Need help understanding percentages

Question

1. I needed the percent of 23 over 50. Which is 46% if you divide the top by the bottom. Why don’t I get the same answer if I turn 23 into .23 and multiply it by 50.

Answer 1

Well, 23/50 = 0.46 = 46/100 = 46%.

 

The way it is taught, (23/50)100 = 46, so 23/50 = 46%.

 

By taking 23 and turning it into 0.23, you've DIVIDED by 100 and are then multiplying by 50, so you are turning it upside down to (23/100)50, which obviously isn't the same.

Answer 2

You don't get the same answer because multiplying 0.23 by 50 is not the right procedure.  If you turn 23 into 0.23, you need to divided it by 0.50:

 

23/50 = 0.23/0.50 = 0.46 = 46%

 

Another way to think of it is that 0.5 = (1/2):

 

0.23/0.5 = 0.23/(1/2) = 0.23·(2/1) = 0.46 = 46%

 

Way #3:

 

23/50 = x/100%

 

Solve for x