<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"17-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So, we\u2019ve covered everything from the definition and properties of integers and how to perform mathematical operations on them. The more you practice, the better you\u2019ll understand integer numbers. Good luck!<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"18-solved-examples-on-integers\">Solved Examples on Integers<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>1. Sort the numbers as integers and non-integers.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">\u2013<strong>5, 7.5, 100, <\/strong>$\\frac{3}{7}$, $\u20134.25$, 0<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Integers $= \u2013$$5$, 100, 0<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Non-integers $= 7.5$, $\\frac{3}{7}$, $\u20134.25$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Integer numbers do not include fractions and decimals. Hence, $\u20135$, $100$, and 0 are integer numbers, but 7.5, $\\frac{3}{7}$, and $\u20134.25$ are not.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>2. Solve: <\/strong>$(\u2013$$8) \u2013$ $(\u2013$$5)$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Step 1: First, we change the operation to an addition operation by changing the sign of the number to be subtracted.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So, (\u20138) \u2013 (\u20135) = \u20138 + 5<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Step 2: Then we follow the addition operation<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Since the signs are different, we need to find the difference in their absolute value.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So, $8$ $\u2013$ $5 = 3$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The sign of the resultant integer will be the sign of the integer with the highest absolute value.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here, 8 is the integer with the highest absolute value, and its sign is negative.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So the answer is $\u20133$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>3. Using the number line, find the integer which is:<\/strong><\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>6 more than 3<\/strong><\/li>\n\n\n\n<li class=\"eplus-wrapper\"><strong>7 less than 4<\/strong><\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"600\" height=\"37\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/Solved-Examples-3-1.png\" alt=\"Number line from positive to negative 10\" class=\"wp-image-13322\" title=\"Number line from positive to negative 10\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/Solved-Examples-3-1.png 600w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/Solved-Examples-3-1-300x19.png 300w\" sizes=\"auto, (max-width: 600px) 100vw, 600px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"600\" height=\"122\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/Solved-Examples-3-answer.png\" alt=\"6 more than 3 and 7 less than 4 on a number line\" class=\"wp-image-13323\" title=\"6 more than 3 and 7 less than 4 on a number line\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/Solved-Examples-3-answer.png 600w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/Solved-Examples-3-answer-300x61.png 300w\" sizes=\"auto, (max-width: 600px) 100vw, 600px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We know that the numbers get larger as we move from left to right. So, to find the number that is 6 more than 3, we have to move six steps to the right from 3. That will give us the answer 9.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Again, to find the number that is 7 less than 4, we have to move 7 steps to the left from 4. That will give us the answer $\u20133$.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"19-practice-problems-on-integers\">Practice Problems on Integers<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Integers<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">Which of the following comparisons are true?<br>$+10$ . . . $\u201310$<br>$+5$ . . . $+15$<br>$\u20138$ . . . $0$<br>$\u201320$ . . . $+2$<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$10  \\lt $$\u2013$$10$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\u20138 \\gt 0$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\u201320 \\lt 2$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$+5 = \u2013$$5$<\/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: $\u201320 \\lt 2$<br\/>We know that the numbers get bigger as we move from left to right on the number line. Therefore, the integer on the right-hand side of the number line is greater than the integer on the left-hand side. Hence, $\u201320 \\lt +2$<\/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\">Which of the following is not true for the closure property of an integer?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">a $+$ b $=$ Integer<\/div><div class=\"spq_answer_block\" data-value=\"1\"> a $\u2013$ b $=$ Integer<\/div><div class=\"spq_answer_block\" data-value=\"2\">a $\\times$ b $=$ Integer<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\frac{a}{b} =$ Integer<\/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: $\\frac{a}{b} =$ Integer<br\/>The closure property states that the addition, subtraction, or multiplication of integer numbers always results in an integer. But the same is not true for the division operation. For two integer numbers a and b, $\\frac{a}{b}$ may not always result in an integer.<\/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\">Solve: $(\u201320)$ $\u2013$ $(+5)$<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\u201325$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$25$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$-15$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$15$<\/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: $\u201325$<br\/>Step 1: Change the operation to the addition operation by changing the sign of the number to be subtracted.<br>\r\nSo, $(\u201320)$ $\u2013$ $(+5) = \u2013$$20 + (\u20135)$<br>\r\nStep 2: Follow the addition operation.<br>\r\nSince both numbers have the same sign, we need to find the sum of their absolute value.<br>\r\nSo, $20 + 5 = 25$<br>\r\nThe resultant integer will have a negative sign.<br>\r\nSo, the answer is $\u201325$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">Solve: $(\u20139) \\times (\u20134)$<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\u20139$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\u20134$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$36$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\u201336$<\/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: $36$<br\/>Step 1: Find the product of their absolute value.<br>\r\n$9 \\times 4 = 36$<br>\r\nStep 2: Decide on the appropriate sign.<br>\r\nIf both numbers have the same sign, the resultant product will have a positive $(+)$ sign.<br>\r\nSo, the answer will be 36.<\/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\">Solve: $(35) \\div (\u20135)$<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$7$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$-7$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$0$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$-1$<\/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\/>Step 1: Divide the numbers normally without considering the sign.<br>\r\n$35 \\div 5 = 7$<br>\r\nStep 2: Decide on the appropriate sign.<br>\r\nIf the numbers have different signs, the result will have a negative $(\u2013)$ sign.<br>\r\nHere, $\u20135$ has a negative sign. So, the answer is $\u20137$.<\/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\": \"Integers\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Integers\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following comparisons are true?<br>$$+10$$ . . . $$\u201310$$<br>$$+5$$ . . . $$+15$$<br>$$\u20138$$ . . . $$0$$<br>$$\u201320$$ . . . $$+2$$\",\n                    \"text\": \"Which of the following comparisons are true?<br>$$+10$$ . . . $$\u201310$$<br>$$+5$$ . . . $$+15$$<br>$$\u20138$$ . . . $$0$$<br>$$\u201320$$ . . . $$+2$$\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"We know that the numbers get bigger as we move from left to right on the number line. 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Hence, $$\u201320 \\\\lt +2$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\u20138 \\\\gt 0$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We know that the numbers get bigger as we move from left to right on the number line. Therefore, the integer on the right-hand side of the number line is greater than the integer on the left-hand side. Hence, $$\u201320 \\\\lt +2$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$+5 = \u2013$$$$5$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We know that the numbers get bigger as we move from left to right on the number line. Therefore, the integer on the right-hand side of the number line is greater than the integer on the left-hand side. Hence, $$\u201320 \\\\lt +2$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\u201320 \\\\lt 2$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"We know that the numbers get bigger as we move from left to right on the number line. Therefore, the integer on the right-hand side of the number line is greater than the integer on the left-hand side. Hence, $$\u201320 \\\\lt +2$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"We know that the numbers get bigger as we move from left to right on the number line. Therefore, the integer on the right-hand side of the number line is greater than the integer on the left-hand side. Hence, $$\u201320 \\\\lt +2$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following is not true for the closure property of an integer?\",\n                    \"text\": \"Which of the following is not true for the closure property of an integer?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The closure property states that the addition, subtraction, or multiplication of integer numbers always results in an integer. But the same is not true for the division operation. For two integer numbers a and b, $$\\\\frac{a}{b}$$ may not always result in an integer.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"a $$+$$ b $$=$$ Integer\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The closure property states that the addition, subtraction, or multiplication of integer numbers always results in an integer. But the same is not true for the division operation. For two integer numbers a and b, $$\\\\frac{a}{b}$$ may not always result in an integer.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \" a $$\u2013$$ b $$=$$ Integer\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The closure property states that the addition, subtraction, or multiplication of integer numbers always results in an integer. But the same is not true for the division operation. For two integer numbers a and b, $$\\\\frac{a}{b}$$ may not always result in an integer.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"a $$\\\\times$$ b $$=$$ Integer\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The closure property states that the addition, subtraction, or multiplication of integer numbers always results in an integer. But the same is not true for the division operation. For two integer numbers a and b, $$\\\\frac{a}{b}$$ may not always result in an integer.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{a}{b} =$$ Integer\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The closure property states that the addition, subtraction, or multiplication of integer numbers always results in an integer. But the same is not true for the division operation. For two integer numbers a and b, $$\\\\frac{a}{b}$$ may not always result in an integer.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The closure property states that the addition, subtraction, or multiplication of integer numbers always results in an integer. But the same is not true for the division operation. For two integer numbers a and b, $$\\\\frac{a}{b}$$ may not always result in an integer.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Solve: $$(\u201320)$$ $$\u2013$$ $$(+5)$$\",\n                    \"text\": \"Solve: $$(\u201320)$$ $$\u2013$$ $$(+5)$$\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Step 1: Change the operation to the addition operation by changing the sign of the number to be subtracted.<br>\r\nSo, $$(\u201320)$$ $$\u2013$$ $$(+5) = \u2013$$$$20 + (\u20135)$$<br>\r\nStep 2: Follow the addition operation.<br>\r\nSince both numbers have the same sign, we need to find the sum of their absolute value.<br>\r\nSo, $$20 + 5 = 25$$<br>\r\nThe resultant integer will have a negative sign.<br>\r\nSo, the answer is $$\u201325$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$25$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Step 1: Change the operation to the addition operation by changing the sign of the number to be subtracted.<br>\r\nSo, $$(\u201320)$$ $$\u2013$$ $$(+5) = \u2013$$$$20 + (\u20135)$$<br>\r\nStep 2: Follow the addition operation.<br>\r\nSince both numbers have the same sign, we need to find the sum of their absolute value.<br>\r\nSo, $$20 + 5 = 25$$<br>\r\nThe resultant integer will have a negative sign.<br>\r\nSo, the answer is $$\u201325$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$-15$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Step 1: Change the operation to the addition operation by changing the sign of the number to be subtracted.<br>\r\nSo, $$(\u201320)$$ $$\u2013$$ $$(+5) = \u2013$$$$20 + (\u20135)$$<br>\r\nStep 2: Follow the addition operation.<br>\r\nSince both numbers have the same sign, we need to find the sum of their absolute value.<br>\r\nSo, $$20 + 5 = 25$$<br>\r\nThe resultant integer will have a negative sign.<br>\r\nSo, the answer is $$\u201325$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$15$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Step 1: Change the operation to the addition operation by changing the sign of the number to be subtracted.<br>\r\nSo, $$(\u201320)$$ $$\u2013$$ $$(+5) = \u2013$$$$20 + (\u20135)$$<br>\r\nStep 2: Follow the addition operation.<br>\r\nSince both numbers have the same sign, we need to find the sum of their absolute value.<br>\r\nSo, $$20 + 5 = 25$$<br>\r\nThe resultant integer will have a negative sign.<br>\r\nSo, the answer is $$\u201325$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\u201325$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Step 1: Change the operation to the addition operation by changing the sign of the number to be subtracted.<br>\r\nSo, $$(\u201320)$$ $$\u2013$$ $$(+5) = \u2013$$$$20 + (\u20135)$$<br>\r\nStep 2: Follow the addition operation.<br>\r\nSince both numbers have the same sign, we need to find the sum of their absolute value.<br>\r\nSo, $$20 + 5 = 25$$<br>\r\nThe resultant integer will have a negative sign.<br>\r\nSo, the answer is $$\u201325$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Step 1: Change the operation to the addition operation by changing the sign of the number to be subtracted.<br>\r\nSo, $$(\u201320)$$ $$\u2013$$ $$(+5) = \u2013$$$$20 + (\u20135)$$<br>\r\nStep 2: Follow the addition operation.<br>\r\nSince both numbers have the same sign, we need to find the sum of their absolute value.<br>\r\nSo, $$20 + 5 = 25$$<br>\r\nThe resultant integer will have a negative sign.<br>\r\nSo, the answer is $$\u201325$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Solve: $$(\u20139) \\\\times (\u20134)$$\",\n                    \"text\": \"Solve: $$(\u20139) \\\\times (\u20134)$$\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Step 1: Find the product of their absolute value.<br>\r\n$$9 \\\\times 4 = 36$$<br>\r\nStep 2: Decide on the appropriate sign.<br>\r\nIf both numbers have the same sign, the resultant product will have a positive $$(+)$$ sign.<br>\r\nSo, the answer will be 36.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\u20139$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Step 1: Find the product of their absolute value.<br>\r\n$$9 \\\\times 4 = 36$$<br>\r\nStep 2: Decide on the appropriate sign.<br>\r\nIf both numbers have the same sign, the resultant product will have a positive $$(+)$$ sign.<br>\r\nSo, the answer will be 36.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\u20134$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Step 1: Find the product of their absolute value.<br>\r\n$$9 \\\\times 4 = 36$$<br>\r\nStep 2: Decide on the appropriate sign.<br>\r\nIf both numbers have the same sign, the resultant product will have a positive $$(+)$$ sign.<br>\r\nSo, the answer will be 36.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\u201336$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Step 1: Find the product of their absolute value.<br>\r\n$$9 \\\\times 4 = 36$$<br>\r\nStep 2: Decide on the appropriate sign.<br>\r\nIf both numbers have the same sign, the resultant product will have a positive $$(+)$$ sign.<br>\r\nSo, the answer will be 36.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$36$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Step 1: Find the product of their absolute value.<br>\r\n$$9 \\\\times 4 = 36$$<br>\r\nStep 2: Decide on the appropriate sign.<br>\r\nIf both numbers have the same sign, the resultant product will have a positive $$(+)$$ sign.<br>\r\nSo, the answer will be 36.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Step 1: Find the product of their absolute value.<br>\r\n$$9 \\\\times 4 = 36$$<br>\r\nStep 2: Decide on the appropriate sign.<br>\r\nIf both numbers have the same sign, the resultant product will have a positive $$(+)$$ sign.<br>\r\nSo, the answer will be 36.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Solve: $$(35) \\\\div (\u20135)$$\",\n                    \"text\": \"Solve: $$(35) \\\\div (\u20135)$$\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Step 1: Divide the numbers normally without considering the sign.<br>\r\n$$35 \\\\div 5 = 7$$<br>\r\nStep 2: Decide on the appropriate sign.<br>\r\nIf the numbers have different signs, the result will have a negative $$(\u2013)$$ sign.<br>\r\nHere, $$\u20135$$ has a negative sign. So, the answer is $$\u20137$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$7$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Step 1: Divide the numbers normally without considering the sign.<br>\r\n$$35 \\\\div 5 = 7$$<br>\r\nStep 2: Decide on the appropriate sign.<br>\r\nIf the numbers have different signs, the result will have a negative $$(\u2013)$$ sign.<br>\r\nHere, $$\u20135$$ has a negative sign. So, the answer is $$\u20137$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$0$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Step 1: Divide the numbers normally without considering the sign.<br>\r\n$$35 \\\\div 5 = 7$$<br>\r\nStep 2: Decide on the appropriate sign.<br>\r\nIf the numbers have different signs, the result will have a negative $$(\u2013)$$ sign.<br>\r\nHere, $$\u20135$$ has a negative sign. So, the answer is $$\u20137$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$-1$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Step 1: Divide the numbers normally without considering the sign.<br>\r\n$$35 \\\\div 5 = 7$$<br>\r\nStep 2: Decide on the appropriate sign.<br>\r\nIf the numbers have different signs, the result will have a negative $$(\u2013)$$ sign.<br>\r\nHere, $$\u20135$$ has a negative sign. So, the answer is $$\u20137$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$-7$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Step 1: Divide the numbers normally without considering the sign.<br>\r\n$$35 \\\\div 5 = 7$$<br>\r\nStep 2: Decide on the appropriate sign.<br>\r\nIf the numbers have different signs, the result will have a negative $$(\u2013)$$ sign.<br>\r\nHere, $$\u20135$$ has a negative sign. So, the answer is $$\u20137$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Step 1: Divide the numbers normally without considering the sign.<br>\r\n$$35 \\\\div 5 = 7$$<br>\r\nStep 2: Decide on the appropriate sign.<br>\r\nIf the numbers have different signs, the result will have a negative $$(\u2013)$$ sign.<br>\r\nHere, $$\u20135$$ has a negative sign. So, the answer is $$\u20137$$.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"20-frequently-asked-questions\">Frequently Asked Questions<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-cf8d66ad-2941-41f0-afe4-34f1fa475399\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n\n<div style=\"border-color:#f1f1f1\" class=\"wp-block-ub-content-toggle-panel wp-block-ub-content-toggle-accordion\"><div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" style=\"background-color:#f1f1f1\"><span class=\"wp-block-ub-content-toggle-accordion-title\" style=\"color:#000000\"><strong>Is 0 an integer?<\/strong><\/span><span class=\"wp-block-ub-content-toggle-accordion-state-indicator dashicons dashicons-arrow-right-alt2 \"><\/span><\/div><div style=\"height:0;padding-top:0;padding-bottom:0\" class=\"wp-block-ub-content-toggle-accordion-content-wrap\">\n<p class=\"eplus-wrapper wp-block-paragraph\">Yes, 0 is an integer because an integer is defined as a number without any fractional part, and zero has no fractional part.<\/p>\n<\/div><\/div>\n\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-cf8d66ad-2941-41f0-afe4-34f1fa475399\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-cf8d66ad-2941-41f0-afe4-34f1fa475399\"><strong>Are integers whole numbers?<\/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-cf8d66ad-2941-41f0-afe4-34f1fa475399\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Integers including 0 and positive integers are whole numbers.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Whole numbers: 0, 1, 2, 3, 4, \u2026<\/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-cf8d66ad-2941-41f0-afe4-34f1fa475399\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-cf8d66ad-2941-41f0-afe4-34f1fa475399\"><strong>Are all integers rational numbers?<\/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-cf8d66ad-2941-41f0-afe4-34f1fa475399\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Any integer \u201c<em>a<\/em>\u201d can be expressed as \u201c$\\frac{a}{1}$\u201d, which is a rational number. So, all integers are rational numbers. However, all rational numbers are not integers.<\/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-cf8d66ad-2941-41f0-afe4-34f1fa475399\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-cf8d66ad-2941-41f0-afe4-34f1fa475399\"><strong>Are decimals integers?<\/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-cf8d66ad-2941-41f0-afe4-34f1fa475399\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">No, decimals are not integers. Integers consist of positive or negative numbers that are whole. They do not include fractions and decimals.<\/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-cf8d66ad-2941-41f0-afe4-34f1fa475399\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-cf8d66ad-2941-41f0-afe4-34f1fa475399\"><strong>Is <\/strong>$\u20131$<strong> an integer? Is <\/strong>$\u20132$<strong> an integer?<\/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-cf8d66ad-2941-41f0-afe4-34f1fa475399\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Yes. Integers include negative numbers that are whole (without fractions or decimals).<\/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-cf8d66ad-2941-41f0-afe4-34f1fa475399\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-cf8d66ad-2941-41f0-afe4-34f1fa475399\"><strong>\u00a0Is <\/strong>$\\frac{-1}{6}$<strong> an integer?<\/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-cf8d66ad-2941-41f0-afe4-34f1fa475399\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">No. $\\frac{-1}{6}$ is a rational number.<\/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-cf8d66ad-2941-41f0-afe4-34f1fa475399\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-cf8d66ad-2941-41f0-afe4-34f1fa475399\"><strong>What are consecutive integers?<\/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-cf8d66ad-2941-41f0-afe4-34f1fa475399\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Consecutive integers are integer numbers that follow each other in order. For example: $\u20134$, $\u20133$, $\u20132$, $\u20131$, 0, 1, 2, 3 . . .<\/p>\n\n<\/div><\/div>\n<\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"21-related-article-links\">Related Article Links<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/whole-numbers#:~:text=Whole%20numbers%20include%20all%20natural,2%2C3%2C%E2%80%A6%7D.\">Whole Numbers<\/a><\/li>\n\n\n\n<li class=\"eplus-wrapper\"><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/natural-numbers\">Natural Numbers<\/a><\/li>\n\n\n\n<li class=\"eplus-wrapper\"><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/number\">Number System<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>What Are Integers? An integer is a Latin word that means \u201cwhole\u201d or \u201cintact.\u201d Hence, integers include all whole numbers and negative numbers without fractions and decimals. Let&#8217;s discuss the definition, types, and properties of integers and conduct arithmetic operations! Integers Definition We can define integers as numbers that can be written without a fractional &#8230; <a title=\"Integers\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/integers\" aria-label=\"More on Integers\">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-13309","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\/13309","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=13309"}],"version-history":[{"count":23,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/13309\/revisions"}],"predecessor-version":[{"id":40828,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/13309\/revisions\/40828"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=13309"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=13309"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=13309"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}