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 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 .
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 a 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 .
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 .
Example 7: Multiply .
Rewrite the whole number 9 with a denominator of 1.