Basic Mathematics for College Students

This example suggests the following procedure.

Writing an Improper Fraction as a Mixed Number

To write an improper fraction as a mixed number:

1. Divide the numerator by the denominator to obtain the whole-number part.


2. The remainder over the divisor is the fractional part.

260 Chapter 3 Fractions and Mixed Numbers

Self Check 3

Write each improper fraction

as a mixed number or a whole

number:

a. b.

c. d.

Now TryProblems 31, 35, 39, and 43



10

3

51

3

50

26

31

7

EXAMPLE (^3) Write each improper fraction as a mixed number or a whole
number: a. b. c. d.
Strategy We will divide the numerator by the denominator and write the
remainder over the divisor.
WHY A fraction bar indicates division.
Solution
a.To write as a mixed number, divide 29 by 6:
d
d
Thus,.
b.To write as a mixed number, divide 40 by 16:
Thus,. Simplify the fractional part:.
c.For , divide 84 by 3:
d
Thus,.
Since the remainder is 0, the improper fraction represents a whole number.
d.To write as a mixed number, ignore the – sign, and use the method for the
positive improper fraction. Once that procedure is completed, write a – sign
in front of the result.
Thus,.

9

5

 1

4

5

1

5  9

 5

4

9

5

 95

84

3

 28

28

3  84

 6

24

 24

0

84

3

8

16 

8

1

2  81 

1

2

40

16

 2

8

16

 2

1

2

2

(^16)  40
 32
8
40
16

29

6

 4

5

6

The whole-number part is 4.

Write the remainder 5 over the

divisor 6 to get the fractional part.

4

6  29

 24

5

29

6

9

5

84

3

40

16

29

6

Graph fractions and mixed numbers on a number line.

In Chapters 1 and 2, we graphed whole numbers and integers on a number line.

Fractions and mixed numbers can also be graphed on a number line.

4