Solving Fraction Equations 5 7 Multiplication and Division

Solving Fraction Equations: 5 -7 Multiplication and Division Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

Solving Fraction Equations: 5 -7 Multiplication and Division Warm Up Solve. 1. x – 5 = 17 x = 22 2. 5 x = 125 x = 25 3. x + 12 = 86 x = 74 4. 9 x = 108 x = 12

Solving Fraction Equations: 5 -7 Multiplication and Division Problem of the Day Stephen forgot his locker number, but he remembered that the sum of the digits is 11 and that the digits are all odd numbers. The locker numbers are from 1 to 120. What is Stephen’s locker number? 119

Solving Fraction Equations: 5 -7 Multiplication and Division Learn to solve equations by multiplying and dividing fractions.

Solving Fraction Equations: 5 -7 Multiplication and Division Remember! Dividing by a number is the same as multiplying by its reciprocal.

Solving Fraction Equations: 5 -7 Multiplication and Division Additional Example 1 A: Solving Equations by Multiplying and Dividing Solve each equation. Write the answer in simplest form. 3 __ 5 j = 25 3 3 3 __ j ÷ __ = 25 ÷ __ 5 5 5 3 Divide both sides of the equation by __. 5 3 __ j • 5 3 5 Multiply by __, the reciprocal of __. 5 3 5 5 __ __ = 25 • 3 3 5 j = 25 • __ 3 25 • 5 j = _____ 1 • 3 j= 125 2 ___ , or 41 __ 3 3

Solving Fraction Equations: 5 -7 Multiplication and Division Additional Example 1 B: Solving Equations by Multiplying and Dividing Solve each equation. Write the answer in simplest form. 2 7 x = __ 5 1 2 7 x 1 __ • __ = __ • __ 7 5 1 7 Multiply both sides by the reciprocal of 7. 2 • 1 x = ____ 5 • 7 2 x = __ 35 The answer is in simplest form.

Solving Fraction Equations: 5 -7 Multiplication and Division Additional Example 1 C: Solving Equations by Multiplying and Dividing Solve each equation. Write the answer in simplest form. 5 y __ = 6 8 5 6 5 5 y __ __ ÷ __ = ÷ __ 8 1 8 8 5 __ Divide both sides by 8. 8 6 5 y 8 __ • __ = __ • __ 5 1 8 5 5 __ Multiply by the reciprocal of. 8 48 3 y = __ , or 9 __ 5 5

Solving Fraction Equations: 5 -7 Multiplication and Division Check It Out: Example 1 A Solve each equation. Write the answer in simplest form. 3 __ 4 j = 19 3 3 3 __ j ÷ __ = 19 ÷ __ 4 4 4 3 Divide both sides of the equation by __. 4 3 __ j • 4 3 4 Multiply by __, the reciprocal of __. 4 3 4 4 __ __ = 19 • 3 3 4 j = 19 • __ 3 19 • 4 j = _____ 1 • 3 j= 76 1 ___ , or 25 __ 3 3

Solving Fraction Equations: 5 -7 Multiplication and Division Check It Out: Example 1 B Solve each equation. Write the answer in simplest form. 1 3 x = __ 7 1 1 3 x 1 __ • __ = __ • __ 3 7 1 3 Multiply both sides by the reciprocal of 3. 1 • 1 x = ____ 7 • 3 1 x = __ 21 The answer is in simplest form.

Solving Fraction Equations: 5 -7 Multiplication and Division Check It Out: Example 1 C Solve each equation. Write the answer in simplest form. 6 y __ = 4 7 6 4 6 y 6 __ ÷ __ = __ ÷ __ 7 1 7 7 6 __ Divide both sides by 7. 7 4 6 y 7 __ • __ = __ • __ 6 1 7 6 6 __ Multiply by the reciprocal of. 7 28 2 y = __ , or 4 __ 6 3

Solving Fraction Equations: 5 -7 Multiplication and Division Additional Example 2: Problem Solving Application __ 2 Dexter makes 3 of a recipe, and he uses 12 cups of powdered milk. How many cups of powdered milk are in the recipe?

Solving Fraction Equations: 5 -7 Multiplication and Division Additional Example 2 Continued 1 Understand the Problem The answer will be the number of cups of powdered milk in the recipe. List the important information: 2 • He makes __ of the recipe. 3 • He uses 12 cups of powdered milk.

Solving Fraction Equations: 5 -7 Multiplication and Division Additional Example 2 Continued 2 Make a Plan You can write and solve an equation. Let x represent the number of cups in the recipe. He uses 12 cups, which is two-thirds of the amount of the recipe. 2 x 12 = __ 3

Solving Fraction Equations: 5 -7 Multiplication and Division Additional Example 2 Continued 3 Solve 12 6 12 __ 1 2 x 12 = __ 3 3 __ Multiply both sides by , the 3 2 3 __ __ __ 2 • = x • 2 2 3 2 reciprocal of __. 3 3 • __ = x Simplify. Then multiply. 2 1 18 = x There are 18 cups of powdered milk in the recipe.

Solving Fraction Equations: 5 -7 Multiplication and Division Additional Example 2 Continued 4 Look Back 2 Check 12 = __ x 3 ? 2 12 = __ (18) 3 12 ? 36 __ 12 = 3 1 ? 12 = 12 Substitute 18 for x. Multiply and simplify. 18 is the solution.

Solving Fraction Equations: 5 -7 Multiplication and Division Check It Out: Example 2 2 of a recipe, and he Nick makes __ 5 uses 8 cups of wheat flour. How many cups of wheat flour are in the recipe?

Solving Fraction Equations: 5 -7 Multiplication and Division Check It Out: Example 2 Continued 1 Understand the Problem The answer will be the number of cups of wheat flour in the recipe. List the important information: 2 of the recipe. • He makes __ 5 • He uses 8 cups of wheat flour.

Solving Fraction Equations: 5 -7 Multiplication and Division Check It Out: Example 2 Continued 2 Make a Plan You can write and solve an equation. Let y represent the number of cups in the recipe. He uses 8 cups, which is two-fifths of the amount of the recipe. 2 __ 8= y 5

Solving Fraction Equations: 5 -7 Multiplication and Division Check It Out: Example 2 Continued 3 Solve 2 8 = __ y 5 5 2 5 8 • __ = __y • __ 2 5 2 48 5 __ • __ =y 1 20 = y 5 Multiply both sides by __ , the 2 2 __ reciprocal of. 5 Simplify. Then multiply. There are 20 cups of wheat flour in the recipe.

Solving Fraction Equations: 5 -7 Multiplication and Division Check It Out: Example 2 Continued 4 Look Back 2 Check 8 = __ y 5 2 __ (20) 8= 5 8 ? 40 __ 8= 5 1 ? ? 8=8 Substitute 20 for y. Multiply and simplify. 20 is the solution.

Solving Fraction Equations: 5 -7 Multiplication and Division Lesson Quizzes Standard Lesson Quiz for Student Response Systems

Solving Fraction Equations: 5 -7 Multiplication and Division Lesson Quiz Solve each equation. Write the answer in simplest form. 1 1 1. 3 x = __ 8 24 1 x=4 2. __ x = 16 4 3 __ __ y =9 2 4. __ 3. x = 14 x = 98 or 32 __ 7 7 3 3 y = 63 1 __ 5. Rebecca used 3 pt of paint to paint of the 4 trim in her bedroom. How many pints will Rebecca use for the trim in the entire bedroom? 12

Solving Fraction Equations: 5 -7 Multiplication and Division Lesson Quiz for Student Response Systems 1. Solve the equation and identify the answer in the simplest form. A. C. B. D.

Solving Fraction Equations: 5 -7 Multiplication and Division Lesson Quiz for Student Response Systems 2. Solve the equation and identify the answer in the simplest form. A. x = 5 C. x = 25 B. x = 10 D. x = 50

Solving Fraction Equations: 5 -7 Multiplication and Division Lesson Quiz for Student Response Systems 3. Solve the equation and identify the answer in the simplest form. A. C. B. D.

Solving Fraction Equations: 5 -7 Multiplication and Division Lesson Quiz for Student Response Systems 4. Solve the equation and identify the answer in the simplest form. A. y = 72 C. B. y = 17 D.

Solving Fraction Equations: 5 -7 Multiplication and Division Lesson Quiz for Student Response Systems 5. Lou is learning to paint pottery. He used 3 pints of paint to paint of a pot. How many pints will Lou use for the entire pot? A. C. 3 pt B. D. 7 pt