Course 2 3-10 Multiplying Fractions and Mixed Numbers 3-10 Multiplying Fractions and Mixed Numbers Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation
Course 2
3-10Multiplying Fractions and Mixed Numbers3-10 Multiplying Fractions and Mixed
Numbers
Course 2
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
Course 2
3-10Multiplying Fractions and Mixed Numbers
Warm Up
What is of each of the following?
1. 24 2. 16
3. 30 4. 28
12 8
15
12
14
Course 2
3-10Multiplying Fractions and 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.
Course 2
3-10Multiplying Fractions and Mixed Numbers
Learn to multiply fractions and mixed numbers.
Course 2
3-10Multiplying Fractions and Mixed Numbers
The San Francisco-Oakland Bay Bridge, which opened in 1936,is a toll bridge used by drivers traveling between the two cities. In 1939 , the toll for a car crossing the
bridge was of the toll in 2005. 215
To find the toll in 1939, you would need to multiply the toll in 2005 by a fraction. See Example 1 in your textbook.
Course 2
3-10Multiplying Fractions and Mixed Numbers
In 2001, the car toll on the George Washington Bridge was $6.00. In 1995 the toll was
Additional Example 1: Transportation Application
23
of that toll. What was the toll in 1995?
23
6 · = 23
+ 23
23
23
23
23
+ + + + +
= 123
=41
Simplify.
= $4.00 Divide 4 by 1 to write the fraction as a decimal.
The 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
Course 2
3-10Multiplying 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?
Check It Out: Example 1
34
4 · = 34
+ 34
34
34
+ +
= 124
=31
Simplify.
= $3.00 Divide 3 by 1 to write the fraction as a decimal.
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
Course 2
3-10Multiplying Fractions and Mixed Numbers
To multiply fractions, multiply the numerators to find the product’snumerator. Then multiply the denominators to find the product’sdenominator.
Course 2
3-10Multiplying Fractions and Mixed Numbers
Multiply. Write the answer in simplest form.
Additional Example 2A: Multiplying Fractions
–12 · 34
–12 · 34
= – 121
· 34
Write –12 as a fraction.
= – 12 · 31 · 4
3
1Simplify.
91
= – = –9 Multiply numerators.Multiply denominators.
You can write any integer as a fraction with a denominator of 1.
Remember!
Course 2
3-10Multiplying Fractions and Mixed Numbers
Multiply. Write the answer in simplest form.
Additional Example 2B: Multiplying Fractions
· 8
= Simplify.
Multiply numerators.Multiply denominators.
313
1
1
= 18
38
·13
13
· 3 8·
Course 2
3-10Multiplying Fractions and Mixed Numbers
Multiply. Write the answer in simplest form.
Additional Example 2C: Multiplying Fractions
· 4
The signs are different, so the answer will be negative.
Multiply numerators.Multiply denominators.
135
–
·35
14
– =35
· 1 4·
–
= 3 20
–
Course 2
3-10Multiplying Fractions and Mixed Numbers
Multiply. Write the answer in simplest form.
Check It Out: Example 2A
–16 · 14
–16 · 14
= – 161
· 14
Write –16 as a fraction.
= – 16 · 11 · 4
4
1Simplify.
41
= – = –4 Multiply numerators.Multiply denominators.
Course 2
3-10Multiplying Fractions and Mixed Numbers
Multiply. Write the answer in simplest form.
Check It Out: Example 2B
· 9
= Simplify.
Multiply numerators.Multiply denominators.
616
1
1
= 19
69
·16
16
· 6 9·
Course 2
3-10Multiplying Fractions and Mixed Numbers
Multiply. Write the answer in simplest form.
Check It Out: Example 2C
· 8
The signs are different, so the answer will be negative.
Multiply numerators.Multiply denominators.
137
–
18
·37
– =37
· 1 8·
–
= 3 56
–
Course 2
3-10Multiplying Fractions and Mixed Numbers
Multiply. Write the answer in simplest form.
Additional Example 3A: Multiplying Mixed Numbers
Write the mixed number as an improper fraction.
Simplify.
Multiply numerators.Multiply denominators.
2
25
· 1 23 = 2
5· 53
= 25
· 53
1
1
5· 1 2
3
= 23
Course 2
3-10Multiplying Fractions and Mixed Numbers
Multiply. Write the answer in simplest form.
Additional Example 3B: Multiplying Mixed Numbers
Write the mixed numbers as improper fractions.
Simplify.
4 15
· 2 17
415
· 17
= 215
·157
= 5·
71521
1
3
1
3
= 91
or 9 Multiply numerators.Multiply denominators.
2
Course 2
3-10Multiplying Fractions and Mixed Numbers
Multiply. Write the answer in simplest form.
Additional Example 3C: Multiplying Mixed Numbers
Multiply numerators.Multiply denominators.
23 · 4 2
56
23 · 4 2
56 = 20
3· 22
5
203
· 225
=4
1
Write the mixed numbers as improper fractions.
Simplify.
3= 88 or 291
3
Course 2
3-10Multiplying Fractions and Mixed Numbers
Multiply. Write the answer in simplest form.
Check It Out: Example 3A
Write the mixed number as an improper fraction.
Simplify.
Multiply numerators.Multiply denominators.
3
35
· 2 13 = 3
5· 73
= 35
· 73 1
1
5· 2 1
3
= or 175
25
Course 2
3-10Multiplying Fractions and Mixed Numbers
Multiply. Write the answer in simplest form.
Check It Out: Example 3B
Write the mixed numbers as improper fractions.
Simplify.
3 36
· 1 13
336
· 13
= 216
· 43
= 6·
3421
1
7
3
2
Multiply numerators.Multiply denominators.
1
= 143
or 423
Course 2
3-10Multiplying 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 the mixed numbers as improper fractions.
Simplify.
9= 38 or 4 2
9
Check It Out: Example 3C
Course 2
3-10Multiplying Fractions and Mixed Numbers
Lesson Quiz: Part I
Multiply. Write each answer in simplest terms.
1. 18
· 56
2. 5 56
· 12
3. 5 110
·123
4. 316
· 4 23
78
3512
or 1112
2
17 2
12
or 8
548
Course 2
3-10Multiplying Fractions and Mixed Numbers
Lesson Quiz: Part II
Multiply. Write the answer in simplest terms.
5. A recipe for clam chowder calls for 2 14 pounds of
butter. If you prepare one-half of the recipe, how
much butter do you need?
118
pounds