{"id":6979,"date":"2014-05-07T16:55:32","date_gmt":"2014-05-07T16:55:32","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=6979"},"modified":"2014-12-02T08:25:30","modified_gmt":"2014-12-02T08:25:30","slug":"math-overview-of-the-distributive-property","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/math-overview-of-the-distributive-property\/","title":{"rendered":"Math Overview of the Distributive Propery"},"content":{"rendered":"

Overview:<\/h3>\n

The Distributive Property in math can be used to solve equations by combining like terms.\u00a0 It is another tool to simplify complicated problems by using common patterns of multiplication over addition or subtraction.<\/span><\/p>\n

Definitions:<\/h3>\n\n\n\n
\n
\n

Figure 1:\u00a0 Formal definition of the Distributive Property<\/p>\n<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\"monohybridcross\"<\/a><\/p>\n

In arithmetic, the distributive property was defined with examples such as 4(3 + 4) = (4\u22193) + (4\u22194), which simplifies to 28 =12 + 16.\u00a0 Similarly, 5(10 – 3) is the same thing as (5\u221910) – (5\u22193) which simplifies to 35 = 50 – 15.\u00a0 Using variables, the distributive property holds true.<\/p>\n

Combining Like Terms:<\/h3>\n

Expressions can be combined that use the same variables because of the Distributive Property.\u00a0 For example, 9x + 2x = 11x because it follows the same pattern, as (9 + 2)x =11x.\u00a0 Similarly, 8x – 4x = 4x because it follows the pattern (8-4)x = 4x.\u00a0 Even a more complicated expression such as 9ab2<\/sup>-6a2<\/sup>b can be factored as 3ab(3b – 2a) because 3ab(3b) \u2013 3ab(2a) = 9ab2<\/sup> \u2013 6a2<\/sup>b. Suppose that the expression were made even difficult looking, as (9ab2<\/sup> \u2013 6a2<\/sup>b)\/(3b – 2a).\u00a0 That expression could be simplified to 3ab, by using the Distributive Property.<\/p>\n

Geometric Explanation of the Distributive Property:<\/h3>\n

Suppose that one rectangle has width c and length a + b.\u00a0 The area of the rectangle, c(a +b), is the same whether it is calculated as the measurement of one rectangle, or the sum of 2 rectangles, ca + cb.\u00a0 This property can be used to solve equations where parentheses are used.\u00a0 For example, suppose the expression is 8(y + 1).\u00a0The parentheses can be eliminated by multiplying, or 8y + 8, and then the rest of the equation can be solved.<\/p>\n\n\n\n
\n
\n

Figure 2:\u00a0 The area of the rectangle is the same whether it is calculated as c(a +b) or ca + cb<\/p>\n<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\"monohybridcross\"<\/a><\/p>\n

Applications of the Distributive Property:<\/h3>\n

Word problems involving discounts, tips, taxes, and overtime can all be solved using applications of the Distributive Property.\u00a0 Suppose the question were, \u201cIf the sale price of an item is $15.00, and it is being offered at a 20% discount, what is the regular price?\u201d\u00a0 If the regular price is x, then the sale price is (1-.20)x or .80x.\u00a0 Solving for x, the regular price is $18.75.\u00a0 It can be checked by subtraction using the Distributive Property, as the sale price will be equal to the regular price of $18.75 \u2013 the 20% discount of $3.75, or $15.00.\u00a0 That also follows the pattern of c(a \u2013 b) =ca\u00a0– cb. Suppose a person is paying 9% sales tax on a purchase.\u00a0 This would be the same as paying for the item and 9% of the item, or paying the price of the item +.09 of the price.\u00a0 If the price of the item is $18.75, the price plus tax is 1.09(18.75) or 20.4375 which the store will round up to $20.44.\u00a0 In order to check the figures, the Distributive Property could again be used, so that $20.4375 = $18.75 +1.6875.<\/p>\n

Interested in 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 Lexington, NE: visit Tutoring in Lexington, NE<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Overview: The Distributive Property in math can be used to solve equations by combining like terms.\u00a0 It is another tool to simplify complicated problems by using common patterns of multiplication over addition or subtraction. Definitions: Figure 1:\u00a0 Formal definition of the Distributive Property In arithmetic, the distributive property was defined with examples such as 4(3 […]<\/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":[519,645],"class_list":["post-6979","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-distributive-property","tag-factoring"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6979","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=6979"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6979\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=6979"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=6979"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=6979"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}