Step by step
The question
Question: simplify this fraction.
On top: 1/3 + 1/6.
At the bottom: 1/2 − 1/4.
A fraction with fractions inside is called a complex fraction.
1 Find the common bottom
The small fractions have bottoms 3, 6, 2 and 4.
The smallest thing they all go into is 12.
12 is in the 3 and 6 and 2 and 4 times tables.
2 Times 12 on top and bottom
12/12 is 1.
Times 1 does not change the value.
We multiply the top and the bottom by 12.
Then the small fractions go away.
3 Multiply every part
Every part times 12.
12 times 1/3: the bottom 3 goes into 12, so we get 4.
12 times 1/6: the bottom 6 goes into 12, so we get 2.
So we get (4 + 2)/(6 − 3).
No more small fractions!
Like terms go together: 6/3.
4 Simplify
Every part, on the top and the bottom, can be divided by 3.
So we divide the top and the bottom by it.
So the answer is 2.
5 Check
Let's check the long way: work out the top and the bottom first.
The top is 1/2, the bottom is 1/4.
Then top divided by bottom: times the flip.
We get 2 again.
It works!
Let's look back.
First: find the common bottom.
Then: times 12 on top and bottom.
Then: multiply every part.
Then: simplify.
Last: check.