Step by step
The question
Question: simplify this fraction.
On top: 2 + 1/4.
At the bottom: 3/8.
A fraction with fractions inside is called a complex fraction.
1 Find the common bottom
The small fractions have bottoms 4 and 8.
The smallest thing they all go into is 8.
8 is in the 4 times table.
Careful!
We multiply EVERY part by 8, also the part with no small bottom.
Leaving it out is the usual mistake.
2 Times 8 on top and bottom
8/8 is 1.
Times 1 does not change the value.
We multiply the top and the bottom by 8.
Then the small fractions go away.
3 Multiply every part
Every part times 8.
8 times 2 is 16.
8 times 1/4: the bottom 4 goes into 8, so we get 2.
So we get (16 + 2)/3.
No more small fractions!
Like terms go together: 18/3.
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 6.
5 Check
Let's check the long way: work out the top and the bottom first.
The top is 9/4, the bottom is 3/8.
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 8 on top and bottom.
Then: multiply every part.
Then: simplify.
Last: check.