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PRE-ALGEBRA

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Solving Equations by Multiplying Fractions (5-8)

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PRE-ALGEBRA Multiplicative Inverse: the reciprocal of a number Rule: Inverse Property of Multiplication: the product of a number and its multiplicative inverse is 1 To isolate the variable in equations involving the multiplication of the variable by a fraction, undo the fraction from the variable side using the Division Property of Equality, which says divide both side by the fraction. Since dividing by a fraction means multiplying by its reciprocal, multiply both side by the reciprocal of the fraction using the Inverse Property of Multiplication. Example: What is a “multiplicative inverse”? What is the “inverse property of multiplication”? How do you solve equations in that involve multiplying fractions? Solving Equations by Multiplying Fractions (5-8)

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PRE-ALGEBRA Solve 7y =. 1313 (7y) = Multiply each side by, the reciprocal of 7. 1313 1717 1717 1717 7y = 1313 y = Identify Property of Multiplication. 1 21 1 y = Inverse Property of Multiplication. 1 21 Solving Equations by Multiplying Fractions LESSON 5-8 Additional Examples

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PRE-ALGEBRA 5252 w = Divide the common factors. 13 15 1 3 w = 2 Write as a mixed number. 1616 Solve w =. 2525 13 15 w = Multiply each side by, the reciprocal of. 2525 5252 5252 5252 2525 13 15 w = 2525 13 15 w = Simplify. 13 6 Solving Equations by Multiplying Fractions LESSON 5-8 Additional Examples

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PRE-ALGEBRA Solve – c =. 4949 20 27 – c = 4949 20 27 c = Divide common factors. 27 4 20 9 1 3 1 5 = – Simplify. 3535 – – c = – Multiply each side by –, the reciprocal of –. 4949 27 20 27 20 27 20 27 Solving Equations by Multiplying Fractions LESSON 5-8 Additional Examples

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PRE-ALGEBRA How many 2 -t trucks can you place on a rail car that has a carrying capacity of 15 t? 1212 Words times is Let n = the number of trucks. Equation 2 n = 15 weight of each truck the number of trucks carrying capacity 1212 Solving Equations by Multiplying Fractions LESSON 5-8 Additional Examples

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PRE-ALGEBRA (continued) 1212 2 n = 15 n = Divide common factors. 2 15 5 1 3 1 n = 15Write 2 as. 5252 5252 1212 n = 15Multiply each side by, the reciprocal of. 5252 5252 2525 2525 2525 = 6 Simplify. You can place 6 trucks on the rail car. Solving Equations by Multiplying Fractions LESSON 5-8 Additional Examples

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PRE-ALGEBRA Solve m = 24. Check the solution. 24 = 24 The solution checks. m = 32Multiply. 3434 m = 24 3434 1m = Inverse Property of Multiplication 24 1 4343 m = Divide 24 and 3 by their GCD, 3. 24 1 4343 8 1 (32) 24Replace m with 32. 3434 3434 m = 24 Multiply each side by, the multiplicative inverse of. 3434 4343 4343 4343 Check m = 24Start with the original equation. 3434 Solving Equations by Multiplying LESSON 5-8 Additional Examples

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PRE-ALGEBRA Mai Li worked 7 hours and earned $150. What amount did she earn per hour? 1212 150 1212 7 Words hours worked earnings per hour=amount earned Let m = earnings per hour. Equation m= Solving Equations by Multiplying LESSON 5-8 Additional Examples

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PRE-ALGEBRA (continued) Mai Li earned $20 per hour. m = Divide 15 and 150 by their GCD, 15. 2 15 150 1 1 10 m = 20Multiply. 7 m = 150 Write the equation. 1212 Solving Equations by Multiplying LESSON 5-8 Additional Examples m = Write 7 as an improper fraction. Write 150 as 15 2 150 1 1212 150 1. ( m) = Multiply each side by the multiplicative inverse of. 15 2 15 2 15 150 1 2 15 2,

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PRE-ALGEBRA – g = Solve each equation. 1.2.3.15 = –3 m = b 7878 5 16 25 32 5858 6 13 5 14 4545 – 1313 –4 Lesson Quiz Solving Equations by Multiplying Fractions LESSON 5-8

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