Comparing Fractions

One of the first things you’ll be asked to do with
fractions
is compare them, which means tell which one is bigger and which
one is smaller.

In order to do this, you’ll need to be familiar with the following signs: < ,="">
, and = . The greater than sign looks like this: > and it means that the first number
is greater than the second number, for example “five is greater than two” would
be written 5 > 2. The less than sign looks like this: < and="" it="" means="" that="" the="" first="" number="" is="" less="" than="" the="" second="" number,="" for="" example="" “three="" is="" less="" than="" six”="" would="" be="" written="" as="" 3="">< 6.="" the="" equals="" sign="" looks="" like="" this:="and" it="" means="" that="" the="" two="" numbers="" are="" exactly="" the="" same,="" for="" example="" two="" equals="" two="" would="" be="" written="" as="" 2="2.">

Just as we can compare whole numbers, we can also compare fractions. There is only
one rule when it comes to comparing fractions: we must have common denominators.
If you do not know how to find common denominators, please review how
to find common denominators
.

First, let’s start out with a simple example where we already have common denominators.

Compare the following using >, <, or=":">

In order to compare these, we look at the numerators of each fraction. Which one
is bigger? We see that 3 is bigger than 2, thus our answer would be >.

Sometimes, however, we may start with two fractions that do not have the same denominator.
In that case, we would first find the common denominator and then compare the fractions.
Here’s an example of a problem that did not have common denominators. Watch closely
to see what happened with this problem:

Now, compare the new fractions:

When you compare the fractions, look at the numerators. The fraction with the larger
numerator is the larger fraction. In this case, 9/15 is the larger fraction, so
the answer is >.

Comparing Fractions Quiz

Compare these fractions:

5/8 ____ 3/5

A.
>
B.
<>
C.
=

The correct answer here would be A.

First, find common denominators for the fractions. After you expand the fractions,
5/8 becomes 25/40, and 3/5 becomes 24/40

Then, compare 25/40 ____ 24/40, and see that the answer is >, greater than.

Compare these fractions:

4/7 ____ 6/10

A.
>
B.
<>
C.
=

The correct answer here would be B.

First, find common denominators for the fractions. After you expand the fractions,
4/7 becomes 40/70, and 6/10 becomes 42/70

Then, compare 40/70 ____ 42/70, and see that the answer is <, less="" than.="">

Compare these fractions:

9/13 ____ 27/39

A.
>
B.
<>
C.
=

The correct answer here would be C.

First, find common denominators for the fractions. You will see that the denominators
will be 39, so you only need to expand 9/13. 9/13 would expand to 27/39. Now, you
have to compare 27/39 ____ 27/39, which you would find to be equal to each other,
=

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