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