Comparing Fractions

Made Easy!

Comparing fractions is different from what you have been doing with integers. It involves a little bit of work to understand initially but then once you have enough practice going into it things becomes dead simple.

Let’s have a look at what all is there in store for you.

While talking of comparison there are three different cases that come into the picture. They are mentioned below

• Fractions with like denominator
• Fractions with unlike denominator
• Mixed fractions

Let’s get deep into the stuff now

Comparing Fractions with Like Denominators

Lets compare 1/3 and 2/3.

The question here is to decide which of the two fractions is greater.

Step #1 Take the numerators of the two numbers. Compare these two numbers against each other. Thus for our example we pick the two numerators as 1 and 2 and then compare them against each other.

Step #2 The fraction corresponding to the greater numerator is greater. Thus when we compare the numerators 1 and 2 it’s easy to access that 2 is greater than 1. Thus the fraction 2/3 corresponding to the greater numerator 2 happens to be the greater of the two given fractions.

Thus, of the two numbers in our example 1/3 and 2/3, 2/3 is the greater fraction.

Comparing Fractions with Unlike Denominators

The two numbers we will compare here are 1/3 and 4/5.

Note that in the two fractions above the denominators are different.

Equivalent Fractions Method

Step #1 The idea here is to convert the fractions to their equivalent form such that the equivalent fractions have similar denominator. We observe that the denominators in the two fractions are 3 and 5 respectively. The common multiple for both these numbers can be 15. Thus we must try to convert the fractions into their equivalent form with denominator being 15.

Step #2 Convert the fractions into their equivalent form.

For fraction 1/3 we have to multiply the denominator with 5 to make it 15. Thus the same number that is 5 is multiplied to the numerator as well to ensure that the new fraction is an equivalent of 1/3. Thus the new denominator is 15 and the new numerator is 5 and the fraction is 5/15.

Similarly for fraction 4/5 the denominator is multiplied by 3 to make it 15. Thus the numerator is to be multiplied by 3 as well. The new numerator becomes 12 and the equivalent fraction is 12/15.

Step #3 Now we have the two equivalent fractions to be compared. From here comparing fractions is similar to comparison of fractions with like denominators. As discussed earlier.

The two fractions at our disposal for comparison are 5/15 and 12/15 respectively. As the denominators are same therefore the higher denominator makes the fraction greater. As you know 12 is greater than 5. Thus 12/15 is greater than 5/15. Hence 4/5 is greater than 1/3.

Lowest Common Denominator Method

Fractions to be compared: ¼ and 2/6

Step #1 Take the denominators of the two fractions and find the lowest common multiple of the two numbers. For the example we have taken the denominators are 4 and 6. The LCM of the two numbers is 12.

Step #2 Now convert the two fractions to their equivalents such that the denominator in each case equals to the LCM from step #1 that is 12.

The denominator in ¼ is 4 which is multiplied by 3 to make the denominator as 12. Thus the numerator is also multiplied by 3 to evaluate the equivalent numerator. Thus the new fraction is 3/12.

Similarly the fraction 2/6 becomes 4/12.

Step #3 The two numbers obtained after step #2 for comparison are 3/12 and 4/12. As you can see here we have two fractions with like denominator. It’s that old time when we got to observe the numerators for comparison. Of 3 and 4, 4 is greater and thus the corresponding fraction 4/12 is greater of the given two.

4/12 happens to be the equivalent form of 2/6. Thus of the two original fractions 2/6 is greater than ¼.

Comparing Mixed Fractions