# 1.5 Visualize Fractions

### Learning Objectives

By the end of this section, you will be able to:

• Find equivalent fractions
• Simplify fractions
• Multiply fractions
• Divide fractions
• Simplify expressions written with a fraction bar
• Translate phrases to expressions with fractions

### Find Equivalent Fractions

Fractions are a way to represent parts of a whole. The fraction 1313 means that one whole has been divided into 3 equal parts and each part is one of the three equal parts. See Figure 1.11. The fraction 2323 represents two of three equal parts. In the fraction 23,23, the 2 is called the numerator and the 3 is called the denominator.

Figure 1.11 The circle on the left has been divided into 3 equal parts. Each part is 1313 of the 3 equal parts. In the circle on the right, 2323 of the circle is shaded (2 of the 3 equal parts).

### Simplify Fractions

A fraction is considered simplified if there are no common factors, other than 1, in its numerator and denominator.

For example,

• 2/3 is simplified because there are no common factors of 2 and 3.
• 10/15 is not simplified because 55 is a common factor of 10 and 15.

We’ll use a model to show you how to multiply two fractions and to help you remember the procedure. Let’s start with 34. Now we’ll take 1/2 of 3/4. Notice that now, the whole is divided into 8 equal parts. So

To multiply fractions, we multiply the numerators and multiply the denominators.

### Section 1.5 Exercises

#### Practice Makes Perfect

Find Equivalent Fractions

In the following exercises, find three fractions equivalent to the given fraction. Show your work, using figures or algebra.

#### Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section. ⓑ After looking at the checklist, do you think you are well prepared for the next section? Why or why not?