Step by step
The question
Question: work out 3/4 + 2/5.
1 Make the bottoms the same
The bottom numbers are 4 and 5.
The bottom tells the size of the pieces.
These pieces are different sizes, so we can't add the tops yet.
We need one bottom number that works for both.
We count up in 4s and 5s.
In 4s: 4, 8, 12, 16, 20.
In 5s: 5, 10, 15, 20.
20 is the first number in both lists.
So 20 works for both.
20 will be the new bottom.
To make 4 into 20, we multiply by 5: 4 × 5 = 20.
To make 5 into 20, we multiply by 4: 5 × 4 = 20.
We multiply the bottom by 5: 4 × 5.
We did it to the bottom, so we must do it to the top too: 3 × 5.
We multiply the bottom by 4: 5 × 4.
We did it to the bottom, so we must do it to the top too: 2 × 4.
Top and bottom times the same number: the fraction keeps its size.
3 × 5 is 15.
4 × 5 is 20.
2 × 4 is 8.
5 × 4 is 20.
Now both have 20 at the bottom.
2 Add the tops
The bottoms are the same, so the pieces are the same size.
We add the tops: 15 + 8.
The bottom stays 20, because the size of the pieces does not change.
15 + 8 is 23.
The bottom stays 20.
Can we make it simpler?
We list the numbers that go into each.
Into 23: 1, 23.
Into 20: 1, 2, 4, 5, 10, 20.
Only 1 is in both lists.
So it stays like this.
So the answer is 23/20.
Let's look back.
First: make the bottoms the same.
Last: add the tops.