Adding Fractions with Unlike Denominators

Adding fractions, just like any other mathematics problem, may seem a bit difficult at first. However, once you know the basic formula and you start practicing it, fraction problem solving will not take more than a couple of minutes. Scroll down for two simple methods of adding fractions with unlike denominators.

Methods of Adding Fractions with Unlike Denominators

Adding fractions with unlike denominators lesson plans should always start with a revision of the basics of fractions. Let's take an example:

In the fraction 3/4 , 3 is the numerator and 4 is the denominator.

There is one rule in fractions, which applies whether we are adding, subtracting or comparing fractions and that is - the denominator is always the same. You may read further on subtracting fractions with unlike denominators. So, if we have to add up fractions 3/4 and 2/4, the denominator is already same i.e. 4. In such a case, adding both these fractions would be like:

3/4 + 2/4 = 5/4

This is pretty easy as all we had to do was to add up the numerators. Now, let's take two such fractions in which the denominator is not the same. For example, 3/5 and 6/7. In such a case, we need to make the denominator same first, only then we can add up the numerators. A simple way to do that is to follow the cross multiplication method.

Cross-multiplication Method

Let's start with adding fractions with unlike denominators examples. If we have to add up 3/5 and 6/7, to make denominator same, we multiply both the denominators. In this case, denominator will be 5*7 = 35.

The denominator is 35. Now, before adding up the numerators, they need to be first of all multiplied with the same number the denominator has been multiplied with. In the fraction 3/5, denominator 5 was multiplied by 7 to arrive at 35, the common denominator. So, the numerator 3 too will be multiplied by 7, hence the numerator becomes 3*7 = 21. Likewise, in the fraction 6/7, the numerator is multiplied by 5 as the denominator 7 was multiplied by 5 too, hence the numerator becomes 30. Let's see this adding fractions with different denominators problem mathematically:

3/5 + 6/7 = 3*7/5*7 + 6*5/7*5 = 21/35 + 30/35 = 51/35

Lowest Common Multiple (LCM) Method

There is another method of adding fractions with unlike denominators, which is called the LCM method. This method however, can only be used if either one the denominators is a factor of the other or if their LCM can be found. Let's take an example here of the fractions 7/10 + 9/20. In this case, if we have to add both these fractions, we need to make the denominator same first. It can be done through the cross multiplication method above, however an easy method here will be the LCM method, since we can see that the denominator 10 is a factor of the denominator 20.

The LCM of the denominators 10 and 20, which are factors of each other, is the bigger number out of the two i.e. 20. So, 20 is now the common denominator. As in the previous method, before adding up numerators, they are multiplied by the same number the denominator is multiplied to arrive at the common denominator. So, for fraction 7/10, to arrive at 20, denominator 10 is multiplied by 2, hence numerator 7 is multiplied by 2 as well. Likewise, for fraction 9/20, to arrive at 20, denominator 20 is multiplied by 1 so numerator is multiplied by 1 as well, hence numerator remains the same as 9*1 = 9. Let us see the problem mathematically:

7/10 + 9/20 = 7*2/10*2 + 9*1/20*1 = 14/20 + 9/20 = 23/20

Here's hoping that the above information will prove useful when you set out to do your homework. Adding fractions with unlike denominators activities and problems need to be practiced everyday if you want to perfect this mathematical concept. So, solve as many fraction problems as you can, till you are able to master the whole concept!