Question

What does 46 out of a 105 equal?

Answer 1

1. We assume, that the number 105 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 105, so we can write it down as 100%=105. 
4. We know, that x% equals 46 of the output value, so we can write it down as x%=46. 
5. Now we have two simple equations:
1) 100%=105
2) x%=46
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%=105/46
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 46 is what percent of 105

100%/x%=105/46
(100/x)*x=(105/46)*x       - we multiply both sides of the equation by x
100=2.2826086956522*x       - we divide both sides of the equation by (2.2826086956522) to get x
100/2.2826086956522=x 
43.809523809524=x 
x=43.809523809524

now we have: 
46 is 43.809523809524% of 105