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

### Reducing fractions

Which of these is larger: 4/8 or 1/2?

If you did the math or even just looked at the picture, you might have been able to tell that they're **equal**. In other words, 4/8 and 1/2 mean the same thing, even though they're written differently.

If 4/8 means the same thing as 1/2, why not just call it that? **One-half** is easier to say than **four-eighths**, and for most people it's also easier to understand. After all, when you eat out with a friend, you split the bill in **half**, not in **eighths**.

If you write 4/8 as 1/2, you're **reducing** it. When we **reduce** a fraction, we're writing it in a simpler form. Reduced fractions are always **equal** to the original fraction.

We already reduced 4/8 to 1/2. If you look at the examples below, you can see that other numbers can be reduced to 1/2 as well. These fractions are all **equal**.

**5/10 = 1/2**

11/22 = 1/2

36/72 = 1/2

These fractions have all been reduced to a simpler form as well.

**4/12 = 1/3**

14/21 = 2/3

35/50 = 7/10

Click through the slideshow to learn how to reduce fractions by **dividing**.

Let's try reducing this fraction: 16/20.

Since the numerator and denominator are **even numbers**, you can divide them by 2 to reduce the fraction.

First, we'll divide the numerator by 2. 16 divided by 2 is 8.

Next, we'll divide the denominator by 2. 20 divided by 2 is 10.

We've reduced 16/20 to 8/10. We could also say that 16/20 is equal to 8/10.

If the numerator and denominator can still be divided by 2, we can continue reducing the fraction.

8 divided by 2 is 4.

10 divided by 2 is 5.

Since there's no number that 4 and 5 can be divided by, we can't reduce 4/5 any further.

This means 4/5 is the **simplest** **form **of 16/20.

Let's try reducing another fraction: 6/9.

While the numerator is even, the denominator is an **odd number**, so we can't reduce by dividing by 2.

Instead, we'll need to find a number that 6 and 9 can be divided by. A multiplication table will make that number easy to find.

Let's find 6 and 9 on the **same** **row**. As you can see, 6 and 9 can both be divided by 1 and 3.

Dividing by 1 won't change these fractions, so we'll use the **largest** number that 6 and 9 can be divided by.

That's 3. This is called the **greatest common divisor**, or **GCD**. (You can also call it the **greatest common factor**, or **GCF**.)

3 is the **GCD** of 6 and 9 because it's the **largest** number they can be divided by.

So we'll divide the numerator by 3. 6 divided by 3 is 2.

Then we'll divide the denominator by 3. 9 divided by 3 is 3.

Now we've reduced 6/9 to 2/3, which is its simplest form. We could also say that 6/9 is equal to 2/3.

#### Irreducible fractions

Not all fractions can be reduced. Some are already as simple as they can be. For example, you can't reduce 1/2 because there's no number other than 1 that both 1 and 2 can be divided by. (For that reason, you can't reduce **any** fraction that has a numerator of 1.)

Some fractions that have larger numbers can't be reduced either. For instance, 17/36 can't be reduced because there's no number that both 17 and 36 can be divided by. If you can't find any **common multiples** for the numbers in a fraction, chances are it's **irreducible**.

#### Try This!

Reduce each fraction to its simplest form.