Step by step
The question
Question: 21 is 35% of what number?
We write it like this: 35% of the number is 21.
21 is a part.
The whole number is what we want.
Careful!
Many people work out 35% of 21.
But 21 is not the whole.
It is only 35% of it.
There are four choices.
First we solve it, the normal way.
Then we pick.
1 Write the percent as a fraction
Percent means out of 100.
So 35% is 35/100.
To make it simpler: What goes into 35 and 100?
We list the numbers that go into each.
Into 35: 1, 5, 7, 35.
Into 100: 1, 2, 4, 5, 10, 20, 25, 50, 100.
5 is the biggest one in both lists.
We divide the top and the bottom by 5.
So 35% is 7/20: 7 of 20 equal parts.
2 Find one part
7 parts make 21.
So one part is 21 divided by 7.
That is 3.
3 Find the whole
The whole is 20 parts.
20 times 3 is 60.
So 21 is 35% of 60.
4 Check
Let's check: is 35% of 60 really 21?
35% is 7/20.
Of means times.
60 divided by 20 is 3.
7 times 3 is 21.
We get 21.
So it is right!
5 Pick the choice
Our answer is 60.
That is choice C.
6 Why not the others
A is 7.35.
Wrong: that is 35% of 21: the other way round.
That is the Careful mistake from before.
B is 56.
Wrong: 21 + 35: added.
D is 735.
Wrong: 21 × 35: forgot that % means out of 100.
Let's look back.
First: write the percent as a fraction.
Then: find one part.
Then: find the whole.
Then: check.
Then: pick the choice.
Last: why not the others.