45.4 is what percent of 40.4 - 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 40.4 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 40.4, so we can write it down as 100%=40.4.
4. We know, that x% equals 45.4 of the output value, so we can write it down as x%=45.4.
5. Now we have two simple equations:
1) 100%=40.4
2) x%=45.4
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%=40.4/45.4
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 45.4 is what percent of 40.4

100%/x%=40.4/45.4
(100/x)*x=(40.4/45.4)*x       - we multiply both sides of the equation by x
100=0.88986784140969*x       - we divide both sides of the equation by (0.88986784140969) to get x
100/0.88986784140969=x
112.37623762376=x
x=112.37623762376

now we have:
45.4 is 112.37623762376% of 40.4