{"id":6436,"date":"2014-02-04T17:43:44","date_gmt":"2014-02-04T17:43:44","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=6436"},"modified":"2014-12-02T08:25:32","modified_gmt":"2014-12-02T08:25:32","slug":"more-problem-solving-strategies-solve-a-simpler-problem","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/more-problem-solving-strategies-solve-a-simpler-problem\/","title":{"rendered":"More Problem-Solving Strategies: Solve a Simpler Problem"},"content":{"rendered":"

Overview:<\/strong><\/p>\n

There are many ways to solve math problems.\u00a0 Some can be solved more easily by drawing a diagram, making a chart or graph of all the values, or looking for a pattern.\u00a0 Another strategy to use is to solve a simpler problem, then use information from the steps and the solution to solve another problem.<\/p>\n

What Is Estimation?<\/strong><\/p>\n

One of the ways simpler problems are solved every day is by rounding numbers and estimating.\u00a0 Suppose you want to buy a book that costs $45.00, but you will need to pay tax of 8.8%.\u00a0 Most people cannot figure what 8.8 % of $45.00 without a calculator, but 10% is an easier problem.\u00a0 By estimating 10% of $45.00 at 4.50 , the final cost of the book will be somewhere around $49.50, which is close enough to know whether there’s enough money to make the purchase.<\/p>\n

What About Smaller Pieces?<\/strong><\/p>\n

Many times problems can be made simpler by breaking them into smaller pieces.\u00a0 A complex geometric figure can be broken up into its component rectangles, squares, and triangles, and the area of each part calculated, then added together for the area of the entire figure.\u00a0 An algebra problem with many variables can be solved for one variable at a time, and the like variables can be grouped together.<\/p>\n

What About Familiar Operations?<\/strong><\/p>\n

In addition, one of the ways to make math problems simpler is to break the problem into a series of familiar operations.\u00a0 For example, when solving the equation 2(c+1) = 8c – 22, the first step is to remove the grouping, in a familiar step of multiplying 2(c + 1) = 2c + 2.\u00a0 The next step is a familiar step of subtraction so that the variables are all on the same side of the equation, so that 2c – 2c + 2 = 8c – 2c – 22, or 2 = 6c – 22.\u00a0 Then the next step is moving the numbers so that the variables are on one side of the equation and the numbers are on the other side, as 2 + 22 = 6c -22 + 22.\u00a0 If 24 = 6c, then a last familiar step: 24\/6 = 6c\/6 or c = 4.<\/p>\n

What About Simpler Patterns?<\/strong><\/p>\n

Suppose the problem were to find the sum of the first 100 natural numbers, starting with 1 + 2 + 3…98 + 99 + 100. It would take a long time, even with a calculator, and there’s always a possibility of a mistake in addition.\u00a0 There’s a simpler way to break it up into smaller pieces, use familiar operations, and use a simpler pattern.\u00a0 One small piece of the problem is to add the first 10 numbers:<\/p>\n

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10.<\/p>\n

There is a pattern to it, but in a different order: 1 + 10 = 11, 2 + 9 = 11, 3 + 8 = 11, 4 + 7 = 11, and 6 + 5 = 11.\u00a0 In other words the sum of the first 10 numbers is 5 (11) or 55.\u00a0 The pattern to the first 100 numbers (still doable, but more time-consuming) is\u00a0 (1 + 100) + (2 +99) + (3 + 98) and so on, or 101 times 50, or 5050.<\/p>\n

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SchoolTutoring Academy<\/span> is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Westminster, CO visit: Tutoring in Westminster, CO<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Overview: There are many ways to solve math problems.\u00a0 Some can be solved more easily by drawing a diagram, making a chart or graph of all the values, or looking for a pattern.\u00a0 Another strategy to use is to solve a simpler problem, then use information from the steps and the solution to solve another […]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[604,1299,1663,1689],"class_list":["post-6436","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-estimation","tag-patterns","tag-smaller-pieces","tag-solving-a-simpler-problem"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6436","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=6436"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6436\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=6436"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=6436"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=6436"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}