Multiplication of fractions is pretty simple compared to addition and subtraction. And guess what? We don't need to find a common denominator. We do need to make sure each number is a fraction, though: no mixed numbers or whole numbers allowed. It's an elite fraction club.
Just follow these four easy steps:
|Multiply the numerators, then multiply the denominators.|
|Reduce the fraction. 12 and 72 have a GCF of 12, so divide the top and bottom by 12.|
|Boom, there's our answer.|
|First convert that second mixed number to an improper fraction:|
|Next, multiply the numerators, then multiply the denominators.|
|There's one answer, but we can also turn this into a mixed number.|
|Why hello there, final answer.|
Instead of reducing the fraction at the end of the problem, we can cross-cancel before we multiply. It's not required, but it'll save a few steps.
Cross-canceling means that when we're multiplying fractions, we can reduce any numerator with any denominator. In this example, 5 and 10 can both be divided by 5, even though they're not in the same fraction.
Let's look at Example 1 again and see how to use this method.
|Here we can reduce the 3 and 9 (by 3) and we can also reduce the 4 and 8 (by 4). Yeah, let's do that.|
|Now we multiply the top by the top and the bottom by the bottom, like normal.|
|Hey, the final answer is the same as in Example 1 from before. Nice.|
Here's another example that includes just about everything we've done so far.
|First convert each to an improper fraction.|
|14 and 7 can each be reduced by 7, so we can cross-cancel.|
|Here's the answer.|
|If you'd like, you can turn it back into a mixed number|
Just remember that all real numbers can be written as fractions. With a whole number, all we need to do is place it over a denominator of 1.
Let's look at an example, shall we?