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

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

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 = __ j ÷ = 25 ÷ 3 5 __ j = __ j = j = _____ j = __ j =, or ___ 2 3 __ Divide both sides of the equation by. 3 5 __ Multiply by, the reciprocal of. 3 5 __ 5 3

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 = x = ____ x = 2 35 __ Multiply both sides by the reciprocal of 7. The answer is in simplest form.

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 ÷ = ÷ y =, or __ Divide both sides by. 5 8 __ 5y5y = Multiply by the reciprocal of. __

5-7 Solving Fraction Equations: Multiplication and Division Check It Out: Example 1A Solve each equation. Write the answer in simplest form. j = __ j ÷ = 19 ÷ 3 4 __ j = 19 __ j = j = _____ 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

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 = x = ____ x = 1 21 __ Multiply both sides by the reciprocal of 3. The answer is in simplest form.

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 ÷ = ÷ y =, or __ Divide both sides by. Multiply by the reciprocal of. 6 7 __ 6y6y =

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?

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.

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

5-7 Solving Fraction Equations: Multiplication and Division Solve __ 12 = x 3 2 __ __ 3 2 = x = 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

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

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

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.

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

5-7 Solving Fraction Equations: Multiplication and Division Solve __ 8 = y 5 2 __ = y = 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

5-7 Solving Fraction Equations: Multiplication and Division Look Back 4 Check 8 = y 2 5 __ = ? (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