LES
SO
N
Mixed Numbers and
Improper Fractions
Goal: Compare and order fractions and mixed numbers.
Vocabulary
Mixed number:
A mixed number has a whole number part and a
fraction part.
Proper fraction:
A fraction whose numerator is less than its
denominator is called a proper fraction.
Improper fraction:
A fraction is called an improper fraction if
its numerator is greater than or equal to its
denominator.
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.
The mixed number
256 is read
5
6
Numbers 2 2p65
6
"two and five sixths."
EXAMPLE
1
17
6
Writing Improper Fractions
2
5
1
9
Write (a) 4 and (b) 3 as improper fractions.
2
a. 4 5
4p52
5
22
5
Lesson 4.6
1
b. 3 9
3p91
9
28
9
Mixed Numbers and Improper Fractions
| 87
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 .
2
17
Numbers → 17 5 3 R2 , or 35
5
2
EXAMPLE
Need help
with dividing whole
numbers?
See page 744
of your textbook.
Writing Mixed Numbers
34
5
Write as a mixed number.
4
6 R4 , or 6 5
53
4
You can write a remainder as a
fraction:
30
remainder
denominator .
4
34
5
4
5
Answer: 6 Guided Practice
1
3
1. 2
Write the number as an improper fraction.
3
4
7
3
2
5
3. 3
2. 7
4. 5
7
1
15
4
27
5
Write the improper fraction as a mixed number.
17
11
19
5
5. 6
11
1
88
|
Chapter 4
Notetaking Guide
22
4
6. 27
8
7. 4
5
3
8. 1
2
5
3
8
3
3
EXAMPLE
Comparing Mixed Numbers and Fractions
23
8
2
3
Compare and 2.
2
3
8
3
2
3
1. Write 2 as an improper fraction: 2 .
23
8
2. Rewrite and using the least common denominator of 24 .
8
3
23
8
23 3
83
88
69
8
3
38
24
69
24
64
24
23
8
2
3. Compare the fractions: > , so EXAMPLE
4
64
24
> 23.
Ordering Mixed Numbers and Fractions
County Fair The county fair holds a pie eating contest. Participants are to
eat as many pies as they can in 10 minutes. Joe ate 4 14 pies, Conan ate
5 pies, David ate 252 pies, and Jonathan ate 4 12 pies. Order the amounts
of pie the contestants ate from least to greatest.
Solution
5
The denominators are 4, 1 because 5 1
, 5, and 2. Write the
numbers as improper fractions using the least common denominator of 20 .
17
1
4 4 4
22
5
22 4
54
17 5
45
85
20
5
5 1 9
88
1
4 2 20
2
5 20
1 20
9 10
2 10
100
20
90
20
Answer: From least to greatest, the amounts of pie the contestants ate are
1 22
1
4 , , 4 , and 5 .
4 5
2
Lesson 4.6
Mixed Numbers and Improper Fractions
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