Basic Mathematics for College Students

Define equivalent fractions.

Fractions can look different but still represent the same part of a whole. To illustrate
this, consider the identical rectangular regions on the right. The first one is divided into
10 equal parts. Since 6 of those parts are red, of the figure is shaded.
The second figure is divided into 5 equal parts. Since 3 of those parts are red, of
the figure is shaded. We can conclude that because and represent the same
shaded portion of the figure. We say that and are equivalent fractions.

Equivalent Fractions

Two fractions are equivalentif they represent the same number.Equivalent

fractionsrepresent the same portion of a whole.

Build equivalent fractions.

Writing a fraction as an equivalent fraction with a largerdenominator is called
buildingthe fraction. To build a fraction, we use a familiar property from Chapter 1
that is also true for fractions:

Multiplication Property of 1

The product of any fraction and 1 is that fraction.

We also use the following rule for multiplying fractions. (It will be discussed in
greater detail in the next section.)

Multiplying Fractions

To multiply two fractions, multiply the numerators and multiply the

denominators.

To build an equivalent fraction for with a denominator of 8, we first ask, “What
number times 2 equals 8?” To answer that question we divide8 by 2 to get 4. Since we
need to multiply the denominator of by 4 to obtain a denominator of 8, it follows that
should be the form of 1 that is used to build an equivalent fraction for

1

Multiply by 1 in the form of Note the form of 1 highlighted in red.

Use the rule for multiplying two fractions. Multiply the numerators.

Multiply the denominators.



4

8



1  4

2  4

4

4.

1

 (^2)

4

4

1

2



1

2

1

2.

4
4

1

2

1

2

4

3

5

6

10

3

5

6

10

6

10 

3

5

3

5

6

10

3

3.1 An Introduction to Fractions 211

The Language of Mathematics Fractions are often referred to as rational

numbers.All integers are rational numbers, because every integer can be

written as a fraction with a denominator of 1. For example,

and 0

0

1

 5 

 5

1

2  ,

2

1

,

––^6

10

(^3) –
5