{"id":6927,"date":"2014-04-21T16:42:09","date_gmt":"2014-04-21T16:42:09","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=6927"},"modified":"2014-12-02T08:25:30","modified_gmt":"2014-12-02T08:25:30","slug":"math-review-of-adding-and-subtracting-fractions","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/math-review-of-adding-and-subtracting-fractions\/","title":{"rendered":"Math Review of Adding and Subtracting Fractions"},"content":{"rendered":"

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

Adding and subtracting fractions is similar to adding and subtracting whole numbers, with one important difference.\u00a0 The denominators must be the same, so that if the fractions do not have the same denominator, they must be changed into equivalent fractions with the same denominator.\u00a0 Then the general pattern of adding or subtracting fractions can be followed.<\/p>\n

What Is the Putting-Together Model for Addition?<\/strong><\/p>\n

By the putting-together model for addition, similar units can be combined.\u00a0 Suppose there are x CD\u2019s in one box and y CD\u2019s in another box.\u00a0 The total number of CD\u2019s in both boxes is x + y.\u00a0 Similarly, if there are t tulip bulbs planted in one flowerbed and 6 more tulip bulbs planted in another flowerbed, there are t + 6 total bulbs planted all together.\u00a0 In order for elements to be combined, they must be the same type of unit.\u00a0 Also, there must not be an overlap in the things to be added together.\u00a0 None of the elements in the x set can be also in the y set for the resulting sum to be x + y.<\/p>\n

How Can Fractions Be Added?<\/strong><\/p>\n

Adding fractions is a type of putting- together.\u00a0 If the fractions have the same denominators, they are the same type of unit, so that 1\/8 and 2\/8 can be added together as 3\/8.\u00a0 Similarly, 4\/16 and 5\/16 can be added together as 9\/16.\u00a0 Generally, the rule using variables is that a\/c + b\/c, when c is not equal to 0 is the same thing as adding (a +b)\/c.<\/p>\n

What about Common Denominators?<\/strong><\/p>\n

In order for fractions to be the same type of unit, they must have common denominators.\u00a0 Suppose the fractions were 1\/3 and 1\/4.\u00a0 In order for them to be added, 1\/3 would have to be changed to its equivalent 4\/12 and \u00bc would have to be changed to its equivalent 3\/12.\u00a0 Then they could be added together as 7\/12.<\/p>\n

How Can Fractions Be Subtracted?<\/strong><\/p>\n

Subtraction is adding the inverse of the number to be subtracted, so that a \u2013 b means the same thing as a + -b.\u00a0 Similarly subtracting a\/c- b\/c means the same thing as a\/c + \u2013b\/c.\u00a0 In order for fractions to be subtracted, they must also have a common denominator. \u00a0Suppose the expression were 5\/6 \u2013 \u00bd .\u00a0 The equivalent of \u00bd is 3\/6, so that 5\/6 \u2013 3\/6 is 2\/6.\u00a0 In simplest terms, 2\/6 is 1\/3.<\/p>\n

Interested in pre-algebra tutoring services<\/a>? Learn more about how we are assisting thousands of students each academic year.<\/p>\n

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 Augusta, ME: visit Tutoring in Augusta, ME<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Overview: Adding and subtracting fractions is similar to adding and subtracting whole numbers, with one important difference.\u00a0 The denominators must be the same, so that if the fractions do not have the same denominator, they must be changed into equivalent fractions with the same denominator.\u00a0 Then the general pattern of adding or subtracting fractions can […]<\/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":[9,13],"tags":[2674,318,2675],"class_list":["post-6927","post","type-post","status-publish","format-standard","hentry","category-fractions-2","category-pre-algebra","tag-adding-fractions","tag-common-denominators","tag-subtracting-fractions"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6927","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=6927"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6927\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=6927"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=6927"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=6927"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}