Step by step
The question
Question: simplify this fraction.
On top: 1 + 1/3.
At the bottom: 2/9.
A fraction with fractions inside is called a complex fraction.
1 Find the common bottom
The small fractions have bottoms 3 and 9.
The smallest thing they all go into is 9.
9 is in the 3 times table.
Careful!
We multiply EVERY part by 9, also the part with no small bottom.
Leaving it out is the usual mistake.
2 Times 9 on top and bottom
9/9 is 1.
Times 1 does not change the value.
We multiply the top and the bottom by 9.
Then the small fractions go away.
3 Multiply every part
Every part times 9.
9 times 1 is 9.
9 times 1/3: the bottom 3 goes into 9, so we get 3.
So we get (9 + 3)/2.
No more small fractions!
Like terms go together: 12/2.
4 Simplify
Every part, on the top and the bottom, can be divided by 2.
So we divide the top and the bottom by it.
So the answer is 6.
5 Check
Let's check the long way: work out the top and the bottom first.
The top is 4/3, the bottom is 2/9.
Then top divided by bottom: times the flip.
We get 6 again.
It works!
Let's look back.
First: find the common bottom.
Then: times 9 on top and bottom.
Then: multiply every part.
Then: simplify.
Last: check.