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7. Addition and Subtraction of Fractions

Recall that to add or subtract fractions, we need to have the same denominator.

Example 1

Add the fractions: `2/3+4/15`

Solution: Here, the lowest common denominator which we can use is `15`. So we have:


Subtraction works in the same way, as we see in the next example.

Example 2



Our lowest common denominator this time is 14. So we have:


When we have algebraic expressions involving fractions, we need to use the same process.

Example 3



The lowest common denominator here will be 6y4.

So we have:


We can write this as:


Example 4



We factor the first denominator to get an idea of what to do:



We can see now that if we multiply the second fraction by 2x2, we will have a common denominator:



We would normally write this as:



Simplify the following.

(1) `2/(s^2)+3/s`





(2) `5+(1-x)/2-(3+x)/4`


The lowest common denominator is 4.





(3) `5/(6y+3)-a/(8y+4)`


`(5)/(6y+3)-(a)/(8y+4)` `=5/(3(2y+1))-a/(4(2y+1))`



We have factored out the 3 at the bottom of the first fraction and the 4 at the bottom of the second fraction.

In the 3rd line, we find the lowest common denominator, 12(2y + 1), and multiply top and bottom of the two fractions accordingly.

The last line is a tidy up step.