5.2 is what percent of 40 - step by step solution

To get the solution, we are looking for, we need to point out what we know.

1. We assume, that the number 40 is 100% - because it's the output value of the task.
2. We assume, that x is the value we are looking for.
3. If 100% equals 40, so we can write it down as 100%=40.
4. We know, that x% equals 5.2 of the output value, so we can write it down as x%=5.2.
5. Now we have two simple equations:
1) 100%=40
2) x%=5.2
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
100%/x%=40/5.2
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 5.2 is what percent of 40

100%/x%=40/5.2
(100/x)*x=(40/5.2)*x       - we multiply both sides of the equation by x
100=7.6923076923077*x       - we divide both sides of the equation by (7.6923076923077) to get x
100/7.6923076923077=x
13=x
x=13

now we have:
5.2 is 13% of 40