# How to Multiply Fractions

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

## Steps in Multiplying 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 the lowest term, if needed.

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

• Dot symbol as a multiplication operator
• Parenthesis as a multiplication operator

### Examples of How to Multiply Fractions

Example 1: Multiply the fractions below.

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 below.

Step 1: Multiply the top numbers together

Step 2: Multiply the bottom numbers together

Step 3: Simplify the answer by reducing to the 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 a fraction with a denominator of $1$. Since

Therefore, we can rewrite the original problem as ${5 \over 1} \times {2 \over {15}}$. 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 .

Step 1: Multiply the numerators

Step 2: Multiply the denominators

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 with Worksheets

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