4-4
Multiplying Fractions and Mixed Numbers
Preview
Warm Up
California Standards
Lesson Presentation
Holt CA Course 1
4-4
Multiplying Fractions and Mixed Numbers
Warm Up
1
What is 2 of each of the following?
1. 24 12
3. 30 15
Holt CA Course 1
2. 16
4. 28
8
14
4-4
Multiplying Fractions and Mixed Numbers
California
Standards
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
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
Additional Example 1: Transportation Application
In 2001, the car toll on the George Washington
Bridge was $6.00. In 1995 the toll was 2 of that toll.
3
What was the toll in 1995?
Think: How much is 2 of 6? Use multiplication to find a
3
fraction of a number.
1 1
1 1
1 1
1
1 1
6  2 = 2+ 2 + 2 + 2 + 2 + 2
+
+
+
+
3 3
3 3
3 3
3
3 3
3
3 3 3 3 3 3
12
= 3
4
= 1
1
3
+
1 1
3 3
1 1 1 1 1 1 1 1 1 1 1 1
3 3 3 3 3 3 3 3 3 3 3 3
1
1
1
1
= $4.00
The George Washington Bridge toll for a car was $4.00 in 1995.
Holt CA Course 1
4-4
Multiplying Fractions and Mixed Numbers
Check It Out! Example 1
In 2002, the fee to park in a parking garage was
3
$4. In 2000 the fee was 4 of the fee in 2002.
What was the fee in 2000?
43 =3 + 3 + 3 +3
4
4
4
4
4
=
12
4
3
= 1
111
444
+
111
444
+
111
444
+
111
444
111111111111
444444444444
1
1
1
= $3.00
The fee to park in the parking garage was $3.00 in 2000.
Holt CA Course 1
4-4
Multiplying Fractions and Mixed Numbers
Holt CA Course 1
4-4
Multiplying Fractions and Mixed Numbers
Additional Example 2A: Multiplying Fractions
Multiply. Write the answer in simplest form.
12  3
4
12  3 = 12  3 Write 12 as a fraction.
4
1 4
3
12  3 Divide a numerator and
=
1  41 denominator by their GCD, 4.
= 9 = 9 Multiply numerators.
1
Multiply denominators.
Remember!
Use the GCD of a numerator and denominator to simplify
before multiplying.
Holt CA Course 1
4-4
Multiplying Fractions and Mixed Numbers
Additional Example 2B: Multiplying Fractions
Multiply. Write the answer in simplest form.
31
5 4
3 1 =
5 4
=
Holt CA Course 1
3  1
5 4
3
20
Multiply numerators.
Multiply denominators.
4-4
Multiplying Fractions and Mixed Numbers
Additional Example 2C: Multiplying Fractions
Multiply. Write the answer in simplest form.
1 3
3 8
1 3 = 1  3
3 8 13 8
= 1
8
Holt CA Course 1
1
Divide a numerator and
denominator by their GCD, 3.
Multiply numerators.
Multiply denominators.
4-4
Multiplying Fractions and Mixed Numbers
Check It Out! Example 2A
Multiply. Write the answer in simplest form.
16  1
4
Write 16 as a fraction.
16  1 = 16  1
4
1 4
4
Divide a numerator and
16  1
=
1  41 denominator by their GCD, 4.
Multiply numerators.
= 4 =4
1
Multiply denominators.
Holt CA Course 1
4-4
Multiplying Fractions and Mixed Numbers
Check It Out! Example 2B
Multiply. Write the answer in simplest form.
3  1
7 8
3 1= 3  1
7 8
7 8
=
Holt CA Course 1
3
56
Multiply numerators.
Multiply denominators.
4-4
Multiplying Fractions and Mixed Numbers
Check It Out! Example 2C
Multiply. Write the answer in simplest form.
1 6
6 9
1 6 = 1  6
6 9 16 9
= 1
9
Holt CA Course 1
1
Divide a numerator and
denominator by their GCD, 6.
Multiply numerators.
Multiply denominators.
4-4
Multiplying Fractions and Mixed Numbers
Additional Example 3A: Multiplying Mixed Numbers
Multiply. Write the answer in simplest form.
2  12
5
3
2 12 = 25
5 3
3
5
Write the mixed number as
an improper fraction.
1 Divide a numerator and
= 2 5
denominator by their GCD, 5.
5 3
1
Multiply numerators.
=2
3
Multiply denominators.
Holt CA Course 1
4-4
Multiplying Fractions and Mixed Numbers
Additional Example 3B: Multiplying Mixed Numbers
Multiply. Write the answer in simplest form.
1
41

2
7
5
41  2 1 = 21  15
5
7
5 7
Write mixed numbers as
improper fractions.
3
3
21  15
Divide numerators and
= 5
denominators by their GCDs, 5
7
1 and 7.
1
or 9
= 9
1
Holt CA Course 1
Multiply numerators.
Multiply denominators.
4-4
Multiplying Fractions and Mixed Numbers
Additional Example 3C: Multiplying Mixed Numbers
Multiply. Write the answer in simplest form.
2
2
6 3  45
6 2  4 2 = 20  22
3
5
3
5
Holt CA Course 1
Write mixed numbers as
improper fractions.
4
= 20  22
3
51
Divide a numerator and
denominator by their GCD, 5.
= 88 or 29 1
3
3
Multiply numerators.
Multiply denominators.
4-4
Multiplying Fractions and Mixed Numbers
Check It Out! Example 3A
Multiply. Write the answer in simplest form.
3 21
5
3
3 2 1 = 3 7
5 3
3
5
Holt CA Course 1
Write the mixed number as an
improper fraction.
13 7

=
5 31
Divide a numerator and
denominator by the GCD, 3.
= 7 or 12
5
5
Multiply numerators.
Multiply denominators.
4-4
Multiplying Fractions and Mixed Numbers
Check It Out! Example 3B
Multiply. Write the answer in simplest form.
1
33

1
3
5
3 3  1 1 = 18  4
5
3
5 3
6
18  4
= 5
3
1
4
24
or
4
= 5
5
Holt CA Course 1
Write mixed numbers as
improper fractions.
Divide a numerator and
denominator by their GCD, 3.
Multiply numerators.
Multiply denominators.
4-4
Multiplying Fractions and Mixed Numbers
Check It Out! Example 3C
Multiply. Write the answer in simplest form.
1
1
36 1 3
3 1  1 1 = 19  4
6
3
6
3
= 19  4
6
3
3
2
= 38 or 4 2
9
9
Holt CA Course 1
Write mixed numbers as
improper fractions.
Divide a numerator and
denominator by their
GCD, 2.
Multiply numerators.
Multiply denominators.
4-4
Multiplying Fractions and Mixed Numbers
Lesson Quiz
Multiply. Write each answer in simplest terms.
1.
3.
5
48
2.
17 or 8 1 4.
2
2
35 or 2 11
12
12
7
8
5. A recipe for clam chowder calls for 2 41 pounds of
butter. If you prepare one-half of the recipe, how
much butter do you need?
1 1 pounds
8
Holt CA Course 1