PRE-ALGEBRA

Solving Equations by Multiplying Fractions (5-8)

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)

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

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

PRE-ALGEBRA Solve – c = – c = c = Divide common factors = – Simplify – – c = – Multiply each side by –, the reciprocal of – Solving Equations by Multiplying Fractions LESSON 5-8 Additional Examples

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

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

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

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

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

PRE-ALGEBRA – g = Solve each equation = –3 m = b – 1313 –4 Lesson Quiz Solving Equations by Multiplying Fractions LESSON 5-8