{"id":8465,"date":"2017-05-25T19:09:51","date_gmt":"2017-05-25T19:09:51","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&p=8465"},"modified":"2019-05-27T05:39:47","modified_gmt":"2019-05-27T05:39:47","slug":"divide-monomials","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/chapter\/divide-monomials\/","title":{"raw":"Introduction to Dividing Monomials","rendered":"Introduction to Dividing Monomials"},"content":{"raw":"

What you'll learn to do: Divide monomials by applying several properties<\/h2>\r\nDivide Monomials\r\n\r\nBefore you get started, take this readiness quiz.\r\n
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readiness quiz<\/h3>\r\n1)\r\n\r\n[ohm_question]146014[\/ohm_question]\r\n\r\nIf you missed the problem, review the following video.\r\n\r\nhttps:\/\/youtu.be\/_2Wk7jXf3Ok\r\n\r\n2)\r\n\r\n[ohm_question]146148[\/ohm_question]\r\n\r\nIf you missed the problem, review the video below.\r\n\r\nhttps:\/\/youtu.be\/Hgu9HKDHTUA\r\n\r\n3)\r\n\r\nSimplify: [latex]{\\Large\\frac{12x}{12y}}[\/latex]\r\n\r\nSolution:\r\n\r\n[latex]{\\Large\\frac{x}{y}}[\/latex]\r\n\r\n<\/div>\r\n \r\n\r\n
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Divide Monomials<\/h1>\r\nWe have now seen all the properties of exponents. We'll use them to divide monomials. Later, you'll use them to divide polynomials.\r\n
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EXAMPLE<\/h3>\r\nFind the quotient: [latex]56{x}^{5}\\div 7{x}^{2}[\/latex]\r\n\r\nSolution\r\n\r\n\r\n\r\n\r\n\r\n\r\n
<\/td>\r\n[latex]56{x}^{5}\\div 7{x}^{2}[\/latex]<\/td>\r\n<\/tr>\r\n
Rewrite as a fraction.<\/td>\r\n[latex]{\\Large\\frac{56{x}^{5}}{7{x}^{2}}}[\/latex]<\/td>\r\n<\/tr>\r\n
Use fraction multiplication to separate the number\r\n\r\npart from the variable part.<\/td>\r\n[latex]{\\Large\\frac{56}{7}}\\cdot {\\Large\\frac{{x}^{5}}{{x}^{2}}}[\/latex]<\/td>\r\n<\/tr>\r\n
Use the Quotient Property.<\/td>\r\n[latex]8{x}^{3}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n \r\n\r\n<\/div>\r\n \r\n
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TRY IT<\/h3>\r\nFind the quotient: [latex]63{x}^{8}\\div 9{x}^{4}[\/latex]\r\n\r\n[latex]7{x}^{4}[\/latex]\u00a0<\/sup>\r\n\r\nFind the quotient: [latex]96{y}^{11}\\div 6{y}^{8}[\/latex]\r\n\r\n[latex]16{y}^{3}[\/latex]\r\n\r\n<\/div>\r\n \r\n\r\nWhen we divide monomials with more than one variable, we write one fraction for each variable.\r\n
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Example<\/h3>\r\nFind the quotient: [latex]{\\Large\\frac{42{x}^{2}{y}^{3}}{-7x{y}^{5}}}[\/latex]\r\n\r\nSolution\r\n\r\n\r\n\r\n\r\n\r\n\r\n
<\/td>\r\n[latex]{\\Large\\frac{42{x}^{2}{y}^{3}}{-7x{y}^{5}}}[\/latex]<\/td>\r\n<\/tr>\r\n
Use fraction multiplication.<\/td>\r\n[latex]{\\Large\\frac{42}{-7}}\\cdot {\\Large\\frac{{x}^{2}}{x}}\\cdot {\\Large\\frac{{y}^{3}}{{y}^{5}}}[\/latex]<\/td>\r\n<\/tr>\r\n
Simplify and use the Quotient Property.<\/td>\r\n[latex]-6\\cdot x\\cdot {\\Large\\frac{1}{{y}^{2}}}[\/latex]<\/td>\r\n<\/tr>\r\n
Multiply.<\/td>\r\n[latex]-{\\Large\\frac{6x}{{y}^{2}}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n \r\n\r\n<\/div>\r\n \r\n
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TRY IT<\/h3>\r\nFind the quotient: [latex]{\\Large\\frac{-84{x}^{8}{y}^{3}}{7{x}^{10}{y}^{2}}}[\/latex]\r\n\r\n[latex]-{\\Large\\frac{12y}{{x}^{2}}}[\/latex]\r\n\r\n \r\n\r\nFind the quotient: [latex]{\\Large\\frac{-72{a}^{4}{b}^{5}}{-8{a}^{9}{b}^{5}}}[\/latex]\r\n\r\n[latex]{\\Large\\frac{9}{{a}^{5}}}[\/latex]\r\n\r\n<\/div>\r\n \r\n
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EXAMPLE<\/h3>\r\nFind the quotient: [latex]{\\Large\\frac{24{a}^{5}{b}^{3}}{48a{b}^{4}}}[\/latex]\r\n\r\nSolution\r\n\r\n\r\n\r\n\r\n\r\n\r\n
<\/td>\r\n[latex]{\\Large\\frac{24{a}^{5}{b}^{3}}{48a{b}^{4}}}[\/latex]<\/td>\r\n<\/tr>\r\n
Use fraction multiplication.<\/td>\r\n[latex]{\\Large\\frac{24}{48}}\\cdot {\\Large\\frac{{a}^{5}}{a}}\\cdot {\\Large\\frac{{b}^{3}}{{b}^{4}}}[\/latex]<\/td>\r\n<\/tr>\r\n
Simplify and use the Quotient Property.<\/td>\r\n[latex]{\\Large\\frac{1}{2}}\\cdot {a}^{4}\\cdot {\\Large\\frac{1}{b}}[\/latex]<\/td>\r\n<\/tr>\r\n
Multiply.<\/td>\r\n[latex]{\\Large\\frac{{a}^{4}}{2b}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n \r\n\r\n<\/div>\r\n \r\n
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TRY IT<\/h3>\r\nFind the quotient: [latex]{\\Large\\frac{16{a}^{7}{b}^{6}}{24a{b}^{8}}}[\/latex]\r\n\r\n[latex]{\\Large\\frac{2{a}^{6}}{3{b}^{2}}}[\/latex]\r\n\r\n \r\n\r\nFind the quotient: [latex]{\\Large\\frac{27{p}^{4}{q}^{7}}{-45{p}^{12}{q}^{}}}[\/latex]\r\n\r\n[latex]-{\\Large\\frac{3{q}^{6}}{5{p}^{8}}}[\/latex]\r\n\r\n<\/div>\r\n \r\n\r\nOnce you become familiar with the process and have practiced it step by step several times, you may be able to simplify a fraction in one step.\r\n
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EXAMPLE<\/h3>\r\nFind the quotient: [latex]{\\Large\\frac{14{x}^{7}{y}^{12}}{21{x}^{11}{y}^{6}}}[\/latex]\r\n\r\nSolution\r\n\r\n\r\n\r\n\r\n
<\/td>\r\n[latex]{\\Large\\frac{14{x}^{7}{y}^{12}}{21{x}^{11}{y}^{6}}}[\/latex]<\/td>\r\n<\/tr>\r\n
Simplify and use the Quotient Property.<\/td>\r\n[latex]{\\Large\\frac{2{y}^{6}}{3{x}^{4}}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n \r\n\r\n<\/div>\r\nBe very careful to simplify [latex]{\\Large\\frac{14}{21}}[\/latex] by dividing out a common factor, and to simplify the variables by subtracting their exponents.\r\n
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TRY IT<\/h3>\r\nFind the quotient: [latex]{\\Large\\frac{28{x}^{5}{y}^{14}}{49{x}^{9}{y}^{12}}}[\/latex]\r\n\r\n[latex]{\\Large\\frac{4{y}^{2}}{7{x}^{4}}}[\/latex]\r\n\r\n \r\n\r\nFind the quotient: [latex]{\\Large\\frac{30{m}^{5}{n}^{11}}{48{m}^{10}{n}^{14}}}[\/latex]\r\n\r\n[latex]{\\Large\\frac{5}{8{m}^{5}{n}^{3}}}[\/latex]\r\n\r\n<\/div>\r\n \r\n\r\nIn all examples so far, there was no work to do in the numerator or denominator before simplifying the fraction. In the next example, we'll first find the product of two monomials in the numerator before we simplify the fraction.\r\n
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EXAMPLE<\/h3>\r\nFind the quotient: [latex]{\\Large\\frac{(3{x}^{3}{y}^{2})(10{x}^{2}{y}^{3})}{6{x}^{4}{y}^{5}}}[\/latex]\r\n\r\nSolution\r\nRemember, the fraction bar is a grouping symbol. We will simplify the numerator first.\r\n\r\n\r\n\r\n\r\n\r\n
<\/td>\r\n[latex]{\\Large\\frac{\\left(3{x}^{3}{y}^{2}\\right)\\left(10{x}^{2}{y}^{3}\\right)}{6{x}^{4}{y}^{5}}}[\/latex]<\/td>\r\n<\/tr>\r\n
Simplify the numerator.<\/td>\r\n[latex]{\\Large\\frac{30{x}^{5}{y}^{5}}{6{x}^{4}{y}^{5}}}[\/latex]<\/td>\r\n<\/tr>\r\n
Simplify, using the Quotient Rule.<\/td>\r\n[latex]5x[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n \r\n\r\n<\/div>\r\n \r\n
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TRY IT<\/h3>\r\nFind the quotient: [latex]{\\Large\\frac{\\left(3{x}^{4}{y}^{5}\\right)\\left(8{x}^{2}{y}^{5}\\right)}{12{x}^{5}{y}^{8}}}[\/latex]\r\n\r\n[latex]2{xy}^{2}[\/latex]\r\n\r\n \r\n\r\nFind the quotient: [latex]{\\Large\\frac{\\left(-6{a}^{6}{b}^{9}\\right)\\left(-8{a}^{5}{b}^{8}\\right)}{-12{a}^{10}{b}^{12}}}[\/latex]\r\n\r\n[latex]-4{ab}^{5}[\/latex]\r\n\r\n<\/div>\r\n \r\n\r\n ","rendered":"

What you’ll learn to do: Divide monomials by applying several properties<\/h2>\n

Divide Monomials<\/p>\n

Before you get started, take this readiness quiz.<\/p>\n

\n

readiness quiz<\/h3>\n

1)<\/p>\n