+2446 Well, I had a plan to respond, but then this happened:
| PLAN | ||
| (P+L)(A+N) | ||
| PA+PN+LA+LN |
My plans were foiled...
+2446
First, convert 62.5% to a fraction or decimal. I personally like fractions, so that is what I'll use:
| \(62.5\%\) | Convert into fraction by putting whatever is to the left of percent over 100 |
| \(\frac{62.5}{100}\) | Multiply each side by 10 on both sides to get rid of the decimal in the numerator |
| \(\frac{625}{1000}\div\frac{125}{125}\) | Divide the numerator and denominator by their GCF, 125, to simplify the fraction fully |
| \(\frac{5}{8}\) | |
Isn't that nice? \(62.5\%\) simplifies to, in a fraction, \(\frac{5}{8}\). By doing this, we have simplified the problem from \(62.5\%*50\) to \(\frac{5}{8}*\frac{50}{1}\). Now, let's simplify further to get our final answer:
| \(\frac{5}{8}*\frac{50}{1}\) | Multiply these fractions by multiplying the numerators and denominators. |
| \(\frac{250}{8}\div\frac{2}{2}\) | Put improper in simplest terms by dividing by 2 on both the numerator and denominator |
| \(\frac{125}{4}=31\frac{1}{4}=31.25\) | I've placed the final answer in different forms. |
Okay, the answer is clearly \(31.25\). However, there is a trick any percentage of 50. Do this:
This is probably best demonstrated by example. I'll use the problem above, which is \(62.5\%*50\).
Step 1 says to remove the percent sign, so \(62.5\%\) becomes \(62.5\).
Step 2 says divide the result by 2. \(62.5/2= 31.25\). Does this answer seem familiar? It should. It is the same answer as we got above but using different steps.
