1. 5-7 Solving Fraction Equations: Multiplication and Division Learn to solve equations by multiplying and dividing fractions.

2. 5-7 Solving Fraction Equations: Multiplication and Division Dividing by a number is the same as multiplying by its reciprocal. Remember!

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

4. 5-7 Solving Fraction Equations: Multiplication and Division Additional Example 1B: Solving Equations by Multiplying and Dividing Solve each equation. Write the answer in simplest form. 7x = 2 5 __ 7x7x 1 2 5 1 7 1 7 = x = 2 1 5 7 ____ x = 2 35 __ Multiply both sides by the reciprocal of 7. The answer is in simplest form.

5. 5-7 Solving Fraction Equations: Multiplication and Division Additional Example 1C: Solving Equations by Multiplying and Dividing Solve each equation. Write the answer in simplest form. = 6 5y5y 8 __ 5y5y 8 6 1 5 8 5 8 ÷ = ÷ y =, or 9 48 5 __ Divide both sides by. 5 8 __ 5y5y 8 6 1 8 5 8 5 = 3 5 5 8 Multiply by the reciprocal of. __

6. 5-7 Solving Fraction Equations: Multiplication and Division Check It Out: Example 1A Solve each equation. Write the answer in simplest form. j = 19 3 4 __ j ÷ = 19 ÷ 3 4 __ 3 4 3 4 j = 19 __ 3 4 4 3 4 3 j = j = 19 4 1 3 _____ 4 j = 19 3 __ 76 ___ 1 3 j =, or 25 3 __ Divide both sides of the equation by. 3 4 __ Multiply by, the reciprocal of. 3 4 __ 4 3

7. 5-7 Solving Fraction Equations: Multiplication and Division Check It Out: Example 1B Solve each equation. Write the answer in simplest form. 3x = 1 7 __ 3x3x 1 1 7 1 3 1 3 = x = 1 7 3 ____ x = 1 21 __ Multiply both sides by the reciprocal of 3. The answer is in simplest form.

8. 5-7 Solving Fraction Equations: Multiplication and Division Check It Out: Example 1C Solve each equation. Write the answer in simplest form. = 4 6y6y 7 __ 6y6y 7 4 1 6 7 6 7 ÷ = ÷ y =, or 4 28 6 __ Divide both sides by. Multiply by the reciprocal of. 6 7 __ 6y6y 7 4 1 7 6 7 6 = 2 3 6 7

9. 5-7 Solving Fraction Equations: Multiplication and Division Additional Example 2: Problem Solving Application 2 3 __ Dexter makes of a recipe, and he uses 12 cups of powdered milk. How many cups of powdered milk are in the recipe?

10. 5-7 Solving Fraction Equations: 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 3 __ He makes of the recipe. He uses 12 cups of powdered milk.

11. 5-7 Solving Fraction Equations: Multiplication and Division 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 3 __ 12 = x Additional Example 2 Continued

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

13. 5-7 Solving Fraction Equations: Multiplication and Division Look Back 4 Check 12 = x 2 3 __ 2 3 12 = ? (18) ‏ 36 3 __ 12 = ? 12 = 12 ? Substitute 18 for x. Multiply and simplify. 18 is the solution. Additional Example 2 Continued 12 1

14. 5-7 Solving Fraction Equations: Multiplication and Division Check It Out: Example 2 2 5 __ Nick makes of a recipe, and he uses 8 cups of wheat flour. How many cups of wheat flour are in the recipe?

15. 5-7 Solving Fraction Equations: 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. 2 5 __ List the important information: He makes of the recipe. He uses 8 cups of wheat flour.

16. 5-7 Solving Fraction Equations: Multiplication and Division 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 5 __ 8 = y Check It Out: Example 2 Continued

17. 5-7 Solving Fraction Equations: Multiplication and Division Solve 3 2 5 __ 8 = y 5 2 __ 2 5 5 2 8 1 5 2 = y 4 1 20 = y There are 20 cups of wheat flour in the recipe. Multiply both sides by, the reciprocal of. 5 2 __ 2 5 Simplify. Then multiply. Check It Out: Example 2 Continued

18. 5-7 Solving Fraction Equations: Multiplication and Division Look Back 4 Check 8 = y 2 5 __ 2 5 8 = ? (20) ‏ 40 5 __ 8 = ? 8 = 8 ? Substitute 20 for y. Multiply and simplify. 20 is the solution. Check It Out: Example 2 Continued 8 1