Read: Multiplying Fractions
Learning Objectives
- Multiply two or more fractions
- Multiply a fraction by a whole number
Multiply Fractions
Just as you add, subtract, multiply, and divide when working with whole numbers, you also use these operations when working with fractions. There are many times when it is necessary to multiply fractions. A model may help you understand multiplication of fractions. When you multiply a fraction by a fraction, you are finding a “fraction of a fraction.” Suppose you have of a candy bar and you want to find of the :![3 out of four boxes are shaded. This is 3/4.](https://s3-us-west-2.amazonaws.com/courses-images/wp-content/uploads/sites/121/2016/06/01182611/image109.gif)
![Six of 8 boxes are shaded. This is 6/8.](https://s3-us-west-2.amazonaws.com/courses-images/wp-content/uploads/sites/121/2016/06/01182612/image110.gif)
![Six of 8 boxes are shaded, and of those six, three of them are shaded purple. The 3 purple boxes represent 3/8.](https://s3-us-west-2.amazonaws.com/courses-images/wp-content/uploads/sites/121/2016/06/01182613/image112.gif)
Multiplying Two Fractions
Multiplying More Than Two Fractions
Example
MultiplyAnswer: Multiply the numerators and multiply the denominators.
Simplify, if possible. This fraction is already in lowest terms.
Answer
- Given , the factors of are: and the factors of are: . is simplified because there are no common factors of and .
- Given , the factors of are: and the factors of are: . is not simplified because is a common factor of and .
Think About It
Multiply . Simplify the answer. What makes this example different than the previous ones? Use the box below to write down a few thoughts about how you would multiply three fractions together. [practice-area rows="2"][/practice-area]Answer: Multiply the numerators and multiply the denominators.
Simplify first by canceling (dividing) the common factors of and . divided by is , and divided by is .