When working with fractions comparing and reducing can be confusing. Get help reducing and comparing fractions here.

### Mixed numbers and improper fractions

In the previous lesson, you learned about **mixed numbers**. A mixed number has both a **fraction **and a **whole number**. An example is 1 2/3. You'd read 1 2/3 like this: **one and two-thirds**.** **

Another way to write this would be 5/3, or **five-thirds**. These two numbers look different, but they're actually the same. 5/3 is an **improper fraction**. This just means the numerator is **larger** than the denominator.

There are times when you may prefer to use an improper fraction instead of a mixed number. It's easy to change a mixed number into an improper fraction. Let's learn how:

Let's convert 1 1/4 into an improper fraction.

First, we'll need to find out how many **parts** make up the whole number: 1 in this example.

To do this, we'll multiply the **whole number**, 1, by the denominator, 4.

1 times 4 equals 4.

Now, let's add that number, 4, to the numerator, 1.

4 plus 1 equals 5.

The denominator stays the same.

Our improper fraction is 5/4, or five-fourths. So we could say that 1 1/4 is equal to 5/4.

This means there are **five** 1/4s in 1 1/4.

Let's convert another mixed number: 2 2/5.

First, we'll multiply the whole number by the denominator. 2 times 5 equals 10.

Next, we'll add 10 to the numerator. 10 plus 2 equals 12.

As always, the denominator will stay the same.

So 2 2/5 is equal to 12/5.

#### Try This!

Try converting these mixed numbers into improper fractions.

Converting improper fractions into mixed numbers

Improper fractions are useful for math problems that use fractions, as you'll learn later. However, they're also more difficult to read and understand than **mixed** **numbers**. For example, it's a lot easier to picture 2 4/7 in your head than 18/7.

Click through the slideshow to learn how to change an improper fraction into a mixed number.

Let's turn 10/4 into a mixed number.

You can think of any fraction as a **division** **problem**. Just treat the line between the numbers like a division sign (/).

So we'll **divide** the numerator, 10, by the denominator, 4.

10 divided by 4 equals 2...

10 divided by 4 equals 2... with a remainder of 2.

The answer, 2, will become our whole number because 10 can be divided by 4 **twice**.

And the **remainder**, 2, will become the numerator of the fraction because we have 2 parts left over.

The denominator remains the same.

So 10/4 equals 2 2/4.

Let's try another example: 33/3.

We'll divide the numerator, 33, by the denominator, 3.

33 divided by 3...

33 divided by 3... equals 11, with no remainder.

The answer, 11, will become our whole number.

There is no remainder, so we can see that our improper fraction was actually a whole number. 33/3 equals 11.

#### Try This!

Try converting these improper fractions into mixed numbers.

### Assessment

Want even more practice? Try out a short assessment to test your skills by clicking the link below:

Start Assessment