{"id":1094,"date":"2022-04-14T06:30:44","date_gmt":"2022-04-14T06:30:44","guid":{"rendered":"https:\/\/www.splashlearn.com\/article-test-new\/?page_id=1094"},"modified":"2023-08-15T16:40:20","modified_gmt":"2023-08-15T16:40:20","slug":"reasonableness-definition-with-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/reasonableness","title":{"rendered":"Reasonableness in Math"},"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-def363ba-783f-4562-ab6c-7b1874b54c93\" 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\/reasonableness#1-what-is-reasonableness-in-math>What Is Reasonableness in Math?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/reasonableness#3-how-do-you-calculate-reasonableness>How Do You Calculate Reasonableness?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/reasonableness#8-solved-examples>Solved Examples<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/reasonableness#9-practice-problems>Practice Problems<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/reasonableness#10-frequently-asked-questions>Frequently Asked Questions<\/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-reasonableness-introduction\">Reasonableness: Introduction<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Have you ever come across a situation where you are attempting a math problem and need to check whether you did it right or not? When you find the solution, a good way to check if the problem is solved correctly is to check for reasonableness.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">While solving a problem, you should always ask yourself whether your answer is logical and appropriate or simply whether it makes sense or not.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let\u2019s see how we can use the concept of reasonableness.<\/p>\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                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"1-what-is-reasonableness-in-math\">What Is Reasonableness in Math?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">What does reasonable mean in math? Well, all it means is being moderate or fair while finding a solution and not excessive than the actual number or what is reasonable within the context of the given factors or values. This is the simple meaning of reasonableness.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">When solving a math problem, we can check if the answer we have derived is reasonable or not, based on an estimate. A reasonable estimate does not exceed the original numbers in a problem. Let us look at a reasonable estimate example:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Example 1: Suppose you want to divide $\\$418$ among 4 people. What would be the reasonable estimate?&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We can round down 418 to the nearest hundreds, 420.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$420 \\div 4=105$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Actual answer $= 104.5$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, our solution is reasonable.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Example: Find $65 \u2212 29$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Actual subtraction:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"402\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/example-of-reasonableness.webp\" alt=\"Example of reasonableness\" class=\"wp-image-33047\" title=\"Example of reasonableness\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/example-of-reasonableness.webp 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/example-of-reasonableness-300x195.webp 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So, $65 \u2212 29 = 36$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">How would you check if it is reasonable or correct?<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Add 36 and 29.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$36 + 29 = 65$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So, the answer is correct!<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-reasonableness-definition\">Reasonableness: Definition<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In math, reasonableness can be defined as checking or verifying whether the result of the solution or the calculation of the problem is correct or not. We can do it by either estimating or plugging in your result to check it.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We use convenient numbers to find an estimate and then compare this estimate to the actual answer to check for reasonableness. Sometimes, this method may not tell you if you have the correct answer, but it will definitely tell you if you are close.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-how-do-you-calculate-reasonableness\">How Do You Calculate Reasonableness?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">There are various situations where we use reasonableness. We use it to cross-verify our addition, multiplication, division, and even other complex mathematical problems.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-how-to-verify-multiplication\">How to Verify Multiplication<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Students often make mistakes while carrying out multiplication of two large numbers. This method helps gain confidence and makes sure that the answer is not outrageous.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example, let\u2019s multiply 51 and 41.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In the first step, round 51 to 50 and 41 to 40.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Multiply 50 and 40.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$50 \\times 40 = 2000$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The actual product is given by<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$50 \\times 40 = 2091$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Now we subtract 2000 from 2091, the answer will be 91.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">This shows that the difference between them is very less; thus, our answer is correct. If we had got a more considerable difference, then we would have had to consider it wrong.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-how-to-verify-division-problems\">How to Verify Division Problems<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We can solve and verify the division problems using estimation. Round the divisor and the dividend to the closer and convenient value and check whether the actual answer is reasonable or not.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example, let\u2019s find the answer to $\\frac{2100}{1518}$.&nbsp;<\/p>\n\n\n\n<ol class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Round up the dividend to 2000 and the divisor to 1500.&nbsp;<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Here you can estimate that the solution to $\\frac{2000}{1500}$ will be close to 1 because $\\frac{20}{15} \\approx 1.3$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">After doing the actual calculation for $\\frac{2100}{1518}$, the answer is about 1.35.<\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Sometimes try to look for patterns that are familiar to you and can help you in solving different problems.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example, let\u2019s solve $\\frac{63}{7}$.&nbsp;<\/p>\n\n\n\n<ol class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The square of 8 is 64; this will allow you to estimate the approximate value quickly to 8.&nbsp;<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Here, the actual answer is 9, which is very close to 8.<\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We can examine the divisor, simply it and check for multiples that are close to the value of the dividend.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example, in $\\frac{8544}{45}$, there are two options:&nbsp;<\/p>\n\n\n\n<ol class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">If you are rounding the dividend to 9000, then your estimate for the quotient will be 200 based on $45 \\times 200 = 9000$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">If you are rounding the divisor to 50, then the estimate will be 171 on the basis of $171 \\times 50 = 8550$.<\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;The actual quotient is 189.8. So, both the estimates are valid; we can use either.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-fun-facts\">Fun Facts!<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Rounding numbers, making numbers compatible, and properties of operations are some strategies that are used to check the reasonableness of answers.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In this article, we learned about the concept of reasonableness. We came across some conditions like multiplication and division and how we use reasonableness in such cases. We can now look at some examples and solve some practice problems to better understand reasonableness.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-solved-examples\">Solved Examples<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>1. Solve <\/strong>$45 \\times 5$<strong> using reasonableness.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">On calculating $45 \\times 5$, we get 225. Now, for the sake of reasonableness, if we divide 225 by 5,&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We get<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\frac{225}{5} = 45$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Hence, we verified using reasonableness.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>2. Anne bought 3.8 pounds of grains. The grains cost her <\/strong>$\\$1.99$<strong> per pound. What was the total cost of Anne\u2019s grains? Also, find a reasonable estimate.<\/strong><\/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\">The grains cost $\\$1.99$ per pound.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">To find the cost of 3.8 pounds, we have to multiply 1.99 and 3.8 as represented below.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"531\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/Reasonable-estimate-example.webp\" alt=\"Reasonable estimate example\" class=\"wp-image-33048\" title=\"Reasonable estimate example\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/Reasonable-estimate-example.webp 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/Reasonable-estimate-example-300x257.webp 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If we round the answer 7.562 to the nearest hundredth place, we get 7.56.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Hence, the cost of 3.8 pounds of grains is $\\$7.56$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Now, let us find a reasonable estimate.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Round 1.99 to the nearest whole number, that is, 2.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Round 3.8 to the nearest whole number, that is, 4.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Multiplying the whole numbers 2 and 4.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">That is, $2 \\times 4 = 8$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The answer is reasonable, because 8 is close to 7.56.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>3. A certain plant grows 3.75 inches per month. If the plant continues to grow at this rate, how much will the plant grow in 6.25 months ?<\/strong><\/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\">A certain plant grows in one month&nbsp; $=&nbsp; 3.75$ inches.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">To find the amount of plant grown in 6.25 months, we have to multiply 3.75 and 6.25 as given below.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"560\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/using-reasonableness-to-verify-the-answer.png\" alt=\"Using reasonableness to verify the answer\" class=\"wp-image-33049\" title=\"Using reasonableness to verify the answer\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/using-reasonableness-to-verify-the-answer.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/using-reasonableness-to-verify-the-answer-300x271.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Hence, the plant will grow 23.4375 inches in 6.25 months.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Now, let us estimate to check if our answer is reasonable.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Round off 3.75 to the nearest whole number, that is, 4.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Round off 6.25 to the nearest whole number, that is, 6.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Multiply the whole numbers 4 and 6, that is, $4 \\times 6 = 24$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Our answer is reasonable, because 24 is closer to 23.437.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>4. Tanya bought 3.4 pounds of yogurt that cost <\/strong>$\\$6.95$<strong> per pound. How much did she spend on yogurt?<\/strong><\/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\">The cost of one pound of yogurt $=&nbsp; \\$6.95$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">To find the cost of 3.4 pounds of yogurt, we have to multiply 3.4 and 6.95.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$3.4 \\times 6.95&nbsp; =&nbsp; 23.63$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Hence, the cost of 3.4 pounds of yogurt is $\\$23.63$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Now, let us estimate to check whether our answer is reasonable.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Rounding off 3.4 to the nearest whole number-<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">That is, 3<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Rounding off 6.95 to the nearest whole number-<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">That is, 7&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Multiplying the whole numbers 3 and 7.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">That is, $3 \\times 7&nbsp; =&nbsp; 21$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Our answer is reasonable. Because 21 is much closer to 23.63.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>5. Cameron earns <\/strong>$\\$9.40$<strong> per hour working at a dairy farm. How much money will he earn for 18.5 hours of work ?<\/strong><\/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\">Cameron\u2019s earning in one hour&nbsp; $=&nbsp; \\$9.40$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">To find his earning of 18.5 hours, we have to multiply 18.5 and 9.40<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$18.5 \\times 9.4&nbsp; =&nbsp; 173.90$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Hence, his earning for 18.5 hours is $\\$173.90$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Now, let us estimate to check if our answer is reasonable.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Rounding off 18.5 to the nearest whole number, that is, 19.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Rounding off 9.40 to the nearest whole number, that is, 9.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Multiplying the whole numbers 19 and 9.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">That is, $19 \\times 9 = 171$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Our answer is reasonable. Because 171 is much closer to 173.90<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-practice-problems\">Practice Problems<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Reasonableness in Math<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">Choose a reasonable estimate for $95 \\times 16$.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">1500<\/div><div class=\"spq_answer_block\" data-value=\"1\">1100<\/div><div class=\"spq_answer_block\" data-value=\"2\">900<\/div><div class=\"spq_answer_block\" data-value=\"3\">1000<\/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: 1500<br\/>Round 95 to 100, and 16 to 15.<br>\r\n$100 \\times 15 = 1500$<br>\r\nActual answer $= 1520$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">Jen calculated the sum $x + y$ to be z. In which case will the answer be correct?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$z + y$ should equal $x$.<\/div><div class=\"spq_answer_block\" data-value=\"1\">$z$ $-$ $y$ should equal $x$.<\/div><div class=\"spq_answer_block\" data-value=\"2\">$yz$ should equal $x$.<\/div><div class=\"spq_answer_block\" data-value=\"3\">$x + z$ should equal $y$.<\/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: $z$ $-$ $y$ should equal $x$.<br\/>As per Jen\u2019s calculations, $x + y = z$\r\nTo check whether it is correct, she can subtract y from z. If the answer is x, then she is right.\r\nSo, $z$ $-$ $y$ should equal x.<\/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\">How to verify $56$ $-$ $14$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$42 + 14$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$42 + 42$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$56 + 14$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$56 + 56$<\/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: $42 + 14$<br\/>$56$ $-$ $14 = 42$<br>\r\nSo, we can verify the answer by adding 42 and 14.<br>\r\n$42 + 14 = 56$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">Rounding 12.99 to the nearest whole number gives us<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">11<\/div><div class=\"spq_answer_block\" data-value=\"1\">10<\/div><div class=\"spq_answer_block\" data-value=\"2\">20<\/div><div class=\"spq_answer_block\" data-value=\"3\">13<\/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: 13<br\/>Rounding 12.99 to the nearest whole number gives us 13.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">$24 \\div 5$ is approximately equal to<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">4<\/div><div class=\"spq_answer_block\" data-value=\"1\">3<\/div><div class=\"spq_answer_block\" data-value=\"2\">5<\/div><div class=\"spq_answer_block\" data-value=\"3\">6<\/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: 5<br\/>We know that, $5^{2} = 25$<br>\r\n$25 \\div 5 = 5$<br>\r\nActual answer $= 4.8$<\/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\": \"Reasonableness in Math\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Reasonableness in Math\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Choose a reasonable estimate for $$95 \\\\times 16$$.\",\n                    \"text\": \"Choose a reasonable estimate for $$95 \\\\times 16$$.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Round 95 to 100, and 16 to 15.<br>\r\n$$100 \\\\times 15 = 1500$$<br>\r\nActual answer $$= 1520$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"1100\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Round 95 to 100, and 16 to 15.<br>\r\n$$100 \\\\times 15 = 1500$$<br>\r\nActual answer $$= 1520$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"900\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Round 95 to 100, and 16 to 15.<br>\r\n$$100 \\\\times 15 = 1500$$<br>\r\nActual answer $$= 1520$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"1000\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Round 95 to 100, and 16 to 15.<br>\r\n$$100 \\\\times 15 = 1500$$<br>\r\nActual answer $$= 1520$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"1500\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Round 95 to 100, and 16 to 15.<br>\r\n$$100 \\\\times 15 = 1500$$<br>\r\nActual answer $$= 1520$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Round 95 to 100, and 16 to 15.<br>\r\n$$100 \\\\times 15 = 1500$$<br>\r\nActual answer $$= 1520$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Jen calculated the sum $$x + y$$ to be z. In which case will the answer be correct?\",\n                    \"text\": \"Jen calculated the sum $$x + y$$ to be z. In which case will the answer be correct?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"As per Jen\u2019s calculations, $$x + y = z$$\r\nTo check whether it is correct, she can subtract y from z. If the answer is x, then she is right.\r\nSo, $$z$$ $$-$$ $$y$$ should equal x.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$z + y$$ should equal $$x$$.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"As per Jen\u2019s calculations, $$x + y = z$$\r\nTo check whether it is correct, she can subtract y from z. If the answer is x, then she is right.\r\nSo, $$z$$ $$-$$ $$y$$ should equal x.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$yz$$ should equal $$x$$.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"As per Jen\u2019s calculations, $$x + y = z$$\r\nTo check whether it is correct, she can subtract y from z. If the answer is x, then she is right.\r\nSo, $$z$$ $$-$$ $$y$$ should equal x.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$x + z$$ should equal $$y$$.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"As per Jen\u2019s calculations, $$x + y = z$$\r\nTo check whether it is correct, she can subtract y from z. If the answer is x, then she is right.\r\nSo, $$z$$ $$-$$ $$y$$ should equal x.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$z$$ $$-$$ $$y$$ should equal $$x$$.\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"As per Jen\u2019s calculations, $$x + y = z$$\r\nTo check whether it is correct, she can subtract y from z. If the answer is x, then she is right.\r\nSo, $$z$$ $$-$$ $$y$$ should equal x.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"As per Jen\u2019s calculations, $$x + y = z$$\r\nTo check whether it is correct, she can subtract y from z. If the answer is x, then she is right.\r\nSo, $$z$$ $$-$$ $$y$$ should equal x.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"How to verify $$56$$ $$-$$ $$14$$?\",\n                    \"text\": \"How to verify $$56$$ $$-$$ $$14$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$56$$ $$-$$ $$14 = 42$$<br>\r\nSo, we can verify the answer by adding 42 and 14.<br>\r\n$$42 + 14 = 56$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$42 + 42$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$56$$ $$-$$ $$14 = 42$$<br>\r\nSo, we can verify the answer by adding 42 and 14.<br>\r\n$$42 + 14 = 56$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$56 + 14$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$56$$ $$-$$ $$14 = 42$$<br>\r\nSo, we can verify the answer by adding 42 and 14.<br>\r\n$$42 + 14 = 56$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$56 + 56$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$56$$ $$-$$ $$14 = 42$$<br>\r\nSo, we can verify the answer by adding 42 and 14.<br>\r\n$$42 + 14 = 56$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$42 + 14$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$56$$ $$-$$ $$14 = 42$$<br>\r\nSo, we can verify the answer by adding 42 and 14.<br>\r\n$$42 + 14 = 56$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$56$$ $$-$$ $$14 = 42$$<br>\r\nSo, we can verify the answer by adding 42 and 14.<br>\r\n$$42 + 14 = 56$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Rounding 12.99 to the nearest whole number gives us\",\n                    \"text\": \"Rounding 12.99 to the nearest whole number gives us\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Rounding 12.99 to the nearest whole number gives us 13.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"11\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Rounding 12.99 to the nearest whole number gives us 13.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"10\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Rounding 12.99 to the nearest whole number gives us 13.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"20\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Rounding 12.99 to the nearest whole number gives us 13.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"13\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Rounding 12.99 to the nearest whole number gives us 13.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Rounding 12.99 to the nearest whole number gives us 13.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"$$24 \\\\div 5$$ is approximately equal to\",\n                    \"text\": \"$$24 \\\\div 5$$ is approximately equal to\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"We know that, $$5^{2} = 25$$<br>\r\n$$25 \\\\div 5 = 5$$<br>\r\nActual answer $$= 4.8$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"4\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We know that, $$5^{2} = 25$$<br>\r\n$$25 \\\\div 5 = 5$$<br>\r\nActual answer $$= 4.8$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"3\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We know that, $$5^{2} = 25$$<br>\r\n$$25 \\\\div 5 = 5$$<br>\r\nActual answer $$= 4.8$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"6\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We know that, $$5^{2} = 25$$<br>\r\n$$25 \\\\div 5 = 5$$<br>\r\nActual answer $$= 4.8$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"5\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"We know that, $$5^{2} = 25$$<br>\r\n$$25 \\\\div 5 = 5$$<br>\r\nActual answer $$= 4.8$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"We know that, $$5^{2} = 25$$<br>\r\n$$25 \\\\div 5 = 5$$<br>\r\nActual answer $$= 4.8$$\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"10-frequently-asked-questions\">Frequently Asked Questions<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-49085ec6-3220-485a-9637-41d7c83dfb00\" 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-0-49085ec6-3220-485a-9637-41d7c83dfb00\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-49085ec6-3220-485a-9637-41d7c83dfb00\"><strong>How do you check reasonableness in math?<\/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-0-49085ec6-3220-485a-9637-41d7c83dfb00\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">You can check for reasonableness either by rounding or by estimation or simply by substituting the values to check if it works.<\/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-1-49085ec6-3220-485a-9637-41d7c83dfb00\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-49085ec6-3220-485a-9637-41d7c83dfb00\"><strong>Where do we use reasonableness ?<\/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-1-49085ec6-3220-485a-9637-41d7c83dfb00\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We use reasonableness in situations where we need to verify the answers or to check for correctness of solutions.<\/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-2-49085ec6-3220-485a-9637-41d7c83dfb00\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-49085ec6-3220-485a-9637-41d7c83dfb00\"><strong>How to check if the sum of two decimals is reasonable?<\/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-2-49085ec6-3220-485a-9637-41d7c83dfb00\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Round both the decimals to the nearest whole numbers and compare the actual answer to the estimated sum.<\/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-3-49085ec6-3220-485a-9637-41d7c83dfb00\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-49085ec6-3220-485a-9637-41d7c83dfb00\"><strong>What are outrageous solutions?<\/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-3-49085ec6-3220-485a-9637-41d7c83dfb00\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The solutions to a math problem which are not reasonable or which are nowhere in the fair range of the actual answer are outrageous solutions.<\/p>\n\n<\/div><\/div>\n<\/div><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Reasonableness: Introduction Have you ever come across a situation where you are attempting a math problem and need to check whether you did it right or not? When you find the solution, a good way to check if the problem is solved correctly is to check for reasonableness.&nbsp; While solving a problem, you should always &#8230; <a title=\"Reasonableness in Math\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/reasonableness\" aria-label=\"More on Reasonableness in Math\">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-1094","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\/1094","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=1094"}],"version-history":[{"count":20,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/1094\/revisions"}],"predecessor-version":[{"id":33050,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/1094\/revisions\/33050"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=1094"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=1094"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=1094"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}