Download Mixed Numbers and Improper Fractions

Page 1 of 5
Mixed Numbers and
Improper Fractions
BEFORE
Now
WHY?
You wrote equivalent fractions.
You’ll rewrite mixed numbers
and improper fractions.
So you can compare lengths, such as
the pole vault records in Ex. 36.
Measuring Inches You can use a ruler to measure lengths to the
nearest half, fourth, eighth, or sixteenth of an inch.
Word Watch
The length of the line segment
mixed number, p. 244
improper fraction, p. 244
proper fraction, p. 245
5
8
21
8
is 2 inches, or inches.
5
8
The number 2 , read as “two and five eighths,” is a mixed number. A
mixed number is the sum of a whole number part and a fraction part.
21
8
An improper fraction , such as , is any fraction in which the
numerator is greater than or equal to the denominator.
EXAMPLE
1
Measuring to a Fraction of an Inch
Industrial Arts You need to measure a piece of wood for a birdhouse.
Write the length as a mixed number and as an improper fraction.
Solution
3
4
First write the length as a mixed number: 3 inches.
15
4
Then count fourths to write the length as an improper fraction: inches.
3
4
There are 15 fourths in 3 .
Your turn now
15
1. in.
2
244
Chapter 5
Number Patterns and Fractions
Draw a line segment that has the given length.
1
2. 6 in.
4
Page 2 of 5
Rewriting Mixed Numbers In the activity on page 243, you may
have seen that 1 whole can be written in different forms. You can use
these forms of 1 to help you write mixed numbers as improper fractions.
1
1
2
2
tch Out!
Wa
3
3
1 1 EXAMPLE
2
4
4
1 5
5
1 1 Rewriting Mixed Numbers
3
5
Write 4 as an improper fraction.
In Example 2,
don’t forget to add the
3
fraction part, , after you
5
write the whole part as
a fraction.
3
5
20 3
5
1 whole , so 4 wholes , or .
23
5
Simplify the numerator.
45
5
5
5
4 20
5
Rewriting Improper Fractions You can also write an improper
fraction as a mixed number. First divide the numerator by the
denominator, and then put the remainder over the denominator. Make
sure that the fraction part is a proper fraction , which is a fraction in
which the numerator is less than the denominator.
EXAMPLE
3
Rewriting Improper Fractions
16
3
Write as a mixed number.
1 Divide 16 by 3.
5 R1
31
6
15
1
1
3
2
3. 3 3
1
still remains.
3
1
3
5 5 2 Write the mixed number.
Your turn now
After you divide,
Write the mixed number as an improper fraction.
1
4. 2 4
5
5. 4 6
Write the improper fraction as a mixed number.
22
6. 5
34
7. 13
Lesson 5.6
41
8. 12
Mixed Numbers and Improper Fractions
245
Page 3 of 5
Comparing Numbers To compare and order mixed numbers and
improper fractions, begin by writing them all in the same form.
Sports
EXAMPLE
4
Ordering Numbers
5
8
3
4
Baseball Bats The widths of three baseball bats are 2 , 2 , and
9
inches. Order the widths from least to greatest.
4
Solution
1 Write all of the widths as improper fractions.
5
8
16 5
8
21
8
3
4
2 83
4
11
4
9
4
2 2 Rewrite all of the widths using the LCD, 8.
■
Baseball bats
11
11 2
22
4
42
8
21
8
Baseball bats come in many
different weights. To find out
which bat size is best for you,
divide your height, in inches,
by 3. Then add 6. This is the
weight, in ounces, of a
baseball bat that is
appropriate for you. What is
the best bat weight for you?
9
92
18
4
42
8
3 Compare the fractions.
18
8
21
8
21
8
22
8
9
4
5
8
5
8
9
4
5
8
3
4
ANSWER The widths, from least to greatest, are , 2 , and 2 inches.
INTERNET
Exercises
eWorkbook Plus
CLASSZONE.COM
More Practice, p. 712
Getting Ready to Practice
1. Vocabulary Explain what it means for a fraction to be an
improper fraction.
Copy and complete the statement.
?
1
2. 6 2
2
?
1
3. 3 4
4
?
17
4. 5 3
3
?
11
5. 2 4
4
Copy and complete the statement with <, >, or .
7
1
6. _?_ 1 4
4
246
Chapter 5
3
4
Because < and < , you know that < 2 and 2 < 2 .
Number Patterns and Fractions
2
11
7. 3 _?_ 3
3
2
28
8. 5 _?_ 5
5
4
20
9. 2 _?_ 7
7
Page 4 of 5
Practice and Problem Solving
with
Example
1
2
3
4
Homework
Exercises
10–12
13–20, 32–35
21–28
29–31
Measurement Use a ruler to measure the candle to the end of its wick.
Write the answer as a mixed number and as an improper fraction.
10.
11.
11
12. Draw a line segment that has a length of inches.
4
Online Resources
CLASSZONE.COM
• More Examples
• eTutorial Plus
Write the mixed number as an improper fraction.
1
13. 4 2
5
14. 1 8
2
15. 3 5
3
16. 5 4
2
17. 7 3
9
18. 1 10
1
19. 10 2
1
20. 12 4
Write the improper fraction as a mixed number.
8
21. 3
25
22. 6
18
23. 5
15
24. 4
13
25. 2
22
26. 3
12
27. 7
33
28. 4
Order the numbers from least to greatest.
7 3
29. , 2 , 3
2 4
23 19 1
30. , , 4 5 4
2
41 17 1
31. 5, , , 5 8 3
6
Write 1 as a fraction using the given denominator.
32. 4
33. 6
34. 10
35. 14
36. Pole Vaulting The pole vault records for four different schools are
shown in the table. Which school’s record is the highest?
School
Pole vault
height (feet)
Oakmont
Chester
49
3
16 3
8
Central
Perry
33
2
16 9
16
Critical Thinking Find a mixed number that is between the numbers.
3 11
37. 1 , 5 5
9
38. , 5
2
27
39. 3, 8
4 29
40. 5 , 9 5
41. Challenge Your friend is thinking of an improper fraction that is more
1
than 2 and less than 2 . The sum of the numerator and the
4
denominator is 19. What is your friend’s number?
Lesson 5.6
Mixed Numbers and Improper Fractions
247
Page 5 of 5
Mixed Review
Evaluate the expression. (Lesson 1.5)
42. 20 x, when x 2
43. x 2, when x 21
44. 15 x 4, when x 3
45. 3x y, when x 4 and y 6
Write the decimal in words. (Lesson 3.1)
46. 14.1
47. 23.5
48. 64.92
49. 78.15
Basic Skills Round the number to the place value of the red digit.
50. 8701
51. 9900
52. 2457
53. 4391
Test-Taking Practice
INTERNET
State Test Practice
CLASSZONE.COM
17
54. Multiple Choice Which mixed number is equivalent to ?
5
2
1
1
2
B. 2 C. 3 D. 3 A. 1 5
5
5
5
5
55. Multiple Choice A jewelry box is 4 inches wide. Write this mixed
8
number as an improper fraction.
20
8
F. inches
32
8
G. inches
What Does it Say?
To find the saying below, write the improper fractions as mixed
numbers. Find the mixed number below the number line and write
the corresponding letter in the blank above the improper fraction.
248
Chapter 5
Number Patterns and Fractions
37
8
H. inches
37
5
I. inches