Basic Mathematics for College Students

3.5 Multiplying and Dividing Mixed Numbers 257

In the next two sections, we show how to add, subtract, multiply, and divide mixed
numbers.These numbers are widely used in daily life.

Identify the whole-number and fractional parts

of a mixed number.

A mixed numberis the sumof a whole number and a proper fraction. For example,
is a mixed number.

 3 

cc c

Mixed number Whole-number part Fractional part

Mixed numbers can be represented by shaded regions. In the illustration below, each
rectangular region outlined in black represents one whole. To represent , we shade
3 wholerectangular regions and 3 out of 4 partsof another.

Caution! Note that means , even though the symbol is not written.

Do not confuse 3 43 with 3 ^34 or 31 342 , which indicate the multiplication of 3 by. 43

3 34 3 ^34

(^3) –
4
(^3) –
3 4
3

3 34

3

4

3

3

4

3 34

1

12

7 65

8 4

3

10 2

11 1

9

12

7 65

8 4

3

10 2

11 1

9

(^1) –
2
The entrance to the park
is 1 miles away.
(Read as “one and one-half.”)
(^3) –
4
It took 3 hours to paint
the living room.
(Read as “three and three-fourths.”)
(^1) –
3
The recipe calls for 2 cups
of flour.
(Read as “two and one-third.”)
National Park
SECTION 3.5
Multiplying and Dividing Mixed Numbers

Objectives

1 Identify the whole-number and

fractional parts of a mixed number.

2 Write mixed numbers as

improper fractions.

3 Write improper fractions as

mixed numbers.

4 Graph fractions and mixed

numbers on a number line.

5 Multiply and divide mixed

numbers.

6 Solve application problems by

multiplying and dividing mixed

numbers.

Self Check 1

In the illustration below, each oval

region represents one whole.

Write an improper fraction and

a mixed number to represent the

shaded portion.

Now TryProblem 19

EXAMPLE (^1) In the illustration below, each disk represents one whole.
Write an improper fraction and a mixed number to represent the shaded portion.
Strategy We will determine the number of equal parts into which a disk is
divided. Then we will determine how many of those partsare shaded and how many
of the wholedisks are shaded.