At a Glance - Multiplying Fractions & Mixed Numbers
Multiplication of fractions is pretty simple compared to addition and subtraction. And guess what, you don't have to find a common denominator. Just follow these four easy steps:
- Convert all mixed numbers to improper fractions.
- Multiply the numerators.
- Multiply the denominators.
- Reduce your final answer.
Multiplication Example 1
If you'd like, you could convert that into a mixed number
|First convert 3½ to an improper fraction|
|Next multiply the numerators, then multiply the denominators|
|This is your answer|
Multiplication Example 2
|Multiply the numerators, then multiply the denominators.|
|Reduce the fraction (12 and 72 have a GCF of 12)|
Instead of reducing the fraction at the end of the problem, you can cross-cancel before you multiply.
Cross-canceling means that when multiplying fractions you can reduce the numerator of one fraction with the denominator of another. In this example, 5 and 10 can both be divided by 5.
Let's look at the three examples again and see how to use this method.
Cross-Canceling Example 1
|In this first example, we cannot use cross-canceling, since 5 and 2 do not share a common factor, and neither do 7 and 6|
Cross-Canceling Example 2
|Here we can reduce the 3 and 9 (by 3) and we can also reduce the 4 and 8 (by 4)|
Cross-Canceling Example 3
|First convert each to an improper fraction|
|14 and 7 can each be reduced by 7|
|Here's the answer|
|If you'd like, you can turn it back into a mixed number|
Multiplying a Whole Number by a Fraction
Well, remember that all real numbers can be written as fractions. With a whole number, all you need to do is place it over a denominator of 1.
Let's look at an example, shall we?