Multiplying and Dividing Fractions

When working with fractions multiplying and dividing can be tricky. Get help multiplying and dividing fractions here.

Using canceling to simplify problems

Sometimes you might have to solve problems like this:

Both of these fractions include large numbers. You could multiply these fractions the same way as any other fractions. However, large numbers like this can be difficult to understand. Can you picture 21/50, or twenty-one fiftieths, in your head?

21/50 x 25/14 = 525/700

Even the answer looks complicated. It's 525/700, or five hundred twenty-five seven-hundredths. What a mouthful!

If you don't like working with large numbers, you can simplify a problem like this by using a method called canceling. When you cancel the fractions in a problem, you're reducing them both at the same time.

Canceling may seem complicated at first, but we'll show you how to do it step by step. Let's take another look at the example we just saw.

Step 1

First, look at the numerator of the first fraction and the denominator of the second. We want to see if they can be divided by the same number.

In our example, it looks like both 21 and 14 can be divided by 7.

Step 2

Next, we'll divide 21 and 14 by 7. First, we'll divide our top number on the left: 21.

21 ÷ 7 = 3

Then we'll divide the bottom number on the right: 14.

14 ÷ 7 = 2

We'll write the answers to each problem next to the numbers we divided. Since 21 ÷ 7 equals 3, we'll write 3 where the 21 was. 14 ÷ 7 equals 2, so we'll write 2 where the 14 was. We can cross out, or cancel, the numbers we started with.

Our problem looks a lot simpler now, doesn't it?

Step 3

Let's look at the other numbers in the fraction. This time we'll look at the denominator of the first fraction and the numerator of the second. Can they be divided by the same number?

Notice they can both be divided by 25! You might have also noticed they can both be divided by 5. We could use 5 too, but generally when you are canceling, you want to look for the biggest number both numbers can be divided by. This way you won't have to reduce the fraction again at the end.

Step 4

Next, we'll cancel just like we did in step 2.
We'll divide our bottom number on the left: 50.

50 ÷ 25 = 2

Then we'll divide the top number on the right: 25.

25 ÷ 25 = 1

We'll write the answers to each problem next to the numbers we divided.

Step 5

Now that we've canceled the original fractions, we can multiply our new fractions like we normally would. As always, multiply the numerators first:

3 x 1 = 3

Then multiply the denominators:

2 x 2 = 4

So 3/2 x 1/2 =3/4, or three-fourths.

Step 6

Finally, let's double check our work. 525/700 would have been our answer if we had solved the problem without canceling. If we divide both 525 and 700 by 175, we can see that 525/700 is equal to 3/4.

We could also say that we're reducing 525/700 to 3/4. Remember, canceling is just another way of reducing fractions before solving a problem. You'll get the same answer, no matter when you reduce them.

Assessment

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