Like Fractions and Unlike Fractions

The concept of like fractions and unlike fractions is used in mathematics to illustrate the concept of operations between fractions. Operations like comparison, addition and division become simple for like fractions and for the most part follow the template of integers or natural numbers. The result of all these operations between like fractions may or may not be a whole number.

Unlike fractions on the other hand arise due to incongruity in scale. Different things need to be evaluated at a different scale. Unlike fractions may be converted into like fractions by multiplying the numerator and the denominator of a fraction with the denominator of the other fraction. For more than one unlike fractions, the step has to be repeated pairwise.

Like Fractions

Like fractions are two or more fractions that share the same denominator. For example:

The fractions written above are all like fractions. They all have the same denominator, that is 2. Adding and comparing unlike fractions is simple. If the denominators of two fractions match, then the larger fraction is the one that has the bigger numerator. This can be explained as below:

We can see that the fraction 3/2 is greater than the fraction ½ because the numerator of the first fraction is bigger than the numerator of the second fraction (3 > 1).

Likewise, we can easily add two like fractions. To add them, we only need to consider the numerator of both the fractions and add them while the denominator of the resultant fraction remains the same unless they have a common divisor greater than one. This can be illustrated below:

We can see above that the resultant fraction is formed by simply adding the numerators while the denominator remains the same.

The same goes for other operations like subtraction. We only need to consider the numerators.

Unlike Fractions

Unlike fractions are two or more fractions with different denominators. Some examples are shown below:

The fractions mentioned above are all unlike fractions. None of them share the same denominator.

Two unlike fractions can be reduced to like fractions if the ratio of the two fractions comes out to be the same. Then the larger fraction can be reduced by dividing it with the HCF of the numerator and the denominator. For example:

Here, the fraction 50/100 can be reduced to ½ if we divide both the numerator and the denominator by 50, which is also the Highest Common Factor of both the numbers.

Operations on Two Unlike Fractions

To perform operations on two unlike fractions we need to convert them first into like fractions. This conversion can be achieved by multiplying the numerator and the denominator of both the fractions by the denominator of the other fraction. This is illustrated below:

Therefore, we have converted two unlike fractions to two like fractions. Now we can apply any operation on them as per the method described for the like fraction.