Download Multiplying Fractions and Mixed Numbers

Page 1 of 4
Multiplying Fractions
and Mixed Numbers
BEFORE
Now
WHY?
You added and subtracted
fractions and mixed numbers.
You’ll multiply fractions and
mixed numbers.
So you can determine the
height of a horse, as in Ex. 10.
In the Real World
Word Watch
Review Words
greatest common factor
(GCF), p. 164
mixed number, p. 185
improper fraction, p. 185
Ice Cream Neapolitan ice cream is
made up of one third chocolate, one
third vanilla, and one third strawberry.
How many gallons of strawberry ice cream
are in a half gallon container?
To find a fraction of an amount, you multiply.
1
3
1
2
1
3
1
2
For the problem above, you need to find of , or p .
Multiplying Fractions
Words The product of two or more fractions is equal to
the product of the numerators over the product of the
denominators.
3
1 3
Numbers p 40
5 8
EXAMPLE
1
a c
apc
Algebra p b d
bpd
(b, d 0)
Multiplying Fractions
1
3
1
2
To find the amount of strawberry ice cream described above, find p .
1 1
1p1
p 3 2
3p2
1
6
Use rule for multiplying fractions.
Multiply.
1
ANSWER A half gallon container has gallon of strawberry ice cream.
6
Your turn now
2 4
1. p 3 5
216
Chapter 5
Fraction Operations
Find the product. Simplify if possible.
1 7
2. p 6 9
5 1
3. p 7 2
3 3
4. p 4 10
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Dividing Out Common Factors When multiplying fractions, you
can divide out common factors from the product’s numerator and
denominator so that the product will be in simplest form.
EXAMPLE
2
Multiplying Whole Numbers and Fractions
Election The winner for class president got
with
Notetaking
If you don’t understand
the process of dividing
out common factors, write
a question down in your
notebook and discuss the
question with a friend or
teacher. Then write down
what you learn.
3
of the vote. If 200 students voted,
5
how many students voted for the winner?
Solution
3
3
200
200 5
5
1
3 200
151
200
1
Write 200 as .
40
Use rule for multiplying
fractions. Divide out GCF of 200 and 5.
120
1
, or 120
Multiply.
ANSWER There were 120 students who voted for the winner.
Multiplying Mixed Numbers When multiplying mixed numbers, you
should first rewrite them as improper fractions. Then use the rule
for multiplying fractions.
EXAMPLE
1
4
3
2
3
Multiplying Mixed Numbers
21
4
14
3
5 4 7
21 14
43
7
1
2
49
2
1
2
3
5. 12 8
2
3
Use rule for multiplying fractions. Divide out
GCF of 21 and 3 and GCF of 14 and 4.
Multiply.
24 Your turn now
1
4
Write 5 and 4 as improper fractions.
Write as a mixed number.
Find the product. Simplify if possible.
2
6. 6
3
Lesson 5.3
3
1
7. 2 3 4
6
4
1
8. 4 1 5
9
Multiplying Fractions and Mixed Numbers
217
Page 3 of 4
INTERNET
Exercises
eWorkbook Plus
CLASSZONE.COM
More Practice, p. 709
Getting Ready to Practice
1. Vocabulary Copy and complete: When multiplying two mixed
numbers, you first write them as _?_.
Find the product. Simplify if possible.
1
3
2. 4
4
3
5
3. 7
6
1
4. 4
3
5
5. 12
6
2
6. 5 11
3
7. 8 4
1
1
8. 1 5 2
2
2
2
9. 1 4 5
7
10. Horses Trainers measure horses in hands, the distance across an
1
adult’s palm. The average height of a horse is 15 hands. If a hand
2
1
is about foot, about how tall is an average horse in feet?
3
Practice and Problem Solving
with
Example
1
2
3
Homework
Exercises
12–23
12–24
12–23, 33
Online Resources
CLASSZONE.COM
• More Examples
• eTutorial Plus
1 1
11. Mental Math Explain how you can use mental math to find 1 p .
2 2
Find the product.
1
1
12. 10
12
2
1
13. 5
9
1
3
14. 8
4
1
15. 6
3
1
16. 5 5
1
17. 2
6
1
18. 50
4
2
1
19. 4 11
8
4
1
20. 1 9
8
7
1
21. 3 2 10
3
5
4
22. 8 5 11
5
1
2
23. 7 4 2
5
24. Water Cooler A water cooler contains 5 gallons of water. If you
3
drink gallon for each of the next 6 days, how many gallons will
5
be left in water cooler at the end of the sixth day?
Algebra Evaluate the expression when x 3 and y 6.
3
25. x
4
1 1
5
26. p 4 x
6
1
27. 3 y
5
1 2
28. p y 5
Estimation Estimate the product by rounding each factor to the
nearest whole number.
9
7
29. 1 10
9
218
Chapter 5
Fraction Operations
1
11
30. 3 5
13
7
2
31. 1 2 8
5
1
6
32. 5 1 4
7
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33. Stained Glass Windows The Darwin D. Martin house, built by Frank
Lloyd Wright, has a rectangular stained glass window with a length of
Art
1
2
1
4
41 feet and a width of 26 feet. What is the area of the window?
Critical Thinking Copy and complete the statement using always,
sometimes, or never.
34. Multiplying a mixed number by a proper fraction _?_ results in
a number greater than 1.
35. The product of two proper fractions is _?_ equal to 1.
Challenge Order the values of the expressions from least to
3
4
greatest when s and t 6.
1
1
36. 2 p t, 2 p s, 2t
4
3
1
37. st, 3s, s
2
1
1
38. s, 2s, t
3
8
Mixed Review
Copy and complete the statement using <, >, or . (Lesson 4.5)
■
Stained Glass Windows
Frank Lloyd Wright
(1867–1959) was an
architect who designed
decorative windows for more
than half of his buildings.
From 1885 to 1923, Wright
designed 4365 stained glass
windows for 97 houses.
Estimate how many windows
were in a typical house.
1
5
39. _?_ 4
6
9
1
40. _?_ 30
2
7
11
41. _?_ 48
12
Find the sum or difference. (Lesson 5.2)
1
1
42. 6 2 3
4
1
4
43. 5 2 3
5
7
2
44. 3 2 18
9
Basic Skills Estimate the quotient.
45. 77 19
46. 38 4
47. 197 24
Test-Taking Practice
INTERNET
State Test Practice
CLASSZONE.COM
48. Multiple Choice Which of the following numbers, when multiplied by
1
1
4 , results in a number greater than 4 ?
3
3
7
1
1
A. 0
B. C. D. 1
10
4
3
49. Short Response Jen wrote a book report that is 4 pages long. It took
3
her hour to write each page. She also spent 1 hour proofreading
4
the report. How much time, in all, did she spend on the report? Write
and evaluate an expression to describe the situation. Explain how you
got your answer.
Lesson 5.3
Multiplying Fractions and Mixed Numbers
219