Lesson 2Converting Fractions to Higher Terms

When performing routine arithmetic operations with fractions, it is often necessary to convert a fraction to higher terms. This means you multiply both the numerator and denominator by a particular integer value. Suppose you have a fraction, 2/3, and you multiply both the numerator and denominator by 7:

2/3 · 7/7 = 14/21

 Procedure To convert any fraction to higher terms, multiply both the numerator and denominator by the same integer value.

Examples:

Note: Multiplying the numerator and denominator by the same number does not change the actual value of the fraction.

After multiplying the numerator and denominator of 3/4 by 4, we see that

3/4 = 12/16

Equal portions, different expressions.

You will be doing a lot of these conversions to higher terms, especially when adding and subtracting fractions. In those situations, however, you are not given the value of the common multiplying factor—you must determine it for yourself. How is this done? The clue is that you are given the value of the denominator for the converted fraction. Like this:

3/5 = ?/10

In this problem, the fraction 3/5 is being raised to a higher power. You can see that the denominator is raised from 5 to 10. It is raised by a factor of 2. But what about the numerator?  When 5 is raised to 10, 3 is raised to ... . Figure it out. Since the numerator is raised by a factor of 2, the denominator must also be raised by a factor of 2. So:

3/5 = 3/5 · 2/2 = 6/10

3/5 = 6/10

Use these interactive examples and exercises to strengthen your understanding and build your skills:

 If you are having any trouble understanding the content of this lesson, you will benefit from a more detailed tutorial on the subject.