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

**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).

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.

**Find Equivalent Fractions**

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

ⓐ 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?

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