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.
Before I show you 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 the fractions below:
We can do 2 × 6 = 12 and 3 × 5 = 15.
Meaning of inequality sign:
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.


and
5
/
6
all have a common denominator

Now, here are two ways to compare fractions.
The
first way is to do a cross product.
Start your cross product by multiplying the numerator of the fraction on the left by the denominator of the fraction on the right. You get 2 × 4 = 8
Then, multiply the numerator of the fraction on the right by the denominator of the fraction on the left. You get 3 × 3 = 9
Since 8 is smaller than 9, then
2
/
3


5 × 8 = 40 and 6 × 6 = 36
Since 40 is bigger than 36, then
5
/
6


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


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.
Since 40 is bigger than 36, then
40
/
48


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 use our Pizza in the lesson about
fractions as an example. If your pizza has 10 slices and you eat 5.
If you eat one more, that is 6 slices
Now it has become obvious that
Rule # 2
When comparing fractions that 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
2
/
10
If you grab 2 slices from the second, the expression for the fraction
2
/
15
Slices for the latter will definitely smaller.
This lesson about comparing fractions is over.
Before I show you 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 the fractions below:
We can do 2 × 6 = 12 and 3 × 5 = 15.
Meaning of inequality sign:
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.
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
Start your cross product by multiplying the numerator of the fraction on the left by the denominator of the fraction on the right. You get 2 × 4 = 8
Then, multiply the numerator of the fraction on the right by the denominator of the fraction on the left. You get 3 × 3 = 9
Since 8 is smaller than 9, then
Let us compare
5 × 8 = 40 and 6 × 6 = 36
Put 40 beneath
Since 40 is bigger than 36, then
A
second method to use when comparing fractions is to first get a common denominator.
Let us compare again
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.
Since 40 is bigger than 36, then
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 use our Pizza in the lesson about
fractions as an example. If your pizza has 10 slices and you eat 5.
If you eat one more, that is 6 slices
Now it has become obvious that
Rule # 2
When comparing fractions that 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
2
/
10
If you grab 2 slices from the second, the expression for the fraction
2
/
15
Slices for the latter will definitely smaller.
This lesson about comparing fractions is over.