Basic Mathematics for College Students

Multiply and divide mixed numbers.

We will use the same procedures for multiplying and dividing mixed numbers as those
that were used in Sections 3.2 and 3.3 to multiply and divide fractions. However, we
must write the mixed numbers as improper fractions before we actually multiply or
divide.

Multiplying and Dividing Mixed Numbers

To multiply or divide mixed numbers, first change the mixed numbers to

improper fractions. Then perform the multiplication or division of the fractions.

Write the result as a mixed number or a whole number in simplest form.

The sign rules for multiplying and dividing integers also hold for multiplying and
dividing mixed numbers.

5

3.5 Multiplying and Dividing Mixed Numbers 261

Self Check 4

Graph and on a

number line.

Now TryProblem 47

− 3 − 2 − 10123

9

(^4)
3
 5 ,
2
 1 3 ,
7
8 ,
EXAMPLE 4
Graph , , , and on a number line.
Strategy We will locate the position of each fraction and mixed number on the
number line and draw a bold dot.
WHY To graph a numbermeans to make a drawing that represents the number.
Solution

• Since 2, the graph of is to the left of2 on the number line.


• The number is between 1 and 2.


• The number is less than 0.


• Expressed as a mixed number,.

(^3) –
4
− 3 − 2
− 2 − 12 –^1 – – 81 ––^135 = 2 –^35
−101 23
13
5 ^2
3
5

^18

 1 12

 2 43  2 43

13

5



1

8

 1

1

2

 2

3

4

EXAMPLE (^5) Multiply and simplify, if possible.
a. b. c.
Strategy We will write the mixed numbers and whole numbers as improper
fractions.
WHY Then we can use the rule for multiplying two fractions from Section 3.2.
Solution
a. Write and as improper fractions.
 4 Write the improper fraction^4912 as a mixed number.

1

12

4

12  49

 48

1

Since there are no common factors to remove,

perform the multiplication in the numerator and in

the denominator. The result is an improper fraction.



49

12

Use the rule for multiplying two fractions.

 Multiply the numerators and the denominators.

7  7

4  3

1 13 4 2 31

3

4

 2

1

3



7

4



7

3

 4

1

9

5 (3)

1

5

a 1

2

13

1 b

3

4

 2

1

3

Self Check 5

Multiply and simplify, if possible.

a. b.

c.

Now TryProblems 51, 55, and 57

 4

5

6

(2)

9

3

5

a 3

3

4

3 b

1

3

# 2 1

3