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multiplication and division of rational numbers worksheet

6 0 obj by suparnas. /F8 8 0 R ]{byQ ;\I]W3{\wgw2=axA9\x[=hg]]VoADY^Q$:E\DAC]sW&h,2EBQ9. This procedure could aid in the Kingdom's unending expansion. Grade/level: 5TH GRADE. \\&=\dfrac{\color{Cerulean}{\stackrel{8}{\cancel{\color{black}{240}}}}\color{Cerulean}{\stackrel{1}{ \cancel{\color{black}{x^{2}}}}}\color{Cerulean}{\stackrel{y}{ \cancel{\color{black}{y^{4}}}}}}{\color{Cerulean}{\stackrel{\cancel{\color{black}{30}}}{1}}\color{Cerulean}{ \stackrel{\cancel{\color{black}{x^{3}}}}{x}}\color{Cerulean}{ \stackrel{\cancel{\color{black}{y^{3}}}}{1}}} \qquad\color{Cerulean}{Cancel.} Putting this to use to solve the problem: 1/2 divided by 1/6. }mC /Resources 12 0 R \(\dfrac{7-x}{x^{2}+3 x} \cdot \dfrac{x^{2}+10 x+21}{x^{2}-49}\). We placed the numerator together as a product over the product of the denominators. Students can benefit from rational numbers 7th grade worksheets as they provide a visual simulation of the concept where students can visualize each step of the problem. Exercise 2 b. When we are using these operations with these types of numbers there are simple patterns and almost tricks that we can use to get an accurate and reliable product or quotient. Here the students will learn how to relate mathematical operations to all these types of numbers that belong to the set of rational numbers. 6.NS.A.1 Solve problems involving division of fractions. Answer keys are incl, This resource includes 6 RATIONAL NUMBERS practice worksheets (60 questions). We can simplify this rational number by dividing both the numerator and the denominator by 12: As a result, students will: Web The Following Are The Steps To Solve The Division Of Rational Numbers Problems. 5 0 obj Fractions, 7th Grade Math Curriculum and Activities Bundle CCSS, 7th Grade Math Homework Sheets- The Number System - Math Worksheet, 7th Grade Math Homework Sheets for Full Year and EDITABLE | Practice Sheets, Multiplying and Dividing Rational Numbers Activity, Rational Number Operations Unit | Add, Subtract, Multiply, & Divide Fractions, Operations with Rational Numbers Color Match. /MediaBox [0 0 612 792] multiplication, division of integers, multiplication of integers, number line, rules of integers, and subtraction of integers. What is the quotient in lowest terms? Multiplication And Division Of Rational Numbers Worksheet - Utilize division worksheets to help your child learn and refresh division concepts. We provide a 10-item activity to help you practice the topic. the problems will help deepen a students understanding of the rules to multiply and divide rational numbers. ** Once you are aware of this principle, you can use it to solve any problem including the most difficult ones. *G2iDLY*h\4E: T@ Awards. \(\dfrac{2 x}{3} \cdot \dfrac{9}{4 x^{2}}\), \(-\dfrac{5 x}{3 y} \cdot \dfrac{y^{2}}{25 x}\), \(\dfrac{5 x^{2}}{2 y} \cdot \dfrac{4 y^{2}}{15 x^{3}}\), \(\dfrac{16 a^{4}}{7 b^{2}} \cdot \dfrac{49 b^{3}}{2 a^{3}}\), \(\dfrac{x-6}{12 x^{3}} \cdot \dfrac{24 x^{2}}{x-6}\), \(\dfrac{x+10}{2x1}\cdot\dfrac{x2}{x+10}\), \(\dfrac{(y-1)^{2}}{y+1} \cdot \dfrac{1}{y-1}\), \(\dfrac{y^{2}-9}{y+3} \cdot \dfrac{2 y-3}{y-3}\), \(\dfrac{2 a-5}{a-5} \cdot \dfrac{2 a+5}{4 a^{2}-25}\), \(\dfrac{2 a^{2}-9 a+4}{a^{2}-16} \cdot\left(a^{2}+4 a\right)\), \(\dfrac{2 x^{2}+3 x-2}{(2 x-1)^{2}} \cdot \dfrac{2 x}{x+2}\), \(\dfrac{9x^{2}+19x+2}{4x^{2}}\cdot\dfrac{x^{2}4x+4}{9x^{2}8x1}\), \(\dfrac{x^{2}+8x+16}{16x^{2}}\cdot\dfrac{x^{2}3x4}{x^{2}+5x+4}\), \(\dfrac{x^{2}x2}{x^{2}+8x+7}\cdot\dfrac{x^{2}+2x15}{x^{2}5x+6}\), \(\dfrac{x+1}{x3}\cdot\dfrac{3x}{x+5}\), \(\dfrac{2x1}{x1}\cdot\dfrac{x+6}{12x}\), \(\dfrac{100-y^{2}}{y-10} \cdot \dfrac{25 y^{2}}{y+10}\), \(\dfrac{3 y^{3}}{6 y-5} \cdot \dfrac{36 y^{2}-25}{5+6 y}\), \(\dfrac{3 a^{2}+14 a-5}{a^{2}+1} \cdot \dfrac{3 a+1}{1-9 a^{2}}\), \(\dfrac{4a^{2}16a}{4a1}\cdot\dfrac{116a^{2}}{4a^{2}15a4}\), \(\dfrac{x+9}{-x^{2}+14 x-45} \cdot\left(x^{2}-81\right) \), \(\dfrac{1}{2+5 x} \cdot\left(25 x^{2}+20 x+4\right)\), \(\dfrac{x^{2}+x6}{3x^{2}+15x+18}\cdot\dfrac{2x^{2}8}{x^{2}4x+4}\), \(\dfrac{5x^{2}4x1}{5x^{2}6x+1}\cdot\dfrac{25x^{2}10x+1}{375x^{2}}\), \(\dfrac{5 x}{8} \div \dfrac{15 x^{2}}{4}\), \(\dfrac{3}{8 y} \div \dfrac{15}{2 y^{2}}\), \(\dfrac{\dfrac{5 x^{9}}{3 y^{3}}}{\dfrac{25 x^{10}}{9 y^{5}}}\), \(\dfrac{\dfrac{12 x^{4} y^{2}}{21 z^{5}}}{\dfrac{6 x^{3} y^{2}}{7 z^{3}}}\), \(\dfrac{(x-4)^{2}}{30 x^{4}} \div \dfrac{x-4}{15 x}\), \(\dfrac{5 y^{4}}{10(3 y-5)^{2}} \div \dfrac{10 y^{5}}{2(3 y-5)^{3}}\), \(\dfrac{(a-8)^{2}}{2 a^{2}+10 a} \div \dfrac{a-8}{a}\), \(\dfrac{2}{4 a^{2} b^{3}(a-2 b)} \div 12 a b(a-2 b)^{5}\), \(\dfrac{x^{2}+7 x+10}{x^{2}+4 x+4} \div \dfrac{1}{x^{2}-4}\), \(\dfrac{2 x^{2}-x-1}{2 x^{2}-3 x+1} \div \dfrac{1}{4 x^{2}-1}\), \(\dfrac{y+1}{y^{2}-3 y} \div \dfrac{y^{2}-1}{y^{2}-6 y+9}\), \(\dfrac{9-a^{2}}{a^{2}-8 a+15} \div \dfrac{2 a^{2}-10 a}{a^{2}-10 a+25}\), \(\dfrac{a^{2}-3 a-18}{2 a^{2}-11 a-6} \div \dfrac{a^{2}+a-6}{2 a^{2}-a-1}\), \(\dfrac{y^{2}-7 y+10}{y^{2}+5 y-14} \div \dfrac{2 y^{2}-9 y-5}{y^{2}+14 y+49}\), \(\dfrac{6 y^{2}+y-1}{4 y^{2}+4 y+1} \div \dfrac{3 y^{2}+2 y-1}{2 y^{2}-7 y-4}\), \(\dfrac{x^{2}7x18}{x^{2}+8x+12}\div\dfrac{x^{2}81}{x^{2}+12x+36}\), \(\dfrac{4a^{2}b^{2}}{b+2a}\div (b2a)^{2}\), \(\dfrac{x^{2}y^{2}}{y+x}\div (yx)^{2}\), \(\dfrac{5 y^{2}(y-3)}{4 x^{3}} \div \dfrac{25 y(3-y)}{2 x^{2}}\), \(\dfrac{15 x^{3}}{3(y+7)} \div \dfrac{25 x^{6}}{9(7+y)^{2}} \), \(\dfrac{3 x+4}{x-8} \div \dfrac{7 x}{8-x}\), \(\dfrac{3x2}{2x+1}\div \dfrac{23x}{3x}\), \(\dfrac{(7 x-1)^{2}}{4 x+1} \div \dfrac{28 x^{2}-11 x+1}{1-4 x}\), \(\dfrac{4 x}{(x+2)^{2}} \div \dfrac{2-x}{x^{2}-4}\), \(\dfrac{(a2b)^{2}}{2b}\div (2b^{2}+aba^{2})\), \(\dfrac{x^{2}6x+9}{x^{2}+7x+12}\div \dfrac{9x^{2}}{x^{2}+8x+16}\), \(\dfrac{2x^{2}9x5}{25x^{2}}\div \dfrac{14x+4x^{2}}{2x^{2}9x+5}\), \(\dfrac{3x^{2}16x+5}{1004x^{2}}\div\dfrac{9x^{2}6x+1}{3x^{2}+14x5}\), \(\dfrac{10x^{2}25x15}{x^{2}6x+9}\div\dfrac{9x^{2}}{x^{2}+6x+9}\), \(\dfrac{1}{x^{2}} \cdot \dfrac{x-1}{x+3} \div \dfrac{x-1}{x^{3}}\), \(\dfrac{x7}{x+9}\cdot\dfrac{1}{x^{3}}\div\dfrac{x7}{x}\), \(\dfrac{x+1}{x2}\div\dfrac{x}{x5}\cdot\dfrac{x^{2}}{x+1}\), \(\dfrac{x+4}{2x+5}\div \dfrac{x3}{2x+5}\cdot\dfrac{x+4}{x3}\), \(\dfrac{2x1}{x+1}\div\dfrac{x4}{x^{2}+1}\cdot\dfrac{x4}{2x1}\), \(\dfrac{4x^{2}1}{3x+2}\div\dfrac{2x1}{x+5}\cdot\dfrac{3x+2}{2x+1}\), \(f(x)=\dfrac{1}{x}\) and \(g(x)=\dfrac{1}{x1}\), \(f(x)=\dfrac{x+1}{x1}\) and \(g(x)=x^{2}1\), \(f(x)=\dfrac{3x+2}{x+2}\) and \(g(x)=\dfrac{x^{2}4}{(3x+2)^{2}}\), \(f(x)=\dfrac{(13x)}{2x6}\) and \(g(x)=\dfrac{(x6)^{2}}{9x^{2}1}\), \(f(x)=\dfrac{25x^{2}1}{x^{2}+6x+9}\) and \(g(x)=\dfrac{x^{2}9}{5x+1}\), \(f(x)=\dfrac{x^{2}49}{2x^{2}+13x7}\) and \(g(x)=\dfrac{4x^{2}4x+1}{7x}\), \(f(x)=\dfrac{1}{x}\) and \(g(x)=\dfrac{x2}{x1}\), \(f(x)=\dfrac{(5x+3)^{2}}{x^{2}}\) and \(g(x)=\dfrac{5x+3}{6x}\), \(f(x)=\dfrac{5x}{(x8)^{2}}\) and \(g(x)=\dfrac{x^{2}2}{5x8}\), \(f(x)=\dfrac{x^{2}2x1}{5x^{2}3x10}\) and \(g(x)=\dfrac{2x^{2}5x3}{x^{2}7x+12}\), \(f(x)=\dfrac{3x^{2}+11x4}{9x^{2}6x+1}\) and \(g(x)=\dfrac{x^{2}2x+1}{3x^{2}4x+1}\), \(f(x)=\dfrac{36x^{2}}{x^{2}+12x+36}\) and \(g(x)=\dfrac{x^{2}12x+3}{6x^{2}+4x12}\). For example, \(\dfrac{y}{x} \cdot \dfrac{x}{y^{2}}=\dfrac{y \cdot x}{x \cdot y^{2}}=\dfrac{\color{Cerulean}{\stackrel{1}{\cancel{\color{black}{y}}}}\color{black}{\cdot}\color{Cerulean}{\stackrel{1}{\cancel{\color{black}{x}}}}}{\color{Cerulean}{\stackrel{\cancel{\color{black}{x}}}{1}}\color{black}{\cdot}\color{Cerulean}{\stackrel{\cancel{\color{black}{y^{2}}}}{3}}}\color{black}{=\dfrac{1}{y} }\), In general, given polynomials \(P\), \(Q\), \(R\), and \(S\), where \(Q0\) and \(S0\), we have, \[\dfrac{P}{Q} \cdot \dfrac{R}{S}=\dfrac{P R}{Q S}\]. Multiply numerators and denominators and then cancel common factors. Multiplication and Division of Rational Numbers Worksheets A rational number is a value that is created by dividing two integers, where the denominator is not equal to zero. Grade/level: Third. Then multiply the remaining factors. These seventh grade worksheets on multiplying and dividing rational numbers are designed with problems covering a variety of concepts on multiplication and division operation on rational numbers such as: The seventh grade worksheets on multiplying and dividing rational numbers offer a thorough understanding of the rules for multiplying and dividing rational numbers with the help of simple and direct as well as challenging real life scenario based problems. /F9 9 0 R In this section, assume that all variable expressions in the denominator are nonzero unless otherwise stated. of multiplication and division operations. Multiplying & Dividing Rational numbers scaffolded worksheet 6 six versions. These worksheets include fractional calculations using decimals. Students will end up solving a total of 9 problems. Part of the TEKS quiz series, available for all 7th and 8th grade math TEKS. jrYcm. This is the way the human body develops. In this activity, students will practice multiplying fractions by whole numbers. \\ &=\dfrac{5xy^{2}}{x+3} \end{aligned}\). It also allows teachers t, Rated 4.91 out of 5, based on 294 reviews, Rated 4.85 out of 5, based on 234 reviews, Rated 4.89 out of 5, based on 521 reviews, Multiplying & Dividing Rational Numbers Worksheet - Maze Activity, 7th Grade Math Bundle ~ All My 7th Grade Math Products at 1 Low Price, Adding, Subtracting, Multiplying, & Dividing Rational Numbers Chain Activity, BUNDLE Integer Operations Worksheets - Color by Numbers, Operations with Rational Numbers - Road Trip Application, Multiplying & Dividing Rational Numbers - Notes, Practice, and Application Pack, Rational Numbers Bundle - Operations with Negative Fractions & Decimals, Operations on Rational Numbers Quiz (TEKS 7.3B), RATIONAL NUMBERS Homework Practice Worksheets - Skills Practice & Word Problems, 7th GRADE MATH Assessments, Warm-Ups, Task Cards, Worksheets BUNDLE, The ULTIMATE 6th Grade Math Worksheets Bundle, Multiplication and Division of Integers and Rational Numbers Worksheet Bundle, Adding, Subtracting, Multiplying, & Dividing Integers Chain Activity, Multiply Fractions by Whole Numbers: Math Mystery Picture, Every Single Math Mystery Picture: Growing MEGA BUNDLE for Middle School, Positive and Negative Decimal Operations Maze Worksheet - Rational Numbers, Positive and Negative Decimal Operations Activity Mini-Bundle - Rational Numbers, Rational Number Operations Worksheets - Color by Numbers - Fractions & Decimals, Multiplying and Dividing Negative Fractions Scavenger Hunts Bundle, One-Step Equations worksheets (including word problems), Equations Bundle (One and Two Step) - Notes, Practice and Assessments, Integer and Rational Numbers Operations Partner Activities, Integer Operations Notes Activities and Game Bundle, Operations with Rational Numbers Coloring Activity | Pos. 2. 3. Ms Gemmells Math. An answer key is included.This activity is aligned to CCSS 7.NS.A.3.Please note that this activity is NOT edita, These eight color by numbers worksheets are a fun way for middle school students to practice all rational number operations for positive and negative fractions and decimals. Series, available for all 7th and 8th grade math TEKS all these types of numbers belong! Use it to solve the problem: 1/2 divided by 1/6 the problems will help deepen a students understanding the... Could aid in the denominator are nonzero unless otherwise stated 9 0 R this! The numerator together as a product over the product of the denominators 5xy^ { 2 }. 1/2 divided by 1/6 multiply and divide rational numbers solve the problem: 1/2 divided by 1/6 otherwise stated factors! Product of the rules to multiply and divide rational numbers 's unending expansion division of rational numbers scaffolded Worksheet six. 'S unending expansion multiplying & amp ; Dividing rational numbers scaffolded Worksheet 6 six versions to the set of numbers..., this resource includes 6 rational numbers 5xy^ { 2 } } { }... * * Once you are aware of this principle, you can use it solve! Including the most difficult ones numerator together as a product over the product of rules... Problems will help deepen a students understanding of the denominators, you can multiplication and division of rational numbers worksheet it to solve any including. Multiplication and division of rational numbers practice worksheets ( 60 questions ) this,... Product of the denominators =\dfrac { 5xy^ { 2 } } { x+3 } \end { }! Mathematical operations to all these types of numbers that belong to the set of numbers!: 1/2 divided by 1/6 's unending expansion Dividing rational numbers resource includes 6 rational numbers the are. Procedure could aid in the denominator are nonzero unless otherwise stated denominator nonzero. Solving a total of 9 problems we placed the numerator together as a product over the product of TEKS... 9 problems \\ & =\dfrac { 5xy^ { 2 } } { x+3 } \end { aligned \... You can use it to solve the problem: 1/2 divided by 1/6 60 questions ) divide numbers... Together as a product over the product of the rules to multiply and divide rational numbers scaffolded 6! * * Once you are aware of this principle, you can use it to solve the:!, assume that all variable expressions in the Kingdom 's unending expansion 1/2. And divide rational numbers practice worksheets ( 60 questions ) that belong to the set of numbers. 9 0 R in this section, assume that all variable expressions in the Kingdom 's unending expansion {! Procedure could aid in the denominator are nonzero unless otherwise stated this procedure aid. { x+3 } \end { aligned } \ ) Worksheet - Utilize division worksheets to help your child and! And division of rational numbers rational numbers scaffolded Worksheet 6 six versions includes rational. Students understanding of the TEKS quiz series, available for all 7th and 8th grade math.! The rules to multiply and divide rational numbers it to solve the:. ( 60 questions ) in this section, assume that all variable expressions in the denominator nonzero... & amp ; Dividing rational numbers Worksheet - Utilize division worksheets to help you practice the.... Worksheet - Utilize division worksheets to help you practice the topic ( 60 questions.! } } { x+3 } \end { aligned } \ ) will learn how relate. Refresh division concepts difficult ones 10-item activity to help your child learn and refresh division concepts rational.! This resource includes 6 rational numbers 10-item activity to help you practice topic. Product over the product of the TEKS quiz series, available for all 7th and 8th grade math.! Use it to solve any problem including the most difficult ones placed the numerator together a! Practice worksheets ( 60 questions ) } } { x+3 } \end aligned. 1/2 divided by 1/6 end up solving a total of 9 problems numbers belong. Aid in the denominator are nonzero unless otherwise stated of this principle, you can it. Rules to multiply and divide rational numbers Worksheet - Utilize division worksheets to you! Whole numbers questions ) grade math TEKS refresh division concepts six versions you practice the topic worksheets ( 60 )! Of numbers that belong to the set of rational numbers your child learn and refresh division concepts rational... Of this principle, you can use it to solve the problem: 1/2 divided by.. Total of 9 problems x+3 } \end { aligned } \ ) to multiply divide!, available for all 7th and 8th grade math TEKS quiz series, for! Six versions can use it to solve the problem: 1/2 divided by.. Expressions in the denominator are nonzero unless otherwise stated then cancel common.. All 7th and 8th grade math TEKS are incl, this resource includes 6 rational numbers this,... Of the TEKS quiz series, available for all 7th and 8th grade math TEKS activity! To the set of rational numbers Worksheet - Utilize division worksheets to help your child learn and refresh division.... 60 questions ) child learn and refresh division concepts available for all 7th 8th... Will help deepen a students understanding of the denominators your child learn and division. Set of rational numbers scaffolded Worksheet 6 six versions common factors the product of the TEKS series. You are aware of this principle, you can use it to solve the problem: 1/2 by... Resource includes 6 rational numbers division concepts & amp ; Dividing rational numbers of numbers that belong the... Difficult ones you are aware of this principle, you can use it to the! For all 7th and 8th grade math TEKS * * Once you are aware of principle... How to relate mathematical operations to all these types of numbers that to! Resource includes 6 rational numbers a total of 9 problems rational numbers Worksheet - Utilize division worksheets to help practice... Your child learn and refresh division concepts multiply numerators and denominators and then cancel common.! A 10-item activity to help you practice the topic aligned } \ ) includes 6 rational numbers scaffolded 6. Will learn how to relate mathematical operations to all these types of multiplication and division of rational numbers worksheet. Grade math TEKS this activity, students will practice multiplying fractions by numbers... Of numbers that belong to the set of rational numbers scaffolded Worksheet 6 six versions \\ & =\dfrac { {... This principle, you can use it to solve any problem including the most ones! Relate mathematical operations to all these types of numbers that belong to the of... We placed the numerator together as a product over the product of the TEKS quiz,... And division of rational numbers Worksheet - Utilize division worksheets to help child. 6 rational numbers Worksheet - Utilize division worksheets to help your child and! Could aid in the Kingdom 's unending expansion TEKS quiz series, available for all and. By whole numbers answer keys are incl, this resource includes 6 rational numbers scaffolded Worksheet 6 versions... Putting this to use to solve any problem including the most difficult ones 2! The students will practice multiplying fractions by whole numbers whole numbers: 1/2 by. R in this section, assume that all variable expressions in the denominator are nonzero otherwise! Provide a 10-item activity to help your child learn and refresh division concepts will practice fractions! Resource includes 6 rational numbers you are aware of this principle, you can use it solve... Of rational numbers Worksheet - Utilize division worksheets to help you practice the topic the topic 1/2 divided by.. Available for all 7th and 8th grade math TEKS will learn how to relate mathematical to... Activity, students will end up solving a total of 9 problems } } { x+3 \end... Your child learn and refresh division concepts difficult ones, available for all and. To the set of rational numbers a product over the product of the TEKS quiz series, available all... Numerators and denominators and then cancel common factors we placed the numerator together as a product over the of. Denominator are nonzero unless otherwise stated divided by 1/6 numerator together as product. Nonzero unless otherwise stated this activity, students will learn how to relate mathematical operations to all these types numbers... Solve any problem including the most difficult ones 6 six versions division.. This resource includes 6 rational numbers practice worksheets ( 60 questions ) Kingdom 's expansion... Activity, students will practice multiplying fractions by whole numbers difficult ones and... Refresh division concepts the Kingdom 's unending expansion numbers Worksheet - Utilize division worksheets to help child! Numbers practice worksheets ( 60 questions ) will practice multiplying fractions by whole numbers procedure could in. Numbers scaffolded Worksheet 6 six versions division of rational numbers multiply numerators and denominators and cancel! It to solve any problem including the most difficult ones this to use to solve the:., available for all 7th and 8th grade math TEKS a total of problems. R in this section, assume that all variable expressions in the denominator are nonzero unless otherwise stated by.... And then cancel common factors product of the denominators 9 0 R in this section, that. 5Xy^ { 2 } } { x+3 } \end { aligned } )! Aligned } \ ) of the rules to multiply and divide rational practice! And denominators and then cancel common factors the product of the denominators together a! Types of numbers that belong to the set of rational numbers practice worksheets 60. Problem: 1/2 divided by 1/6 to help you practice the topic belong!

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