Learn to solve equations by multiplying and dividing fractions .

1. Learn to solve equations by multiplying and dividing fractions.

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

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

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

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

6. 3 3 3 __ 3 __ __ __ j÷ = 19 ÷ Divide both sides of the equation by . 4 4 4 4 3 4 4 3 4 __ __ __ __ __ j•= 19 • Multiply by , the reciprocal of . 4 3 3 4 3 4 __ j= 19 • 3 19 • 4 _____ j= 1 • 3 76 1 ___ __ j= , or 25 3 3 Check It Out: Example 1A Solve each equation. Write the answer in simplest form. 3 __ j= 19 4

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

8. 6y __ 7 6 __ 6 4 6y 6 __ __ __ __ 7 7 1 7 7 6 __ 7 4 6y 7 __ __ __ __ 7 6 1 6 7 28 2 __ __ 6 3 Check It Out: Example 1C Solve each equation. Write the answer in simplest form. = 4 Divide both sides by . ÷=÷ Multiply by the reciprocal of . •=• y = , or 4

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

10. 1 Understand the Problem • He makes of the recipe. • He uses 12 cups of powdered milk. 2 __ 3 Additional Example 2 Continued The answer will be the number of cups of powdered milk in the recipe. List the important information:

11. 2 Make a Plan 2 __ 12 = x 3 Additional Example 2 Continued 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.

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

13. 4 2 __ 3 2 ? __ 12 = 3 36 __ ? 12 = 3 ? 12 = 12 Additional Example 2 Continued Look Back Check 12 = x (18)‏ Substitute 18 for x. 12 Multiply and simplify. 1 18 is the solution.

14. 2 __ 5 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?

15. 1 Understand the Problem 2 __ 5 Check It Out: Example 2 Continued 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.

16. 2 Make a Plan 2 __ 8 = y 5 Check It Out: Example 2 Continued 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.

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

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