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