Fractions

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 75/12, or seventy five twelfths, in your head?

  20/50  x  75/12  =  1500/600 

Even the answer looks complicated. It's 1500/600, or fifteen hundred six-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 for a numerator and a denominator that can be divided by the same number. The numerator and denominator can't be from the same fraction. This means we can't choose 20 and 50 from the problem on the left, even though they both could be divided by 10. 

In our example, it looks like both 50 and 75 can be divided by 25. We can use these numbers because they're not from the same fraction.

Step 2

Next, we'll divide 50 and 75 by 25. First, we'll divide our bottom number on the left: 50.

50 / 25 = 2

Then we'll divide the top number on the right: 75.

75 / 25 = 3

We'll write the answers to each problem next to the numbers we divided. Since 50/25 equals 2, we'll write 2 where the 50 was. 75 / 25 equals 3, so we'll write 3 where the 75 was. We can cross out, or cancel, the numbers we started with.

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

Step 3

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

20 x 3 = 60

Then multiply the denominators:

2 x 12 = 24

So 20/2  x  3/12  =  60/24, or sixty twenty-fourths.

Step 4

Finally, let's double check our work. 1500/600 would have been our answer if we had solved the problem without canceling. If we divide both 1500 and 600 by 25, we can see that 1500/600 is equal to 60/24.

We could also say that we're reducing 1500/600 to 60/24. 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.