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.
You might also be interested in:
Adding and Subtracting Fractions with the Same Denominator
Add and Subtract Fractions with Different Denominators
Dividing Fractions
Simplifying Fractions
Equivalent Fractions
Reciprocal of a Fraction