Basic Mathematics for College Students

208 Chapter 3 Fractions and Mixed Numbers

SECTION 3.1

An Introduction to Fractions

Objectives

1 Identify the numerator and

denominator of a fraction.

2 Simplify special fraction forms.

3 Define equivalent fractions.

4 Build equivalent fractions.

5 Simplify fractions.

Whole numbers are used to count objects, such as CDs, stamps, eggs, and magazines.

When we need to describe a part of a whole, such as one-half of a pie, three-quarters

of an hour, or a one-third-pound burger, we can use fractions.

One-half Three-quarters One-third

of a cherry pie of an hour pound burger

Identify the numerator and denominator of a fraction.

A fractiondescribes the number of equal parts of a whole. For example, consider the

figure below with 5 of the 6 equal parts colored red. We say that (five-sixths) of the

figure is shaded.

In a fraction, the number above the fraction baris called the numerator,and the

number below is called the denominator.

Fraction bar —numerator

¡

—denominator

5

6

5

6

1

1

3

3

4

1

2

(^121)
2
3
4
7 6 5
8
9
10
11
The Language of Mathematics The word fractioncomes from the Latin
word fractiomeaning "breaking in pieces."
EXAMPLE (^1) Identify the numerator and denominator of each fraction:
a. b.
StrategyWe will find the number above the fraction bar and the number below it.
WHYThe number above the fraction bar is the numerator, and the number below
is the denominator.
Solution
—numerator —numerator
a. b.
—denominator —denominator

8

3

11

12

8

3

11

12

Self Check 1

Identify the numerator and

denominator of each fraction:

a.

b.

Now TryProblem 21

21

20

7

9