Page 1 of 5
Mixed Numbers and
Improper Fractions
BEFORE
Now
WHY?
You compared and ordered
fractions.
You’ll compare and order
fractions and mixed numbers.
So you can compare long jump
distances, as in Ex. 40.
Word Watch
mixed number, p. 185
proper fraction, p. 185
improper fraction, p. 185
A mixed number has a whole
number part and a fraction part.
3
4
Model A
3
4
2
The number 2 is a mixed number.
3
4
Model A represents 2 .
A fraction whose numerator is less
than its denominator is called a
proper fraction . A fraction is called
an improper fraction if its
numerator is greater than or equal to
its denominator. The mixed number
3
4
2 Model B
8
4
3
4
3
4
2 can be written as an improper
fraction by dividing each of the
2 wholes into 4 equal sized parts,
then counting the number of fourths.
This is shown in Model B.
11
4
Writing Mixed Numbers as Improper Fractions
Words To write a mixed number as an improper fraction,
multiply the whole number part and the denominator, add
the numerator, and write the sum over the denominator.
3
2p43
11
Numbers 2 4
4
4
with
Reading
The mixed number
3
4
2 is read “two and
three fourths.”
EXAMPLE
1
Writing Improper Fractions
5
6
3
8
Write (a) 3 and (b) 2 as improper fractions.
Solution
5
3p65
23
a. 3 6 6 6
Lesson 4.6
3
2p83
19
b. 2 8 8 8
Mixed Numbers and Improper Fractions
185
Page 2 of 5
Writing Improper Fractions as Mixed Numbers
Words To write an improper fraction as a mixed number,
divide the numerator by the denominator and write any
remainder as a fraction.
7
Numbers 3
2
EXAMPLE
with
Review
1
3
7 3 2 R1, or 2 Writing Mixed Numbers
23
6
Write as a mixed number.
Need help with dividing
whole numbers?
See p. 690.
5
3 R5, or 3
6
3
62
18
5
23
6
You can write a remainder
remainder
as a fraction: .
denom
inator
5
6
ANSWER 3 Your turn now
Write the number as an improper fraction.
2
1. 1
5
1
3. 4 2
2. 2
3
4. 3 4
Write the improper fraction as a mixed number.
17
5. 11
13
6. 6
EXAMPLE
3
17
7. 3
15
8. 7
Comparing Mixed Numbers and Fractions
17
1
6
4
1
1
9
1 Write 2 as an improper fraction: 2 .
4
4
4
Compare and 2 .
17
9
2 Rewrite 6 and 4 using the least common denominator of 12.
17
17 2
34
6
62
12
9
93
27
4
43
12
34
27
17
1
3 Compare the fractions: 12 > 12, so 6 > 2 4.
186
Chapter 4
Number Patterns and Fractions
Page 3 of 5
EXAMPLE
Health
4
Ordering Mixed Numbers and Fractions
Fitness The Presidential Physical Fitness Award involves a flexibility test
called the V-sit reach. The distances, in inches, that four students were
able to reach are listed below. Order the distances from least to greatest.
5
8
3
3
17
4
1
2
3
Solution
3
1
The denominators are 8, 1 because 3 , 4, and 2. Write the numbers
as improper fractions using the least common denominator of 8.
■
5
8
Fitness
Another fitness test of the
Presidential Physical Fitness
Award involves curl-ups.
Boys age 12 must complete
50 curl-ups in one minute.
In how many seconds must
one curl-up be done?
29
8
38
18
3
1
24
8
3 3 17
17 2
34
4
42
8
3 1
2
7
2
74
24
1
2
28
8
5
8
17
4
ANSWER From least to greatest, the distances are 3, 3 , 3 , and .
INTERNET
Exercises
eWorkbook Plus
CLASSZONE.COM
More Practice, p. 708
Getting Ready to Practice
Vocabulary Tell whether the number is a mixed number, a proper
fraction, or an improper fraction.
12
1. 12
12
2. 17
3
3. 8 8
21
4. 20
5. Find the Error Describe and
correct the error in writing
2
5 as an improper fraction.
3
2
(5 3) p 2
16
5 3
3
3
12
6. Write as a mixed number.
7
Copy and complete the statement using <, >, or .
3
1
7. _?_ 3 2
2
8
2
8. _?_ 2 3
3
22
1
9. _?_ 7 3
4
29
3
10. _?_ 6 5
5
11. Walking to School You walk to and from school five days a week. You
live a quarter mile away from the school. Write the total distance you
walk in a week as an improper fraction and as a mixed number.
Lesson 4.6
Mixed Numbers and Improper Fractions
187
Page 4 of 5
Practice and Problem Solving
with
Example
1
2
3
4
Homework
Exercises
14–23
24–33
36–38, 40
36–38, 40
Online Resources
CLASSZONE.COM
• More Examples
• eTutorial Plus
Write an improper fraction and a mixed number to describe the model.
12.
13.
Write the mixed number as an improper fraction.
1
14. 5 3
2
15. 4 7
4
16. 2 9
3
17. 3 11
1
18. 4 8
4
19. 3 15
2
20. 10 5
3
21. 11 8
6
22. 8 7
5
23. 4 16
Write the improper fraction as a mixed number.
27
24. 5
45
25. 8
67
26. 8
24
27. 11
95
28. 6
99
29. 4
149
30. 10
58
31. 21
107
32. 13
159
33. 16
34. Critical Thinking Which number is greater, an improper fraction or
a proper fraction? Explain your reasoning.
35. Bubbles You are filling 5 bottles with bubble solution. To fill one bottle,
1
you need 1 cups of water. You can find only a quarter-cup measure.
4
How many quarter-cups of water do you need?
Order the numbers from least to greatest.
22 2 22 20
36. , 2 , , 2 2
3 11 33
40 49 22 1
37. , , , 1 40 42 20 9
1
38 20
38. 7 , 7, , 5
5 7
1 3 2
1
39. Writing How could you order 3 , 3 , 3 , and 3 from least to greatest
4 4 7
8
without writing them as improper fractions? Explain your reasoning.
7
40. Long Jumps The top four long jumps at a track meet are 18 feet,
12
2
3
1
18 feet, 18 feet, and 18 feet. Order the numbers from least to
3
4
3
greatest. What is the distance of the longest jump?
Challenge Order the numbers from least to greatest.
4 11 21 19 28
41. 9 , 9 , 9 , , 9 20 40 2 3
188
Chapter 4
Number Patterns and Fractions
3 45
2 34 147
42. 11 , , , 11 , 11 4
7 3 13
Page 5 of 5
Mixed Review
43. The table shows the number of households,
in millions, with cable television for the years
from 1996 through 2000. Use the information
in the table to graph the data in an
appropriate data display. Explain your
choice. (Lesson 3.6)
Year
Households
1996
63
1997
64
1998
66
1999
67
2000
69
Order the fractions from least to greatest. (Lesson 4.5)
11 17 7 3
44. , , , 18 24 12 4
13 2 11 7
45. , , , 25 5 20 15
15 7 3 5
46. , , , 28 14 8 7
Basic Skills Find the sum or difference.
47.
48.
624
359
2008
1333
49.
3258
1699
Test-Taking Practice
50. Multiple Choice Write thirteen sevenths numerically.
INTERNET
State Test Practice
3
17
7
13
A. CLASSZONE.COM
13
7
B. C. D. 137
51. Multiple Choice Which mixed number is equivalent to its paired
improper fraction?
1 35
7 7
GG. .5 15, 51
F. 5 , 2 22
5 5
H. 3 , 10 43
11 11
I. 3 , Missing Numerators
Copy and complete the fractions using 2, 3, 4, 6, and 8.
Each number should be chosen so that the fractions are
in order from least to greatest, and each number can be
used only once.
?
24
?
12
?
16
?
20
?
18
Lesson 4.6
Mixed Numbers and Improper Fractions
189