Step by step
The question
Question: work out 1/2 + 1/3 × 3/4.
1 Times and divide
Times comes before plus.
Before we multiply, we make the numbers smaller.
3 on top and 3 at the bottom both divide by 3.
A top and a bottom divided by the same number: the answer stays the same.
So we multiply smaller numbers.
To multiply fractions, we do top times top, and bottom times bottom.
1 times 1 is 1.
1 times 4 is 4.
2 Plus and minus
The bottom numbers are 2 and 4.
They are different, so we can't add the tops yet.
We count up in 2s and in 4s.
4 is the first number in both lists.
So 4 will be the new bottom.
2 times 2 is 4.
So 1/2 gets times 2/2.
1/4 already has 4 at the bottom.
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.
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.
2 plus 1 is 3.
Can we make it simpler?
No number goes into both 3 and 4, except 1.
So it stays like this.
So the answer is 3/4.
Let's look back.
First: times and divide.
Last: plus and minus.