Basic Mathematics for College Students

304 Chapter 3 Summary and Review

SECTION 3.5 Multiplying and Dividing Mixed Numbers

A mixed numberis the sum of a whole number

and a proper fraction.

DEFINITIONS AND CONCEPTS EXAMPLES

Mixed number Whole-number Fractional part

part

2

3

4

 2 

3

4

There is a relationship between mixed numbers

and improper fractionsthat can be seen using

shaded regions.

Each disk represents one whole.

(^3) –
(^24)
2
=^11 –– 4
23
14
67
58
10 11
9
(^3) –
4
To write a mixed number as an improper
fraction:

1. Multiply the denominator of the fraction
   by the whole-number part.


2. Add the numerator of the fraction to the
   result from Step 1.


3. Write the sum from Step 2 over the
   original denominator.

Write as an improper fraction.

Step 2: Add

Step 1: Multiply Step 3: Use the same denominator

From this result, it follows that 3.

4

5



19

5

 

3

4

5



5  3  4

5



15  4

5



19

5



3

4

5

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.

Write as mixed number.

Thus,. From this result, it follows that.

47

6

 7

5

6

47

6

 7

5

6

The whole-number part is 7.

Write the remainder 5 over the divisor 6

to get the fractional part.



7 

(^6)  47
 42
5

47

6

Fractions and mixed numbers can be graphed

on a number line.

Graph on a number line.

(^1) –
3
− 4 − 2
− 3 – – 87 141 –^18 –– 5 = 35 –^3
− 31234 − 10

 3

1

3

, 1

1

4

,

18

5

, and 

7

8