PRE-ALGEBRA

PRE-ALGEBRA

Solving Equations by Multiplying Fractions (5-8)

PRE-ALGEBRA

Multiplicative Inverse: the reciprocal of a number

Rule: Inverse Property of Multiplication: the product of a number and its multiplicative inverse is 1

To isolate the variable in equations involving the multiplication of the variable by a fraction, undo the fraction from the variable side using the Division Property of Equality, which says divide both side by the fraction. Since dividing by a fraction means multiplying by its reciprocal, multiply both side by the reciprocal of the fraction using the Inverse Property of Multiplication.

Example:

What is a “multiplicative inverse”?

What is the “inverse property of multiplication”?

How do you solve equations in that involve multiplying fractions?

Solving Equations by Multiplying Fractions (5-8)

PRE-ALGEBRA

Solve 7y = .13

• (7y) = • Multiply each side by , the reciprocal of 7.13

17

17

17

7y = 13

y = Identify Property of Multiplication. 121

1 y = Inverse Property of Multiplication. 121

Solving Equations by Multiplying FractionsLESSON 5-8

Additional Examples

PRE-ALGEBRA

52

w = • Divide the common factors.1315

1

3

w = 2 Write as a mixed number.16

Solve w = .25

1315

• w = • Multiply each side by , the reciprocal of .25

52

52

52

25

1315

w = 25

1315

w = Simplify.13 6

Solving Equations by Multiplying FractionsLESSON 5-8

Additional Examples

PRE-ALGEBRA

Solve – c = .49

2027

– c = 49

2027

c = Divide common factors.27 • 420 • 9

13

15

= – Simplify.3 5

– – c = – Multiply each side by – , the

reciprocal of – .

49

2720

2027

2720

2720

2027

Solving Equations by Multiplying FractionsLESSON 5-8

Additional Examples

PRE-ALGEBRA

How many 2 -t trucks can you place on a rail car

that has a carrying capacity of 15 t?

12

Words times is

Let n = the number of trucks.

Equation 2 • n = 15

weight ofeach truck

the number of trucks

carrying capacity

12

Solving Equations by Multiplying FractionsLESSON 5-8

Additional Examples

PRE-ALGEBRA

(continued)

12 2 • n = 15

n = Divide common factors.2 • 155 • 1

3

1

n = 15 Write 2 as .52

52

12

• n = • 15 Multiply each side by , the reciprocal of .52

52

25

25

25

= 6 Simplify.

You can place 6 trucks on the rail car.

Solving Equations by Multiplying FractionsLESSON 5-8

Additional Examples

PRE-ALGEBRA

Solve m = 24. Check the solution.

24 = 24 The solution checks.

m = 32 Multiply.

34

m = 2434

1m = • Inverse Property of Multiplication 24 1

43

m = • Divide 24 and 3 by their GCD, 3. 24 1

43

8

1

(32) 24 Replace m with 32.34

34

• m = 24 • Multiply each side by , the multiplicative inverse of .

34

43

43

43

Check m = 24 Start with the original equation.34

Solving Equations by MultiplyingLESSON 5-8

Additional Examples

PRE-ALGEBRA

Mai Li worked 7 hours and earned $150. What

amount did she earn per hour?

12

15012

7

Words hours worked earnings per hour = amount earned

Let m = earnings per hour.

Equation m =

Solving Equations by MultiplyingLESSON 5-8

Additional Examples

PRE-ALGEBRA

(continued)

Mai Li earned $20 per hour.

m = • Divide 15 and 150 by their GCD, 15.215

15011

10

m = 20 Multiply.

7 m = 150 Write the equation.12

Solving Equations by MultiplyingLESSON 5-8

Additional Examples

m = Write 7 as an improper fraction. Write 150 as152

1501

12

150 1

.

• ( m) = • Multiply each side by the multiplicative inverse of .

152

215

215

1501

2 15 15

2

,

PRE-ALGEBRA

– g =

Solve each equation.

1. 2. 3. 15 = –3 m= b78

516

2532

58

613

514

45–

13–4

Lesson Quiz

Solving Equations by Multiplying FractionsLESSON 5-8