Solving algebraic eqn

Course 1

5-10Solving Fraction Equations: Multiplication and Division5-10 Solving Fraction Equations: Multiplication

and Division

Course 1

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Warm UpWarm Up

Course 1

5-10Solving Fraction Equations: Multiplication and Division

Warm UpSolve.

1. x – 5 = 17

2. 5x = 125

3. x + 12 = 86

4. 9x = 108

x = 22

x = 25

x = 74

x = 12

Course 1

5-10Solving Fraction Equations: 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

Course 1

5-10Solving Fraction Equations: Multiplication and Division

Learn to solve equations by multiplying and dividing fractions.

Course 1

5-10Solving Fraction Equations: Multiplication and Division

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

Remember!

Course 1

5-10Solving Fraction Equations: Multiplication and DivisionAdditional Example 1A: Solving Equations by

Multiplying and Dividing

Solve each equation. Write the answer in simplest form.

j = 25 35__

j ÷ = 25 ÷ 35__ 3

5__ 3

5__

j • = 25 • 35__ 5

3__ 5

3__

j = 25 • 51 • 3_____

j = 25 • 53__

j = , or 41125

3___ 2

3__

Divide both sides of the equation by .

35__

Multiply by , the reciprocal of .

35__5

3__

Course 1

5-10Solving Fraction Equations: Multiplication and Division

Additional Example 1B: Solving Equations by Multiplying and Dividing

Solve each equation. Write the answer in simplest form.

7x = 25__

7x1__ 2

5__ 1

7__1

7__• = •

x =

2 • 15 • 7____

x =

235__

Multiply both sides by the reciprocal of 7.

The answer is in simplest form.

Course 1

5-10Solving Fraction Equations: Multiplication and Division

Additional Example 1C: Solving Equations by Multiplying and Dividing

Solve each equation. Write the answer in simplest form.

= 65y8__

5y8__ 6

1__ 5

8__5

8__÷ = ÷

y = , or 9 485__

Divide both sides by .

58__

5y8__ 6

1__ 8

5__8

5__• = •

35__

58Multiply by the reciprocal of .

__

Course 1

5-10Solving Fraction Equations: Multiplication and Division

Check It Out: Example 1A

Solve each equation. Write the answer in simplest form.

j = 19 34__

j ÷ = 19 ÷ 34__ 3

4__ 3

4__

j • = 19 • __3

4__ 4

343__

j = 19 • 41 • 3_____

4j = 19 • 3__

76___ 13

j = , or 253

__

Divide both sides of the equation by .

34__

Multiply by , the reciprocal of .

34__4

3__

Course 1

5-10Solving Fraction Equations: Multiplication and Division

Check It Out: Example 1B

Solve each equation. Write the answer in simplest form.

3x = 17__

3x1__ 1

7__ 1

3__1

3__• = •

x =

1 • 17 • 3____

x =

121__

Multiply both sides by the reciprocal of 3.

The answer is in simplest form.

Course 1

5-10Solving Fraction Equations: Multiplication and Division

Check It Out: Example 1C

Solve each equation. Write the answer in simplest form.

= 46y7__

6y7__ 4

1__ 6

7__6

7__÷ = ÷

y = , or 4 286__

Divide both sides by .

Multiply by the reciprocal of .

67__

6y7__ 4

1__ 7

6__7

6__• = •

23__

67__

Course 1

5-10Solving Fraction Equations: Multiplication and Division

Additional Example 2: Problem Solving Application

23__

Dexter makes of a recipe, and he uses 12

cups of powdered milk. How many cups of

powdered milk are in the recipe?

Course 1

5-10Solving Fraction Equations: Multiplication and Division

Additional Example 2 Continued

11 Understand the Problem

The answer will be the number of cups of powdered milk in the recipe.

List the important information:

23__• He makes of the recipe.

• He uses 12 cups of powdered milk.

Course 1

5-10Solving Fraction Equations: Multiplication and Division

22 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.

23__12 = x

Additional Example 2 Continued

Course 1

5-10Solving Fraction Equations: Multiplication and Division

Solve33

23__12 = x

12 • = x •32__ 2

3__ 3

2__

121__ 3

2__• = x

6

118 = x

There are 18 cups of powdered milk in the recipe.

Multiply both sides by , the

reciprocal of .

32__

23__

Simplify. Then multiply.

Additional Example 2 Continued

Course 1

5-10Solving Fraction Equations: Multiplication and Division

Look Back44

Check 12 = x23__

23__12 =

? (18)

363__12 =

?

12 = 12?

Substitute 18 for x.

Multiply and simplify.

18 is the solution.

Additional Example 2 Continued

12

1

Course 1

5-10Solving Fraction Equations: Multiplication and Division

Check It Out: Example 2

25__Nick makes of a recipe, and he uses 8

cups of wheat flour. How many cups of

wheat flour are in the recipe?

Course 1

5-10Solving Fraction Equations: Multiplication and Division

Check It Out: Example 2 Continued

11 Understand the Problem

The answer will be the number of cups of wheat flour in the recipe.

25__

List the important information:

• He makes of the recipe.

• He uses 8 cups of wheat flour.

Course 1

5-10Solving Fraction Equations: Multiplication and Division

22 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.

25__8 = y

Check It Out: Example 2 Continued

Course 1

5-10Solving Fraction Equations: Multiplication and Division

Solve33

25__ 8 = y

8 • = y •52__ 2

5__ 5

2__

81__ 5

2__• = y

4

120 = y

There are 20 cups of wheat flour in the recipe.

Multiply both sides by , the

reciprocal of .

52__

25__

Simplify. Then multiply.

Check It Out: Example 2 Continued

Course 1

5-10Solving Fraction Equations: Multiplication and Division

Look Back44

Check 8 = y25__

25__ 8 =

? (20)

405__ 8 =

?

8 = 8?

Substitute 20 for y.

Multiply and simplify.

20 is the solution.

Check It Out: Example 2 Continued

8

1

Course 1

5-10Solving Fraction Equations: Multiplication and Division

Lesson QuizSolve 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?

18__ 1

4__

37__ y

7__

14__

x = 16124__x =

983__ 2

3__x = or 32 y = 63

12