GRE Math: How to find Percents

GRE Math: How to find Percents

Percent is another method of describing parts of a whole. We can think of a percent as a part

over the total number. We describe a percent as Part / Whole , where whole = 100.

Example: Out of 100 students (the total number of students and also the “whole”), 85 of them (the

“part”) slept till noon the day after their finals ended.

From this word problem, we can set up the fraction.

Percents can be fractions or decimals when a conversion step is made. The following shows

these steps:

Percents & Fractions:

Percents means hundredths (1/100): So 75% converts to 75 x 1/100 without the symbol (%).

From this we see that when we have a percentage we can simply take the number, in this case

75, and put it over 100 making a fraction.

Example: 4% = 4/100, 2.5% = 2.5/100, 3000% = 3000/100

In the same way we might want to convert from a fraction back to a percent. (This conversion is

usually used when one needs a percent for an answer to a word problem). To do this conversion we

simply do away with the denominator, usually a hundred, and add the percentage symbol (%).

Example: 2/100 = 2%, 600/100 = 600%, 3.4/100 = 3.4% 

Percents & Decimals:

Since percent means hundreds (1/100) we can also look at a hundredth in decimal form (.01).

So 75% also converts 75 x (.01) = .75 without the symbol (%).

Example: 4% = 4 x .01 = .04, 3000 x .01 = 30, 2.5 % x .01 = .025

From this we see that when we have a percentage we can simply take the number, in this case 75, and

multiply it by the number .01.

Note that 75% = 75/100 = .75

Again, in the same way, we might want to convert from a decimal back to a percent. (This conversion is usually used when one needs a percent for an answer to a word problem). To do this conversion we take the number, sometimes a decimal and multiply it by 100%. To do this we multiply the number by 100 and add on a percentage symbol (%).

Example:     .02 x 100% = 2%,                            3.4 x 100% = 340%

                   600 x 100% = 60,000%                    .58 x 100% = 58% 

What to do when the denominator is not 100:

In order to convert a fraction to a percent we must realize a fraction is simply a division

problem. 

Example:

Now we have a number (sometimes a decimal) to convert to a percent, which we already

have done.

Example:      4 x 100% = 400%                                       .5 x 100% = 50%

                .625 x 100% = 62.5%

Note: We can omit the multiplying step and just move the decimal 2 to the right.

To convert a mixed number (a whole number and a fraction) to a percentage, we can convert

it to a complete fraction. To do this, multiply the whole number and the denominator (the

bottom number of the fraction) and add that result to the numerator (the top number of the

fraction). The final result is left over the denominator of the fraction. 

Example: 3 ½ ⇒ (1) 3 x 2 = 6                           4 5/6 ⇒ (1) 4 x 6 = 24

                             (2) 6 + 1 = 7                                        (2) 24 + 5 = 29

                             (3) 7/2                                                  (3) 29/6 

From this point we can go back to the directions on how to convert a fraction to a percent.

Example: