Step by step
The question
Question: work out −3/4 + 1/2.
1 Make the bottoms the same
The bottom numbers are 4 and 2.
They are different, so we can't add the tops yet.
We count up in 4s and in 2s.
4 is the first number in both lists.
So 4 will be the new bottom.
−3/4 already has 4 at the bottom.
2 times 2 is 4.
So 1/2 gets times 2/2.
We multiply the top and the bottom by the same number.
2/2 is 1.
Times 1 does not change the size.
So the fraction stays the same, only the bottom changes.
Top times top.
Bottom times bottom.
1 times 2 is 2.
2 times 2 is 4.
Now both have 4 at the bottom.
2 Add the tops
The bottoms are the same, so the pieces are the same size.
We add the tops.
The bottom stays 4, because the size of the pieces does not change.
−3 plus 2 is −1.
Can we make it simpler?
No number goes into both 1 and 4, except 1.
So it stays like this.
So the answer is −1/4.
Let's look back.
First: make the bottoms the same.
Last: add the tops.