GRE Math : Fractions

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Example Question #441 : Arithmetic

A clothing store can only purchase socks in crates. Each crate has 200 socks and costs $2091.

Quantity A: The amount of socks that can be bought with $12651.

Quantity B: The amount of socks that can be bought with $14574.

Possible Answers:

Quantity B is greater.

The relationship cannot be determined.

Quantity A is greater.

The two quantities are equal.

Correct answer:

The two quantities are equal.

Explanation:

For this problem, realize that the store cannot buy part of a crate of socks. If they only have enough to pay for part of a crate, they might as well not have any money at all.

For the amount of money listed, figure out how many crates can be purchased:

Quantity A

$\frac{12651}{2091}=6.05$

So six crates can be purchased.

Quantity B:

$\frac{14574}{2091}=6.97$

Not quite enough for seven; only six crates can be purchased.

The two quantities are equal.

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Example Question #31 : Fractions

Write 0.45 as a fraction.

Possible Answers:

$\frac{9}{20}$

$\frac{11}{20}$

$\frac{3}{4}$

$\frac{2}{5}$

$\frac{5}{9}$

Correct answer:

$\frac{9}{20}$

Explanation:

.45 is equivalent to 45 out of 100, or $\frac{45}{100}$ .

Divide both the numerator and denominator by 5 to simplify the fraction:

$\frac{9}{20}$

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Example Question #441 : Arithmetic

Choose the answer below which best expresses the following decimal as a fraction (choose the answer which has been reduced/simplified the most):

Possible Answers:

$\frac{61}{500}$

$\frac{122}{1000}$

$\frac{122}{500}$

$\frac{61}{250}$

$\frac{61}{1000}$

Correct answer:

$\frac{61}{500}$

Explanation:

To convert from a decimal to a fraction, simply put the digits over followed by a number of zeroes equal to the number of digits:

$.122 = \frac{122}{1000}$

Then, you can reduce:

$\frac{122}{1000}=\frac{2\cdot 61}{2 \cdot 500}=\frac{61}{500}$

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Example Question #448 : Arithmetic

Choose the answer below which best expresses the following decimal as a fraction (choose the answer which has been reduced/simplified the most):

0.47

Possible Answers:

$\frac{94}{200}$

$\frac{47}{100}$

$\frac{47}{10}$

$\frac{47}{1000}$

$\frac{23}{56}$

Correct answer:

$\frac{47}{100}$

Explanation:

To convert from a decimal to a fraction, simply put the digits over one followed by a number of zeroes equal to the number of digits:

$0.47=0.47 \cdot \frac{100}{100}=\frac{47}{100}$

is prime, so there's no way to reduce. You're done!

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Example Question #449 : Arithmetic

Choose the answer below which best expresses the following decimal as a fraction (choose the answer which has been reduced/simplified the most):

0.022

Possible Answers:

$\frac{11}{50}$

$\frac{11}{500}$

$\frac{22}{1000}$

$\frac{22}{100}$

$\frac{11}{250}$

Correct answer:

$\frac{11}{500}$

Explanation:

To convert from a decimal to a fraction, simply put the digits over one followed by a number of zeroes equal to the number of digits:

$0.022=0.022\cdot \frac{1000}{1000}=\frac{022}{1000}$

The zero in front of the can be removed, leaving: $\frac{22}{1000}$ , which can be reducted to:

$\frac{22}{1000}=\frac{2\cdot 11}{2\cdot 500}=\frac{11}{500}$

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Example Question #451 : Arithmetic

Choose the answer below which best expresses the following decimal as a fraction (choose the answer which has been reduced/simplified the most):

0.97

Possible Answers:

$\frac{97}{100}$

$\frac{9}{10}$

$\frac{97}{10}$

$\frac{34}{10}$

$\frac{34}{50}$

Correct answer:

$\frac{97}{100}$

Explanation:

To convert from a decimal to a fraction, simply put the digits over one followed by a number of zeroes equal to the number of digits:

$0.97=0.97\cdot \frac{100}{100}=\frac{97}{100}$

You cannot reduce, as one of the numbers in the fraction is prime, so that's your final answer.

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Example Question #31 : Fractions

Choose the answer below which best expresses the following decimal as a fraction (choose the answer which has been reduced/simplified the most):

0.82

Possible Answers:

$\frac{820}{1000}$

$\frac{82}{100}$

$\frac{82}{1000}$

$\frac{41}{50}$

$\frac{51}{100}$

Correct answer:

$\frac{41}{50}$

Explanation:

To convert from a decimal to a fraction, simply put the digits over one followed by a number of zeroes equal to the number of digits:

$0.82=0.82\cdot \frac{100}{100}=\frac{82}{100}$

Then, you can reduce for your final answer:

$\frac{82}{100}=\frac{2\cdot 41}{2\cdot 50}=\frac{41}{50}$

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Example Question #1 : Operations

What is the result of adding $20\%$ of $\frac{2}{7}$ to $\frac{1}{4}$ ?

Possible Answers:

$\frac{23}{11}$

$\frac{43}{140}$

$\frac{47}{140}$

$\frac{3}{28}$

$\frac{3}{39}$

Correct answer:

$\frac{43}{140}$

Explanation:

Let us first get our value for the percentage of the first fraction. 20% of 2/7 is found by multiplying 2/7 by 2/10 (or, simplified, 1/5): (2/7) * (1/5) = (2/35)

Our addition is therefore (2/35) + (1/4). There are no common factors, so the least common denominator will be 35 * 4 or 140. Multiply the numerator and denominator of 2/35 by 4/4 and the numerator of 1/4 by 35/35.

This yields:

(8/140) + (35/140) = 43/140, which cannot be reduced.

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Example Question #1 : How To Add Fractions

Reduce to simplest form: $\frac{1}{4}+(\frac{4}{3}\times \frac{3}{8})-(\frac{1}{4}\div \frac{3}{8})$

Possible Answers:

$\frac{1}{4}$

$\frac{1}{12}$

$\frac{3}{8}$

$\frac{3}{4}$

$\frac{1}{3}$

Correct answer:

$\frac{1}{12}$

Explanation:

Simplify expressions inside parentheses first: $\dpi{100} \small \left (\frac{4}{3} \times \frac{3}{8} \right ) = \frac{12}{24} = \frac{1}{2}$ and $\dpi{100} \small \left (\frac{1}{4} \div \frac{3}{8} \right ) = \left (\frac{1}{4} \times \frac{8}{3} \right ) = \frac{8}{12} = \frac{2}{3}$

Now we have: $\frac{1}{4} + \frac{1}{2} - \frac{2}{3}$

Add them by finding the common denominator (LCM of 4, 2, and 3 = 12) and then multiplying the top and bottom of each fraction by whichever factors are missing from this common denominator:

$\dpi{100} \small \frac{1\times 3}{4\times 3} + \frac{1\times 6}{2\times 6} - \frac{2\times 4}{3\times 4} =\frac{3}{12} + \frac{6}{12} - \frac{8}{12} = \frac{1}{12}$

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Example Question #2 : How To Add Fractions

Quantity A: $\frac{15}{x}+\frac{12}{y}$

Quantity B: $\frac{15y+12x}{xy}$

Which of the following is true?

Possible Answers:

Quantity A is larger.

The two quantities are equal.

Quantity B is larger.

The relationship between the two quantities cannot be determined.

Correct answer:

The two quantities are equal.

Explanation:

Start by looking at Quantity A. The common denominator for this expression is . To calculate this, you perform the following multiplications:

$\frac{15}{x}*\frac{y}{y}+\frac{12}{y}*\frac{x}{x}$

This is the same as:

$\frac{15y}{xy}+\frac{12x}{xy}$ , or $\frac{15y+12x}{xy}$

This is the same as Quantity B. They are equal!

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GRE Math : Fractions

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #441 : Arithmetic

Example Question #31 : Fractions

Example Question #441 : Arithmetic

Example Question #448 : Arithmetic

Example Question #449 : Arithmetic

Example Question #451 : Arithmetic

Example Question #31 : Fractions

Example Question #1 : Operations

Example Question #1 : How To Add Fractions

Example Question #2 : How To Add Fractions

All GRE Math Resources

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