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How to Add Fractions

In this page we will learn How to Add Fractions help. Fractions is an important topic in Math. Fractions are numbers expressed in the form of ' a / b '. They are ratios expressed differently. They consist of a numerator and a denominator. In calculations, we do not deal always with the whole numbers. Many a time we need to work with fractions. Hence knowledge in operations with fraction is very important. Let us see the procedure of adding fractions in this section.

What is Adding Fractions

Various mathematical operations can be conducted on Fractions like Addition, multiplication, division and subtraction. Adding fractions involves adding up or summing two 'parts'. Like adding a quarter (1/4) and a half (1/2) of something would result in a 3/4th. Adding fractions can be of different types based on the kind of fractions involved. The kind of fractions are determined on the values of the Numerators and the denominators. They are:

  • Addition of Like fractions ( same denominator value) Example: `1/2 + 3/2`
  • Addition of Unlike fractions ( different denominators) Example: `1/2 +3/4`

If the fractions in question are Like fractions, there is no need to find the equivalent fraction for the process of addition , else the fraction equivalent to the value of the denominator of one of the selected fractions has to be figured before adding them.

Adding Fractions with the same Denominator

There are some websites which provide free online help on adding fractions. The algorithm in such online calculators is based on the techniques of adding fractions. The concept behind such add fraction calculators is explained below.

Let 3/8 and 1/8 are given fractions. The denominators are same. Hence they are added in the following way.

`3/8+1/8=(3+1)/8=4/8=1/2`

Suppose the fractions are 3/4 and 1/6. Since the denominators are different we can not add the numerators directly.

Here we have to find a common denominator for which 4 and 6 are the factors. The product 4 x 6 = 24 could be a solution but we need to check whether any other smaller number is available. By finding the lowest common multiple of 4 and 6, we find 12 could be the common denominator.

Hence always find the lowest common multiple of the given denominators and use that as the common denominator.

Convert the given fraction into their equivalent fractions, with the denominator as the common denominator figured out. Now since the denominators are common, the addition of fractions becomes simple. Students can also learn how to add fractions with different denominators from the tutors online.

Adding Fractions with Different Denominators

The equivalent fraction of 1/3 with denominator 15 is 5/15 and the equivalent fraction of 1/5 with denominator 15 is 3/15 Therefore, the answer to add the fractions is,

`1/3 +1/5`

=`5/15+3/15` ( `1/3``5/5` , `1/5` X`3/3` The fraction is multiplied by the denominator of the other)

= `8/15`

Adding Fractions Examples

The following algebra homework example illustrates how to add fractions.

Example 1:

`1/2+3/4` = ?

`1/2+3/4= 2/4+3/4` (L.C.M of 2 and 4 is 4. So the equivalent fraction of `1/2` having 4 as the denominator would be `2/4` )

= `(2+3)/4`

= `5/4`

= `1/4`


Example 2:

`5/6+1/8` = ?

`5/6+1/8` = `20/24+3/24` (L.C.M of 6 and 8 is 24. So the equivalent fraction of `5/6` with 24 as the denominator is `20/24` )

=`(20+3)/24`

=`23/24`