When working with fractions comparing and reducing can be confusing. Get help reducing and comparing fractions here.
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.
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.
Reduce each fraction to its simplest form.