Step by step
The question
Question: work out 1 and 1/2 + 2 and 2/3.
1 Make one fraction
1 and 1/2 is a mixed number.
Each whole one is 2/2.
So we do 1 times 2, plus 1.
The bottom stays 2.
1 times 2 plus 1 is 3.
So it is 3/2.
2 and 2/3 is a mixed number.
Each whole one is 3/3.
So we do 2 times 3, plus 2.
The bottom stays 3.
2 times 3 plus 2 is 8.
So it is 8/3.
2 Make the bottoms the same
The bottom numbers are 2 and 3.
They are different, so we can't add the tops yet.
We count up in 2s and in 3s.
6 is the first number in both lists.
So 6 will be the new bottom.
2 times 3 is 6.
So 3/2 gets times 3/3.
3 times 2 is 6.
So 8/3 gets times 2/2.
We multiply the top and the bottom by the same number.
3/3 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.
3 times 3 is 9.
2 times 3 is 6.
8 times 2 is 16.
3 times 2 is 6.
Now both have 6 at the bottom.
3 Add the tops
The bottoms are the same, so the pieces are the same size.
We add the tops.
The bottom stays 6, because the size of the pieces does not change.
9 plus 16 is 25.
4 Write as a mixed number
25 divided by 6 is 4, with 1 left over.
So it is 4 and 1/6.
So the answer is 4 and 1/6.
Let's look back.
First: make one fraction.
Then: make the bottoms the same.
Then: add the tops.
Last: write as a mixed number.