Basic Mathematics for College Students

We have found that is equivalent to To build an equivalent fraction for with

a denominator of 8, we multiplied by a factor equal to 1in the form of Multiplying

by changes its appearance but does not change its value, because we are multiplying

it by 1.

Building Fractions

To build a fraction,multiply it by a factor of 1in the form and so on.

The Language of Mathematics Building an equivalent fraction with a larger

denominator is also called expressing a fraction in higher terms.

2

2

,

3

3

,

4

4

,

5

5

,

4

4

1

2

4

4.

1

2

1

2.

4

8

212 Chapter 3 Fractions and Mixed Numbers

EXAMPLE 4

Write as an equivalent fraction with a denominator of 35.

StrategyWe will compare the given denominator to the required denominator

and ask, “What number times 5 equals 35?”

WHYThe answer to that question helps us determine the form of 1 to use to build

an equivalent fraction.

Solution

To answer the question “What number times 5 equals 35?” we divide35 by 5 to get 7.

Since we need to multiply the denominator of by 7 to obtain a denominator of 35, it

follows that should be the form of 1 that is used to build an equivalent fraction for

1

Multiply by a form of 1:.

Multiply the numerators.

Multiply the denominators.

We have found that is equivalent to.

3

5

21

35



21

35



3  7

5  7

7

7 ^1

3

 (^5)

7

7

3

5



3

5

3

5.

7

7

3

5

3

5

Success TipTo build an equivalent fraction in Example 4, we multiplied by 1

in the form of As a result of that step, the numerator and the denominator of

were multiplied by 7:

—The numerator is multiplied by 7.

—The denominator is multiplied by 7.

This process illustrates the following property of fractions.

The Fundamental Property of Fractions

If the numerator and denominator of a fraction are multiplied by the same

nonzero number, the resulting fraction is equivalent to the original fraction.

Since multiplying the numerator and denominator of a fraction by the same

nonzero number produces an equivalent fraction, your instructor may allow you to

begin your solution to problems like Example 4 as shown in the Success Tip above.

3  7

5  7

3

5

7

7

.

3

5

Self Check 4

Write as an equivalent fraction

with a denominator of 24.

Now TryProblems 37 and 49

5

8