46.5 is what percent of 406 - 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 406 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 406, so we can write it down as 100%=406.
4. We know, that x% equals 46.5 of the output value, so we can write it down as x%=46.5.
5. Now we have two simple equations:
1) 100%=406
2) x%=46.5
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%=406/46.5
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 46.5 is what percent of 406

100%/x%=406/46.5
(100/x)*x=(406/46.5)*x       - we multiply both sides of the equation by x
100=8.7311827956989*x       - we divide both sides of the equation by (8.7311827956989) to get x
100/8.7311827956989=x
11.453201970443=x
x=11.453201970443

now we have:
46.5 is 11.453201970443% of 406