Multiplying Fractions

To multiply fractions is as easy as following the 3 suggested steps below.

 Steps How To Multiply Fractions Given two fractions with nonzero denominators Step 1: Multiply the numerators together This will be the numerator of the "new" fraction. Step 2: Multiply the denominators together This will be the denominator of the "new" fraction. Step 3: Simplify the resulting fraction by reducing it to lowest term, if needed.

Before we go over some examples, these are other ways to mean multiplication.

 Dot symbol as multiplication operator. Parenthesis as multiplication operator.

Example 1: Multiply the fractions .

Multiply the numerators of the fractions

Similarly, multiply the denominators together.

The resulting fraction after multiplication is already in its reduced form. That becomes our final answer!

Example 2: Multiply the fractions .

 Step 1: Multiply the top numbers together Step 2: Multiply the bottom numbers together Step 3: Simplify the answer by reducing to lowest term. Divide the top and bottom by its greatest common divisor (GCD) which is 10.

Example 3: Multiply the three fractions .

You may encounter a problem where you will be asked to multiply three fractions.

The general idea remains the same just like when you multiply two fractions, as shown in previous examples.

 Step 1: Get the product of the numerators Step 2: Get the product of the denominators Step 3: Reduce the answer to the lowest term Divide both the numerator and denominator by the greatest common divisor that is 12.

Example 4: Multiply a whole number and a fraction .

When you multiply a whole number to a fraction, think of the whole number as fraction with a denominator of 1. Since

Therefore, we can rewrite the original problem as . With that, it should allow us to multiply the fractions as usual.

Finally, reduce the answer by dividing the numerator and denominator by 5.

Example 5: Multiply .

Solution:

Step 1: Multiply the numerators

5 x 6 = 30

Step 2: Multiply the denominators

3 x 15 = 45

Step 3: Reduce the answer to the lowest term by dividing the top and bottom by the greatest common divisor which is 15.

Example 6: Multiply .

Solution:

Example 7: Multiply .

Solution:

Rewrite the whole number 9 with a denominator of 1.

 Practice Problems with Answers Worksheet 1 Worksheet 2

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