Fractions and Percentage - GRE Quantitative Reasoning

To do this problem, translate each expression into mathematical terms:

is percent of :

is percent of :

Quantity B is greater.

To solve this problem, consider writing the quantities in terms of only fractions:

Quantity A: 20% of

Quantity B: 30% of

Quantity B has the smaller denominator for an equal numerator. There is no need for calculation beyond this, and time on the GRE would be best spent elsewhere.

Quantity B is greater.

This problem is fairly simple. If we know he scored a , then we know that he got correct answers.

Both the numerator and denominator of the expression are divisible by two, so your final, simplified answer should be:

.

To solve this problem, first convert the percentage into a decimal by dividing the percentage by 100:

Then, you can convert the decimal into a fraction:

Both the numerator and the denomenator are divisible by , so now you may simplify:

To find your answer, first convert the percentage into a decimal:

Then, you can place the digits of the decimal over one, followed by a number of zeroes equal to the number of digits (in this case, 1,000):

Both the numerator and denomenator are divisible by , so you can simplify to:

To convert, simply first convert the percentage into a decimal:

Then, you can convert the decimal into a fraction, by putting the digits over one, followed by a number of zeroes equal to the number of digits:

Both are divisible by five, so you can simplify:

To convert, first express the percentage as a decimal:

Then, you can place the digits of the decimal over one followed by a number of zeroes equal to the number of digits:

Both of these numbers are divisible by , so you can simplify:

First, you must find the total amount of solution. This is , or .

Now, the percentage of the solution that is blood can be represented:

, or

This is the same as % Rounded, it is %

Recall that the formula for percentage increase is:

, where is your ending value and is your starting value.

For our numbers, this would be:

Recall that to find a percentage from a decimal, you multiply by :

First write the percent as a decimal. To convert the decimal into a fraction, multiply the decimal by , then place that number over :

.

Then place over : .

Therefore,

.

Then, reduce the fraction to its lowest terms by dividing through by the greatest common factor of and , which is :

.

So, Lauren has finished of her homework.

To convert percentages to fractions, take the value and divide by .

Let's get rid of the decimal by multiplying top and bottom by or moving the decimal places to the right and adding zeroes to the bottom.

Then reduce by dividing the bottom by to get .

To convert percentages to fractions, take the value and divide it by .

Then simplify as follows.

First convert the complex fraction into an improper fraction.

Multiply the number in front of the fraction with the denominator and then add that to the numerator.

Then to convert percentages to fractions, take the value and divide by .

The first step is to figure out the percentage of construction employees that have stayed in the same role for 5 years or more—this would include both the "5 to 9 year" and "10+ years" ranges. This would be 0.25 + 0.4 = 65% of all construction employees. To convert to the number of employees, we take the percentage of their total, 0.65 * 8,000,000 = 5,200,000 workers. However, since the probability we are attempting to find is of workers between both industries, we must add the 8 million to the 12 million = 20 million workers total. 5,200,000/20,000,000 = 0.26, or a 26% chance.

Simplify Quantity A by dividing the number of oatmeal raisin cookies by the total number of cookies to find the percentage of oatmeal raisin cookies. Since a percentage is defined as being out of 100, either multiply the resulting decimal by 100 or reduce the fraction until the denominator is 100. You will find that the two quantities are equal.

students failed.

which equals 28%.

To solve this problem, first convert the fraction into a decimal, by dividing one by eight:

Then you can convert the decimal into a percentage, by putting the first two digits in the tens and ones digit of the percent (respectively), and any ensuing digits after a decimal for the percentage. Or in otherwords multiply the decimal by 100:

To solve this problem, first you have to convert the fraction into a decimal, which you can do by dividing three by seven:

The decimal appears to be non-repeating, non-terminating, but that's irrelevant, as the problem cautioned you to round to the nearest tenth of a percent. You can convert to a percent, the first two digits of the decimal will be the percentage, and the third will be the tenth of a percent place, and the fourth will determine whether you round up or down:

%

To convert, first divide four by three:

repeating

Now, to convert the decimal into a percentage, the ones digit becomes the hundredes digit of the percentage, and the others follow suit. As the decimal above is repeating, and repeats at three, when you round to the nearest tenth a percent, you will have a three as your final digit:

%