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.