Multiplying Fractions and
3-6 Mixed Numbers
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
Multiplying Fractions and
3-6 Mixed Numbers
Warm Up
1
What is 2 of each of the following?
1. 24 12
3. 30 15
2. 16
4. 28
8
14
Multiplying Fractions and
3-6 Mixed Numbers
Learn to multiply fractions and mixed
numbers.
Multiplying Fractions and
3-6 Mixed Numbers
To multiply fractions, multiply the
numerators to find the product’s
numerator. Then multiply the
denominators to find the product’s
denominator.
Multiplying Fractions and
3-6 Mixed Numbers
Example 1: Multiplying Fractions
A. Multiply. Write the answer in simplest form.
–12 · 3
4
3 = – 12 · 3 Write –12 as a fraction.
–12 ·
4
1 4
3
12 · 3 Simplify.
=–
1 · 41
= – 9 = –9 Multiply numerators.
1
Multiply denominators.
Helpful Hint
The product of two positive proper fractions is less than either
fraction.
Multiplying Fractions and
3-6 Mixed Numbers
Example 1: Multiplying Fractions
B. Multiply. Write the answer in simplest form.
1 · 3
3 8
1 ·3 = 1 · 3
3 8 13· 8
= 1
8
1
Simplify.
Multiply numerators.
Multiply denominators.
Multiplying Fractions and
3-6 Mixed Numbers
Example 1: Multiplying Fractions
C. Multiply. Write the answer in simplest form.
3 · –1
5
4
3 · –1 = – 3 · 1
5· 4
4
5
=– 3
20
The signs are different, so
the answer will be negative.
Multiply numerators.
Multiply denominators.
Multiplying Fractions and
3-6 Mixed Numbers
Check It Out
D. Multiply. Write the answer in simplest form.
–16 · 1
4
1 = – 16 · 1 Write –16 as a fraction.
–16 ·
4
1 4
4
16 · 1 Simplify.
=–
1 · 41
= – 4 = –4 Multiply numerators.
1
Multiply denominators.
Multiplying Fractions and
3-6 Mixed Numbers
Check It Out
E. Multiply. Write the answer in simplest form.
1 · 6
6 9
1 ·6 = 1 · 6
6 9 16· 9
= 1
9
1
Simplify.
Multiply numerators.
Multiply denominators.
Multiplying Fractions and
3-6 Mixed Numbers
Check It Out
F. Multiply. Write the answer in simplest form.
–3 · 1
7
8
3 · 1
–3 · 1 = –
7
8
7· 8
=– 3
56
The signs are different, so
the answer will be negative.
Multiply numerators.
Multiply denominators.
Multiplying Fractions and
3-6 Mixed Numbers
Example 2: Multiplying Mixed Numbers
A. Multiply. Write the answer in simplest form.
2 · 12
5
3
2 ·12 = 2·5
5 3
3
5
= 2· 5
5 3
1
=2
3
Write the mixed number as an
improper fraction.
1
Simplify.
Multiply numerators.
Multiply denominators.
Multiplying Fractions and
3-6 Mixed Numbers
Example 2: Multiplying Mixed Numbers
B. Multiply. Write the answer in simplest form.
·21
41
7
5
41 · 2 1 = 21 · 15
Write the mixed numbers as
5
7
5 7
improper fractions.
3
3
21 · 15
Simplify.
= 5
7
1
1
or 9
= 9
1
Multiply numerators.
Multiply denominators.
Multiplying Fractions and
3-6 Mixed Numbers
Example 2: Multiplying Mixed Numbers
C. Multiply. Write the answer in simplest form.
2
2
63 · 4 5
6 2 · 4 2 = 20 · 22
3
5
3
5
4
= 20 · 22
3
51
= 88 or 29 1
3
3
Write the mixed numbers
as improper fractions.
Simplify.
Multiply numerators.
Multiply denominators.
Multiplying Fractions and
3-6 Mixed Numbers
Check It Out
D. Multiply. Write the answer in simplest form.
3 · 21
5
3
3 ·21 = 3·7
5 3
3
5
Write the mixed number as an
improper fraction.
13 7
=
·
Simplify.
5 31
= 7 or 12 Multiply numerators.
5
5 Multiply denominators.
Multiplying Fractions and
3-6 Mixed Numbers
Check It Out
E. Multiply. Write the answer in simplest form.
·11
33
3
6
33 · 1 1 = 21 ·
6
3
6
7
21 ·
= 6
3
4
3
2
4
3
1
Write the mixed numbers as
improper fractions.
Simplify.
2 Multiply numerators.
14
or
4
= 3
3 Multiply denominators.
Multiplying Fractions and
3-6 Mixed Numbers
Check It Out
F. Multiply. Write the answer in simplest form.
1
1
36 · 1 3
3 1 · 1 1 = 19 · 4
6
3
6
3
2
19
4
=
·
6
3
3
= 38 or 4 2
9
9
Write the mixed numbers
as improper fractions.
Simplify.
Multiply numerators.
Multiply denominators.
Multiplying Fractions and
3-6 Mixed Numbers
Multiplying Fractions and
3-6 Mixed Numbers
End Day #1
Multiplying Fractions and
3-6 Mixed Numbers
Day #2
Multiplying Fractions and
3-6 Mixed Numbers
Problem of the Day
At midnight Caitlin heard a forecaster say
that it would be cloudy for exactly 72 hours
and then would be sunny. Caitlin knew the
forecaster was wrong. Explain.
There are 24 hours in a day, so 72 hours
equals 3 days. In 3 days it would be
midnight again, not sunny.
Multiplying Fractions and
3-6 Mixed Numbers
Example 3: Transportation Application
In 2001, the car toll on the George Washington
Bridge was $6.00. In 1995 the toll was 2 of that
3
toll. What was the toll in 1995?
6 · 2 = 2+ 2 + 2 + 2 + 2 + 2
3
3 3 3 3 3 3
=
12
3
1 1
3 3
+
1 1
3 3
+
1 1
3 3
+
1 1
3 3
+
1 1
3 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
4
= 1
Simplify.
= $4.00
Divide 4 by 1 to write the fraction as a decimal.
1
1
1
1
The George Washington Bridge toll for a car was $4.00 in 1995.
Multiplying Fractions and
3-6 Mixed Numbers
Check It Out
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
111
444
+
111
444
+
111
444
+
111
444
111111111111
444444444444
3
= 1
Simplify.
= $3.00
Divide 3 by 1 to write the fraction as a decimal.
1
1
1
The fee to park in the parking garage was $3.00 in 2000.
Multiplying Fractions and
3-6 Mixed Numbers
Lesson Quizzes
Multiplying Fractions and
3-6 Mixed Numbers
Lesson Quiz: Part I
Multiply. Write each answer in simplest form.
1. 1 · 5
8 6
5
48
2. 5 5 · 1
6 2
35 or 2 11
12
12
3. 5 1 · 1 2
10 3
17 or 8 1
2
2
4. 3 · 4 2
16
3
7
8
Multiplying Fractions and
3-6 Mixed Numbers
Lesson Quiz: Part II
Multiply. Write the answer in simplest form.
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