Comparing and ordering fractions

All fractions are not same in value. One fraction may be smaller than the other fractions and it may be larger than

some other fractions. Hence, kids need to know comparing fractions. Comparing can be subdivided into three

sections. So kids need to know three tricks to learn this skill.

Trick Number 1:

First trick to compare fractions is to see if they have got the same numerators. If the numerators are same then the

fraction with the largest denominator is smallest. For example; consider the following fractions:

3/5, 3/4, 3/8 and 3/7

As all of the above fractions have the same numerator (3), so to compare them we need to compare their

denominators. The largest denominator makes the fraction smallest, therefore 3/8 is smallest of all and 3/4 is the

largest. Let's rewrite all of the fractions in an order from smallest to largest as shown below:

3/8, 3/7, 3/5 and 3/4

The above order (smallest to largest) is also known as ascending order.

Trick Number 2:

The second trick is same easy as the first one. This trick is about comparing fractions, when they have same

denominators. When the denominators are same, then the fraction with the smallest numerator is smallest and one

with largest numerator is the largest. For example;

Consider we want to compare 3/9, 1/9, 7/9 and 2/9; write them in ascending order.

Look at the given fractions, all of them have the same denominator (9). So, 1/9 is the smallest because it has the

smallest numerator and 7/9 is the largest with largest numerator. Below they are written in ascending order.

1/9, 2/9, 3/9 and 7/9

Trick Number 3:

Above two tips explain the comparing fractions with either same numerators or same denominators. But most often

the kids are asked to compare and order fractions with different numerators and denominators.

In such a case they need to make denominator of all the fractions same. To do this they need to know the least

common factor (lcm) of all the denominators also known as least common denominator (lcd).

Consider the following example on comparing fractions:

Write the following fractions in descending order (largest to smallest)

2/3, 1/4, 5/6, 3/4 and 1/2

Solution: Look, most of fractions got different denominators. Write all the denominators as shown below and write first

six multiples of all of them.

2 = 2, 4, 6, 8, 10, 12 3 = 3, 6, 9, 12, 15, 18 4 = 4, 8, 12, 16, 20, 24 6 = 6, 12, 18, 24, 30, 36

Now, look at the factors of all the numbers and find the smallest and common in all, which is 12 in this case. Hence

the lcm or lcd is 12. The next step is to rewrite all of the fractions into equivalent fractions with denominator as 12.

This step is shown below:

2/3, we need to multiply its denominator (3) with 4 to change it to 12. But to keep the value of the fraction same, don't

forget to multiply the numerator (2) with the same number 4. Let's do it;

(2 x 4)/(3 x 4) = 8/12

Similarly write all the fractions with denominator equal to 12 as shown below:

1/4 = (1 x 3)/(4 x 3) = 3/12 5/6 = (5 x 2)/(6 x 2) = 10/12 3/4 = (3 x 3)/(4 x 3) = 9/12 1/2 = (1 x 6)/(2 x 6) = 6/12

Now all the fractions have been written into equivalent fractions with same denominator 12 and it's easy to compare

these. Write all the equivalent fractions in descending order (largest to smallest)

10/12, 9/12, 8/12, 6/12 and 3/12

But these are not the fractions asked to be compared. So, this is not our answer, but now it's very easy to write the

original fractions in the required order by looking at above order. We know 10/12 is equal to 5/6 and 3/12 is equal to

1/4 hence write the original fractions in order

5/6, 3/4, 2/3, 1/2 and 1/4

Finally, it can be said that to compare and order fractions, kids need to keep above three tips in mind. Of course, the

knowledge of least common multiple (lcm) is the key to compare two or more fractions with different denominators.

For more information about comparing fractions and any other math homework help on fractions or fractions

worksheets and lessons for all grades, any of the given links can be clicked. One of our co-tutor have some excellent

content on the topic.

Also you can keep visiting this site for more math content by me.

Thank you very much for sharing your time.

Manjit

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Comparing FractionsSometimes we need to compare two fractions to discover which is larger or smaller. There are two easy ways to compare fractions: using decimals; or using the same denominator

The Decimal Method of Comparing Fractions

Just convert each fraction to decimals, and then compare the decimals.

Example: which is bigger: 3 /8 or 5 /12 ?

You need to convert each fraction to a decimal. You can do this using your calculator (3÷8 and 5÷12), or you can read about  Converting Fractions to Decimals .

Anyway, these are the answers I get:

Search

3 /8 = 0.375, and 5 /12 = 0.4166...

So, 5 /12 is bigger.

The Same Denominator Method

The denominator is the bottom number in a fraction.

It shows how many equal parts the item is divided into

If two fractions have the same denominator then they are easy to compare:

Example:4 /9 is less than 5 /9 (because 4 is less than 5)

But if the denominators are not the same you need to make them the same (using  Equivalent Fractions ).

Example: Which is larger: 3 /8 or 5 /12 ?

If you multiply 8 × 3 you get 24 , and if you multiply 12 × 2 you also get 24, so let's try that (important: what you do to the bottom, you must also do to the top):

× 3

3  = 9

and × 2

5  = 10

8 24

× 3

12 24

× 2

It is now easy to see that 9 /24 is smaller than 10 /24, (because 9 is smaller than 10).

so 5 /12 is the larger fraction.

How to Make the Denominators the Same

The trick is to find the  Least Common Multiple  of the two denominators. In the previous example, the Least Common Multiple of 8 and 12 was 24.

Then it is just a matter of changing each fraction to make it's denominator the Least Common Multiple.

Example: Which is larger: 5 /6 or 13 /15?

The Least Common Multiple of 6 and 15 is 30. So, let's do some multiplying to make each denominator equal to 30 :

× 5

5

 =

25

6 30

× 5

and

× 2

13

 =

26

15 30

× 2

Now we can easily see that 26 /30 is the larger fraction

so 13 /15 is the larger fraction.

 

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