How to find fractional percentages - GRE Quantitative Reasoning

Card 0 of 6

Question

What percentage of a solution is blood if it contains ml blood and ml water? Round to the nearest thousandth?

Answer

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

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

$\frac{1.4}{8418.4}$ , or

This is the same as % Rounded, it is %

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Question

What is the percentage increase of an account that began with a balance of and increased to ?

Answer

Recall that the formula for percentage increase is:

$\frac{(B-A)}{A}$ , where is your ending value and is your starting value.

For our numbers, this would be:

$\frac{250005-250000}{250000}=\frac{5}{250000}=0.00002$

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

$0.00002 \cdot100 = 0.002%$

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Question

Lauren has finished of her homework.

Express her percent of homework finished as a fraction in simplest form.

Answer

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

$0.65\cdot100=65$ .

Then place over : $\frac{65}{100}$ .

Therefore,

$0.65=\frac{65}{100}$ .

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

$\frac{65}{100}=\frac{13}{20}$ .

So, Lauren has finished $\frac{13}{20}$ of her homework.

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Question

Convert to a fraction.

Answer

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

$\frac{.0005}{100}$ 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.

$\frac{5}{1000000}$ Then reduce by dividing the bottom by to get $\frac{1}{200000}$ .

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Question

Convert $\frac{2}{5}%$ to a fraction.

Answer

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

Then simplify as follows.

$\frac{\frac{2}{5}}{100}=\frac{2}{5\cdot 100}=\frac{1}{5\cdot50}=\frac{1}{250}$

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Question

Convert $49\tfrac{3}{4}%$ to a fraction.

Answer

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.

$49\frac{3}{4}=\frac{196+3}{4}=\frac{199}{4}$

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

$\frac{\frac{199}{4}}{100}=\frac{199}{400}$

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