5-10 Solving Fraction Equations: Multiplication and Division Warm Up Course 1 Warm Up Problem of the Day Lesson Presentation

Warm Up Solve. 1. x – 5 = 17 2. 5x = 125 3. x + 12 = 86 4. 9x = 108 x = 22 x = 25 x = 74 x = 12

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

Learn to solve equations by multiplying and dividing fractions.

Dividing by a number is the same as multiplying by its reciprocal. Remember!

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

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

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

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

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

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

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

Understand the Problem 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 3 __ He makes of the recipe. He uses 12 cups of powdered milk.

Additional Example 2 Continued 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 3 __ 12 = x

Additional Example 2 Continued Solve 3 2 3 __ 12 = x 3 2 __ Multiply both sides by , the reciprocal of . 3 2 __ 2 3 __ 3 2 __ 12 • = x • 2 3 __ 6 12 1 __ 3 2 __ • = x Simplify. Then multiply. 1 18 = x There are 18 cups of powdered milk in the recipe.

Additional Example 2 Continued 4 Look Back 2 3 __ Check 12 = x 12 = ? 2 3 __ (18) Substitute 18 for x. 12 = ? 36 3 __ 12 Multiply and simplify. 1 12 = 12 ? 18 is the solution.

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

Understand the Problem 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: He makes of the recipe. He uses 8 cups of wheat flour. 2 5 __

Check It Out: Example 2 Continued 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 5 __ 8 = y

Check It Out: Example 2 Continued Solve 3 2 5 __ 8 = y 5 2 __ Multiply both sides by , the reciprocal of . 5 2 __ 2 5 __ 5 2 __ 8 • = y • 2 5 __ 4 8 1 __ 5 2 __ • = y Simplify. Then multiply. 1 20 = y There are 20 cups of wheat flour in the recipe.

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

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