{"id":6534,"date":"2014-02-07T17:40:24","date_gmt":"2014-02-07T17:40:24","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=6534"},"modified":"2014-12-02T08:25:32","modified_gmt":"2014-12-02T08:25:32","slug":"math-review-of-combining-operations","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2014\/02\/07\/math-review-of-combining-operations\/","title":{"rendered":"Math Review of Combining Operations"},"content":{"rendered":"

\u00a0Overview:<\/strong><\/p>\n

Some algebra equations can be solved by combining operations.\u00a0 For example, students can use the Distributive Property with Multiplication over Addition to solve many different equations\u00a0when the variables are the same.\u00a0 Combining operations can lead to shortcuts to solve problems.<\/p>\n

What Is the Distributive Property?<\/strong><\/p>\n

The Distributive Property of Multiplication over Addition (or its sibling, the Distributive Property of Multiplication over Subtraction) is stated in algebra as true for any numbers a, b, and x, so that ax + bx = (a + b)x.\u00a0 For example, 2m + 3m equals (2 + 3)m or 5m.\u00a0 Simplifying 5y – 3y equals (5 – 3)y or 2y, showing that it works for subtraction, also.<\/p>\n

Using an Alternate Form<\/strong><\/p>\n

Another form of the Distributive Property can be stated in algebraic terms as x(a + b) = xa + xb.\u00a0 This form of the equation works the same way because of the commutative property.\u00a0 For example, suppose you have two rectangles that are x units wide.\u00a0 One rectangle is 20 units long, and the other rectangle is 85 units long.\u00a0 The total area can be found by using the alternate form, as x(85 + 20) = x85 + x20 or x105.<\/p>\n

Shortcuts for Mental Math<\/strong><\/p>\n

The Distributive Property can be used in a shortcut to do math mentally.\u00a0 For example, suppose one wants to leave a 20 percent tip on a meal that costs 25 dollars.\u00a0 A 10% tip on a meal that costs 25 dollars would be $2.50 and a 20% tip would be 2 times 10% or 2 times 2.50 or 5.00.\u00a0 Add 5 dollars to $25.00 and the total cost of the meal would be 30 dollars.<\/p>\n

Equations in the Pattern ax + b = cx + d<\/strong><\/p>\n

This form of equations can be solved by combining operations.\u00a0 Suppose the problem were\u00a0 3x + 5 = 10x + 26.\u00a0 The variable is on both sides of the equation, but operations can be combined so that all the variables will be on one side and all the constants will be on the other.\u00a0 In the next step, 3x – 10x + 5 = 10x – 10x + 26, or -7x + 5 = 26.\u00a0 Then -7x = 26 – 5, or -7x = 21 or -7x\/-7 = 21\/-7 or x = -3.\u00a0 To check, 3(-3) + 5 = -4 and 10(-3) + 26 = -30 + 26 = -4.<\/p>\n

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\u00a0Overview: Some algebra equations can be solved by combining operations.\u00a0 For example, students can use the Distributive Property with Multiplication over Addition to solve many different equations\u00a0when the variables are the same.\u00a0 Combining operations can lead to shortcuts to solve problems. What Is the Distributive Property? The Distributive Property of Multiplication over Addition (or its […]<\/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":[13],"tags":[316,519,1108],"class_list":["post-6534","post","type-post","status-publish","format-standard","hentry","category-pre-algebra","tag-combining-operations","tag-distributive-property","tag-mental-math"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6534","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=6534"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6534\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=6534"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=6534"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=6534"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}