4-7 multiplying fractions and mixed numbers course 2 warm up warm up problem of the day problem of...
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4-7 Multiplying Fractions and Mixed Numbers
Course 2
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
Warm Up
1. What is
2. What is
3. What is
12
815
12 of 24?12 of 16?12 of 30?
4. What is 14 of 28? 7
Course 2
4-7 Multiplying Fractions and Mixed Numbers
Problem of the Day
Caitlin was watching television. In a weather forecast at midnight the forecaster indicated that it would be cloudy for exactly 72 hours and then would be sunny. Caitlin called the station to tell the forecaster he was wrong. How did she know?
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
4-7 Multiplying 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 1977 , the toll for a car crossing the
bridge was of the toll in 2001.38
To find the toll in 1977, you will need to multiply the toll in 2001 by a fraction.
Course 2
4-7 Multiplying 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 the toll in 2001. What was the toll in 1995?
23
6 · = 23
+ 23
23
23
23
23
+ + + + +
= 123
=41
Simplify.
= $4.00 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
4-7 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?
Try This: Example 1
34
4 · = 34
+ 34
34
34
+ +
= 124
=31
Simplify.
= $3.00 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
4-7 Multiplying 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
4-7 Multiplying Fractions and Mixed Numbers
Multiply. Write the answer in simplest form.
Additional Example 2A: Multiplying Fractions
A. –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
4-7 Multiplying Fractions and Mixed Numbers
Multiply. Write the answer in simplest form.
Additional Example 2B: Multiplying Fractions
B. · 8
= Simplify.
Multiply numerators.Multiply denominators.
313
1
1
= 18
38
·13
13
· 3 8·
Course 2
4-7 Multiplying Fractions and Mixed Numbers
Multiply. Write the answer in simplest form.
Additional Example 2C: Multiplying Fractions
C. · 5
The signs are different, so the answer will be negative.
Multiply numerators.Multiply denominators.
423
–
45
·23
– =23
· 4 5·
–
= 8 15
–
Course 2
4-7 Multiplying Fractions and Mixed Numbers
Multiply. Write the answer in simplest form.
Try This: Example 2A
A. –16 · 14
–16 · 14
= – 161
· 14
Write –16 as a fraction.
= – 16 · 11 · 4
4
1Simplify.
41
= – = –4 Multiply numerators.Multiply denominators.
Course 2
4-7 Multiplying Fractions and Mixed Numbers
Multiply. Write the answer in simplest form.
Try This: Example 2B
B. · 9
= Simplify.
Multiply numerators.Multiply denominators.
616
1
1
= 19
69
·16
16
· 6 9·
Course 2
4-7 Multiplying Fractions and Mixed Numbers
Multiply. Write the answer in simplest form.
Try This: Example 2C
C. · 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
4-7 Multiplying 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.
A. 2
25
· 1 23 = 2
5· 53
= 25
· 53
1
1
5· 1 2
3
= 23
Course 2
4-7 Multiplying 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.
B. 4 15
· 2 17
415
· 17
= 215
·157
= 5·
71521
1
3
1
3
= 91
or 9 Multiply numerators.Multiply denominators.
2
Course 2
4-7 Multiplying Fractions and Mixed Numbers
Multiply. Write the answer in simplest form.
Additional Example 3C: Multiplying Mixed Numbers
Multiply numerators.Multiply denominators.
C. 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
4-7 Multiplying Fractions and Mixed Numbers
Multiply. Write the answer in simplest form.
Try This: Example 3A
Write the mixed number as an improper fraction.
Simplify.
Multiply numerators.Multiply denominators.
A. 3
35
· 2 13 = 3
5· 73
= 35
· 73 1
1
5· 2 1
3
= or 175
Course 2
4-7 Multiplying Fractions and Mixed Numbers
25
Multiply. Write the answer in simplest form.
Try This: Example 3B
Write the mixed numbers as improper fractions.
Simplify.
B. 3 36
· 1 13
336
· 13
= 216
· 43
= 6·
3421
1
7
3
2
Multiply numerators.Multiply denominators.
1
= 143
or 423
Course 2
4-7 Multiplying Fractions and Mixed Numbers
Multiply. Write the answer in simplest form.
Try This: Example 3C
Multiply numerators.Multiply denominators.
C. 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
Course 2
4-7 Multiplying Fractions and Mixed Numbers
Lesson Quiz: Part 1
Multiply. Write each answer in simplest terms.
1. 18
· 56
2. 5 56 · 1
2
3. 5 110
·123
4. 316
· 4 23
78
3512
or 1112
2
17 2
12
or 8
548
Course 2
4-7 Multiplying Fractions and Mixed Numbers