Fractions

Multiplying and Dividing Fractions

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A fraction is a **part** of a **whole**. In the last lesson, you learned how to add and subtract fractions. But that’s not the only kind of math you can do with fractions. There are times when it will be useful to multiply fractions too.

Click through the slideshow to learn how to write a multiplication problem with fractions.

Try setting up the multiplication problem below. Don't worry about solving it yet!

A recipe calls for 2/3 of a cup of milk. You want to cut the recipe in half.

**Note**: Although our example says the correct answer is 2/3 x 1/2, remember, with multiplying order does not matter. 1/2 x 2/3 would also be correct.

Now that we know how to set up multiplication problems with fractions, let's practice solving a few. If you feel comfortable multiplying whole numbers, you're ready to multiply fractions.

Click through slideshow to learn how to multiply two fractions.

Try solving the multiplication problems below.

Multiplying a fraction and a whole number is similar to multiplying two fractions. There's just one extra step: Before you can multiply, you'll need to turn the whole number into a fraction. This slideshow will show you how to do it.

Click through the slideshow to learn how to multiply a fraction and a whole number.

Try solving the multiplication problems below.

Over the last few pages, you've learned how to **multiply** fractions. You might have guessed that you can **divide** fractions too. You divide fractions to see how many parts of something **are in** something else. For example, if you wanted to know how many fourths of an inch are in four inches, you could divide 4 by 1/4.

Let's try another example. Imagine a recipe calls for 3 cups of flour, but your measuring cup only holds 1/3, or **one-third**, of a cup. How many **thirds **of a cup should you add?

We'll need to find out how many **thirds** of a cup are in **three** cups. In other words, we'll need to divide three by one-third.

We'd write the problem like this:

3 ÷ 1/3

Try setting up these division problems with fractions. Don't worry about solving them yet!

A recipe calls for 3/4 of a cup of water. You only have a 1/8 measuring cup.

Now that we know how to write division problems, let's practice by solving a few. Dividing fractions is a lot like multiplying. It just requires one extra step. If you can multiply fractions, you can divide them too!

Click through the slideshow to learn how to divide a whole number by a fraction.

Try solving these division problems. **Don't** worry about reducing the answer for now.

We just learned how to divide a **whole number** by a **fraction**. You can use the same method to divide **two** **fractions**.

Click through the slideshow to learn how to divide with two fractions.

Try solving these division problems. **Don't** worry about reducing the answer for now.

How would you solve a problem like this?

As you learned in the previous lesson, whenever you're solving a problem with a **mixed** **number** you'll need to convert it into an **improper** **fraction** first. Then you can multiply or divide as usual.

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.

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.

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?

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.

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.

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**.

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.

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