Holt CA Course 1

4-4 Multiplying Fractions and Mixed Numbers

NS2.1 Solve problems involving addition, subtraction, multiplication, and division of positive fractions and explain why a particular operation was used for a given situation.Also covered: NS2.4, NS2.2

California Standards

Holt CA Course 1

4-4 Multiplying Fractions and Mixed Numbers

Recall that multiplication can be written as repeated addition. For example, 3 5 = 5 + 5 + 5 = 15. You can use repeated addition to multiply a whole number by a fraction.

Holt CA Course 1

4-4 Multiplying Fractions and Mixed Numbers

Transportation ApplicationIn 2001, the car toll on the George Washington Bridge was $6.00. In 1995 the toll was 2

3of that toll.

What was the toll in 1995?

23

6 = 23

+ 23

23

23

23

23

+ + + + +

= 123

=41

= $4.00The George Washington Bridge toll for a car was $4.00 in 1995.

+ + + +13

13

13

13

13

13

13

13

13

13

13

13

13

13

13

13

13

13

13

13

13

13

13

13

1 1 1 1

Think: How much is of 6? Use multiplication to find a fraction of a number.

23

Holt CA Course 1

4-4 Multiplying Fractions and Mixed Numbers

In 2002, the fee to park in a parking garage was

$4. In 2000 the fee was of the fee in 2002.

What was the fee in 2000?

34

4 = 34

+ 34

34

34

+ +

= 124

=31

= $3.00

The fee to park in the parking garage was $3.00 in 2000.

34

+14

14

14

14

14

14 + +1

414

14

14

14

14

14

14

14

14

14

14

14

14

14

14

14

14

1 1 1

Holt CA Course 1

4-4 Multiplying Fractions and Mixed Numbers

Holt CA Course 1

4-4 Multiplying Fractions and Mixed Numbers

Multiply. Write the answer in simplest form.

Teacher Example 1A: Multiplying Fractions

12 34

12 34

= 121

34

Write 12 as a fraction.

= 12 31 4

3

1

Divide a numerator and denominator by their GCD, 4.

91

= = 9 Multiply numerators.Multiply denominators.

Use the GCD of a numerator and denominator to simplify before multiplying.

Remember!

Holt CA Course 1

4-4 Multiplying Fractions and Mixed Numbers

Multiply. Write the answer in simplest form.

Teacher Example 1B: Multiplying Fractions

Multiply numerators.Multiply denominators.

413

5

35

14

=35

1 4

= 3 20

Holt CA Course 1

4-4 Multiplying Fractions and Mixed Numbers

Multiply. Write the answer in simplest form.

Teacher Example 1C: Multiplying Fractions

8

=Divide a numerator and denominator by their GCD, 3.

Multiply numerators.Multiply denominators.

313

1

1

= 18

38

13

13

3 8

Holt CA Course 1

4-4 Multiplying Fractions and Mixed Numbers

Multiply. Write the answer in simplest form.

Practice 1A:

16 14

16 14

= 161

14

Write 16 as a fraction.

= 16 11 4

4

1

Divide a numerator and denominator by their GCD, 4.

41

= = 4 Multiply numerators.Multiply denominators.

Holt CA Course 1

4-4 Multiplying Fractions and Mixed Numbers

Multiply. Write the answer in simplest form.

Practice 1B:

8

Multiply numerators.Multiply denominators.

137

18

37 =

37

1 8

= 3 56

Holt CA Course 1

4-4 Multiplying Fractions and Mixed Numbers

Multiply. Write the answer in simplest form.

Student Practice 1C:

9

= Divide a numerator and denominator by their GCD, 6.

Multiply numerators.Multiply denominators.

616

1

1

= 19

69

16

16

6 9

Holt CA Course 1

4-4 Multiplying Fractions and Mixed Numbers

Multiply. Write the answer in simplest form.

Teacher Example 2A: Multiplying Mixed Numbers

Write the mixed number as an improper fraction.

Divide a numerator and denominator by their GCD, 5.

Multiply numerators.Multiply denominators.

2

25

1 23 = 2

5 53

= 25

53

1

1

5 1 2

3

= 23

Holt CA Course 1

4-4 Multiplying Fractions and Mixed Numbers

Multiply. Write the answer in simplest form.

Teacher Example 2B: Multiplying Mixed Numbers

Write mixed numbers as improper fractions.

Divide numerators and denominators by their GCDs, 5 and 7.

4 15 2 1

7

415

17

= 215

157

= 5

71521

1

3

1

3

= 91

or 9 Multiply numerators.Multiply denominators.

2

Holt CA Course 1

4-4 Multiplying Fractions and Mixed Numbers

Multiply. Write the answer in simplest form.

Teacher Example 2C: Multiplying Mixed Numbers

Multiply numerators.Multiply denominators.

23 4

256

23 4 2

56 = 20

3 22

5

203

225

=4

1

Write mixed numbers as improper fractions.

Divide a numerator and denominator by their GCD, 5.

3= 88 or 291

3

Holt CA Course 1

4-4 Multiplying Fractions and Mixed Numbers

Multiply. Write the answer in simplest form.

Student Practice 2A:

Write the mixed number as an improper fraction.

Divide a numerator and denominator by the GCD, 3.

Multiply numerators.Multiply denominators.

3

35

2 13 = 3

5 73

= 35

73 1

1

5 2 1

3

= or 175

25

Holt CA Course 1

4-4 Multiplying Fractions and Mixed Numbers

Multiply. Write the answer in simplest form.

Student Practice 2B:

Write mixed numbers as improper fractions.

Divide a numerator and denominator by their GCD, 3.

3 35 1 1

3

335

113

= 185

43

= 5

3418

1

6

Multiply numerators.Multiply denominators.= 24

5or 44

5

Holt CA Course 1

4-4 Multiplying Fractions and Mixed Numbers

Multiply. Write the answer in simplest form.

Multiply numerators.Multiply denominators.

16 1 1

33

16 1 1

33 = 19

6 4

3

196

43

=3

2

Write mixed numbers as improper fractions.

Divide a numerator and denominator by their GCD, 2.

9= 38 or 4 2

9

Student Practice 2C: