Multiplying Fractions

Learning Objectives

  • Multiply fractions
    • Multiply two or more fractions

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 3434 of a candy bar and you want to find 1212 of the 3434:

3 out of four boxes are shaded. This is 3/4.

By dividing each fourth in half, you can divide the candy bar into eighths.

Six of 8 boxes are shaded. This is 6/8.

Then, choose half of those to get 3838.

Six of 8 boxes are shaded, and of those six, three of them are shaded purple. The 3 purple boxes represent 3/8.

In both of the above cases, to find the answer, you can multiply the numerators together and the denominators together.

Multiplying Two Fractions

ab⋅cd=a⋅cb⋅d=product of the numeratorsproduct of the denominatorsab⋅cd=a⋅cb⋅d=product of the numeratorsproduct of the denominators

Multiplying More Than Two Fractions

ab⋅cd⋅ef=a⋅c⋅eb⋅d⋅fab⋅cd⋅ef=a⋅c⋅eb⋅d⋅f

Example

Multiply 23⋅4523⋅45.

To review: if a fraction has common factors in the numerator and denominator, we can reduce the fraction to its simplified form by removing the common factors.

For example,

  • Given 815815, the factors of 8 are: 1, 2, 4, 8 and the factors of 15 are: 1, 3, 5, 15.  815815 is simplified because there are no common factors of 8 and 15.
  • Given 10151015, the factors of 10 are: 1, 2, 5, 10 and the factors of15 are: 1, 3, 5, 15. 10151015 is not simplified because 5 is a common factor of 10 and 15.

You can simplify first, before you multiply two fractions, to make your work easier. This allows you to work with smaller numbers when you multiply.

In the following video you will see an example of how to multiply two fractions, then simplify the answer.

Think About It

Multiply 23⋅14⋅3523⋅14⋅35. 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.