Step by step
The question
Question: simplify this fraction.
On top: 2 + 1/2.
At the bottom: 5/4.
A fraction with fractions inside is called a complex fraction.
1 Find the common bottom
The small fractions have bottoms 2 and 4.
The smallest thing they all go into is 4.
4 is in the 2 times table.
Careful!
We multiply EVERY part by 4, also the part with no small bottom.
Leaving it out is the usual mistake.
2 Times 4 on top and bottom
4/4 is 1.
Times 1 does not change the value.
We multiply the top and the bottom by 4.
Then the small fractions go away.
3 Multiply every part
Every part times 4.
4 times 2 is 8.
4 times 1/2: the bottom 2 goes into 4, so we get 2.
So we get (8 + 2)/5.
No more small fractions!
Like terms go together: 10/5.
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 2.
5 Check
Let's check the long way: work out the top and the bottom first.
The top is 5/2, the bottom is 5/4.
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 4 on top and bottom.
Then: multiply every part.
Then: simplify.
Last: check.