7. Addition and Subtraction of Fractions
Recall that to add or subtract fractions, we need to have the same denominator.
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.
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.
The lowest common denominator here will be 6y4.
So we have:
We can write this as:
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.
The lowest common denominator is 4.
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.