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Comparing Fractions

In this lesson, you will learn about comparing fractions.Before you start this lesson, I recommend that you study or review my lesson about fractions

Once you have mastered that, you are ready to study this lesson.Before I show you those two ways to compare fractions, you will need to learn the following.

Cross product: the answer obtained by multiplying the numerator of one fraction by the denominator of another

For instance, to get the cross products of 2/5 and 3/6, we can do 2 times 6 = 12 and 3 times 5 to get 15.

The sign (>) means greater or bigger than.

For instance, 6 > 4

The sign (<) means smaller than.

For instance, 4 < 6

Common denominator: When two or more fractions have the same denominator, we say that the fractions have a common denominator.

2/6, 1/6, 5/6 all have a common denominator.

Now, here are two ways to compare fractions.

The first way is to do a cross product.

Let us compare 2/3 and 3/4

Start your cross product by multiplying the numerator for the fraction on the left by the denominator for the fraction on the right. You get 2 times 4 = 8

Then, multiply the numerator for the fraction on the right by the denominator for the fraction on the left. You get 3 times 3 = 9

Put 8 beneath 2/3 and 9 beneath 3/4.

Because 8 is smaller than 9, 2/3 is smaller than 3/4 or 2/3 < 3/4

let us compare 5/6 and 6/8.

5 times 8 = 40 and 6 times 6 = 36

Put 40 beneath 5/6 and 36 beneath 6/8

Because 40 is bigger than 36, 5/6 is bigger than 6/8

A second method to use when comparing fractions is to first get a common denominator.Let us compare again 5/6 and 6/8

Notice that you can multiply the denominator for the first fraction, which is 6 by 8 and multiply the denominator for the second fraction, which is 8 by 6 to get your common denominator.

Warning! Whatever you multiply the denominator, you have to multiply your numerator by the same thing so that you are in fact getting equivalent fractions.

So, 5/6 will become 40/48 and 6/8 will become 36 /48

Because 40 is bigger than 36, 40/48 is bigger than 36/48.

Therefore, 5/6 > 6/8

The following rules are helpful!

Rule #1

When two fractions have the same denominator, the bigger fraction is the one with the bigger numerator. Does that make sense?

Let's again our Pizza in lesson # 1 as an example. If your pizza has 10 slices and you eat 5. That's 5/10

If you eat one more,which gives you 6 slices, that's 6/10. Now it has become obvious that 6/10 > 5/10

Rule # 2

When two fractions have the same numerator, the bigger fraction is the one with the smaller denominator.

Once again, let us use our pizza as an example. Say that you bought two large pizzas and they are the same size.

Let's say that the first pizza was cut into 10 slices and the second was cut into 15 slices. No doubt if the second pizza is cut into 15 slices, slices will be smaller.

If you grab 2 slices from the first, the expression for the fraction is 2/10 and if you grab 2 slices from the second,the expression for the fraction is 2/15. Slices for the latter will definitely smaller.

Therefore, 2/10 > 2/15.

This lesson about comparing fractions is over. You can learn about

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