Step by step
The question
Question: 26 is 40% of what number?
We write it like this: 40% of the number is 26.
26 is a part.
The whole number is what we want.
Careful!
Many people work out 40% of 26.
But 26 is not the whole.
It is only 40% of it.
1 Write the percent as a fraction
Percent means out of 100.
So 40% is 40/100.
To make it simpler: What goes into 40 and 100?
We list the numbers that go into each.
Into 40: 1, 2, 4, 5, 8, 10, 20, 40.
Into 100: 1, 2, 4, 5, 10, 20, 25, 50, 100.
20 is the biggest one in both lists.
We divide the top and the bottom by 20.
So 40% is 2/5: 2 of 5 equal parts.
2 Find one part
2 parts make 26.
So one part is 26 divided by 2.
That is 13.
3 Find the whole
The whole is 5 parts.
5 times 13 is 65.
So 26 is 40% of 65.
4 Check
Let's check: is 40% of 65 really 26?
40% is 2/5.
Of means times.
65 divided by 5 is 13.
2 times 13 is 26.
We get 26.
So it is right!
Let's look back.
First: write the percent as a fraction.
Then: find one part.
Then: find the whole.
Last: check.