Addition of Fractions

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Fractions Units

Adding fractions is done differently than the usual numbers. Normally, while adding or subtracting fractions you will find two types of problems:

Type 1: where the fractions being added have the same denominator eg.

Type 2: where the fractions being added have different denominators eg.

As you know, fractions represent parts of the whole. So, when these parts are from the whole broken into same number of parts it is easy to add them.
For Type 1 problems, we just need to add the top parts (numerator) of the fractions and leave the denominator as such. So, to solve the problem in the above example the solution will be:

For Type 2 problems where the denominator is different, we can not add these fractions by simply adding the numerators. In order to solve these problems first we will need to make into fractions with the same denominator. See how this is done in examples below.

Examples

Example 1

Solve:

changing both fractions to a common denominator (see comments on the right)

Comments:

To solve this problem, first we will need to look at the denominators 3 and 5 and see what multiples of these numbers are common.

Multiples of 3 are:
3 6 9 12 15 18 21

Multiples of 5 are:
5 10 15 20 25

so, in multiples of 3 and 5 the least common multiple is 15.
now, we will change 1/3 and 2/5 into their equivalent fractions with denominator 15:

Example 2

Solve:

Changing both fractions to a common denominator (see comments on the right)

Comments:
Again, we need to look at the denominators first and see what multiples of them are common:

Multiples of 12:
12 24 36

Multiples of 2:
2 4 6 8 10 12 14

So, we find that 12 is the least common multiple.

Have a Go

Problem 1

Solve:

Problem 2

Solve:

Practice Questions

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Solution 1

Solve:
First we need to find the least common multiple of 6 and 9:
6= 6 12 18 24
9= 9 18 27
Now we need to convert both fractions to a common denomintor of 18

This is an improper fraction with the numerator larger than the denominator. We can simply this by dividing 31 by 18 and writing the remainder as a fraction:

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Solution 2

Solve:
This is addition of mixed fractions. Here we can add the whole numbers separately and re-write the fraction as:

Changing the fractions to their equivalent fractions with a common denominator

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