Three tips for ordering and comparing fractions

Compare and order fractions

All fractions do not have the same value. A fraction can be smaller than other fractions and it can be larger than some other fractions. Therefore, children need to know how to compare fractions. The comparison can be subdivided into three sections. So kids need to know three tricks to learn this skill.

Trick number 1:

The first trick to comparing fractions is to see if they have the same numerators. If the numerators are the same, then the fraction with the largest denominator is the smallest. For example; Consider the following fractions:

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

Since all the above fractions have the same numerator (3), to compare them we need to compare their denominators. The larger denominator makes the fraction smaller, so 3/8 is the smallest of all and 3/4 is the largest. Let’s rewrite all the fractions in order from least to greatest as shown below:

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

The order above (lowest to highest) is also known as ascending order.

Trick number 2:

The second trick is just as easy as the first. This trick consists of comparing fractions, when they have the same denominator. When the denominators are the same, then the fraction with the smallest numerator is the smallest and the one with the largest numerator is the largest. For example;

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

Look at the given fractions, they all have the same denominator (9). So 1/9 is the smallest because it has the smallest numerator and 7/9 is the largest with the largest numerator. They are then written in ascending order.

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

Trick number 3:

The two tips above explain comparing fractions with the same numerators or the same denominators. But most of the time children are asked to compare and order fractions with different numerators and denominators.

In such a case, they need to make the denominator of all the fractions the same. To do this they need to know the least common divisor (lcm) of all the denominators, also known as the least common denominator (lcm).

Consider the following example of comparing fractions:

Write the following fractions in descending order (from greatest to least)

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

Solution: Look, most fractions have different denominators. Write all the denominators as shown below and write the 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 least common of all of them, which in this case is 12. So, lcm or gcd is 12. The next step is to rewrite all the fractions into equivalent fractions with a denominator of 12. This step is shown below:

2/3, we need to multiply its denominator (3) by 4 to change it to 12. But to keep the value of the same fraction, don’t forget to multiply the numerator (2) by the same number 4. Let’s do that;

(2×4)/(3×4) = 8/12

In the same way, write all the fractions with a 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 the same denominator 12 and it is easy to compare them. Write all the equivalent fractions in descending order (from greatest to least)

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

But these are not the fractions you are asked to compare. So this is not our answer, but now it is very easy to write the original fractions in the required order by noting the above order. We know that 10/12 equals 5/6 and 3/12 equals 1/4, so 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, children must take into account the three previous tips. Of course, knowledge of the Least Common Multiple (LCM) is the key to comparing two or more fractions with different denominators.