Basic Mathematics for College Students

In this section, we will work with negative as well as positive mixed numbers. For

example, the negative mixed number could be used to represent feet below

sea level. Think of as or as.

Write mixed numbers as improper fractions.

In Example 1, we saw that the shaded portion of the illustration can be represented

by the mixed number and by the improper fraction. To develop a procedure to

write any mixed number as an improper fraction, consider the following steps that

show how to do this for. The objective is to find how many fifthsthat the mixed

number represents.

Write the mixed number as a sum.

Write 2 as a fraction:.

To build so that its denominator is 5, multiply it by a form of 1.

Thus, 2 15 ^115.

Add the numerators and write the sum over

 (^) the common denominator 5.

11

5

Multiply the numerators.

 (^) Multiply the denominators.

10

5



1

5

2

 1

2

1



5

5



1

5

 2 ^21

2

1



1

5

2 2 51

1

5

 2 

1

5

2 15

2 15

11

2 5

1

5

2

 3 43  3  43  3 ( (^43) )

 3 43 3 43

258 Chapter 3 Fractions and Mixed Numbers

WHY To write an improper fraction, we need to find its numerator and its

denominator. To write a mixed number, we need to find its whole number part and

its fractional part.

Solution

Since each disk is divided into 5 equal parts, the denominator of the improper

fraction is 5. Since a total of 11 of those parts are shaded, the numerator is 11, and

we say that

is shaded. Write:

Since 2 whole disks are shaded, the whole number part of the mixed number

is 2. Since 1 out of 5 of the parts of the last disk is shaded, the fractional part of the

mixed number is , and we say that

is shaded.

2 wholes^1 – 5

2

1

5

1

5

10 11

7 9

6

8

5

2 4

1

3

total number of parts shaded

number of equal parts in one disk

11

5