Step by step
The question
Question: work out 3/5 − 1/2 + 1/10.
1 Plus and minus
Plus and minus: we go from left to right.
The bottom numbers are 5 and 2.
They are different, so we can't take away the tops yet.
We count up in 5s and in 2s.
10 is the first number in both lists.
So 10 will be the new bottom.
5 times 2 is 10.
So 3/5 gets times 2/2.
2 times 5 is 10.
So 1/2 gets times 5/5.
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.
3 times 2 is 6.
5 times 2 is 10.
1 times 5 is 5.
2 times 5 is 10.
Now both have 10 at the bottom.
The bottoms are the same, so the pieces are the same size.
We take away the tops.
The bottom stays 10, because the size of the pieces does not change.
6 minus 5 is 1.
The bottoms are the same, so the pieces are the same size.
We add the tops.
The bottom stays 10, because the size of the pieces does not change.
1 plus 1 is 2.
Both 2 and 10 can be divided by 2.
That makes it simpler.
So it is 1/5.
Can we make it simpler?
No number goes into both 1 and 5, except 1.
So it stays like this.
So the answer is 1/5.