GRE Math : Fractions

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Example Question #461 : Arithmetic

Car A traveled 120 miles with 5 gallons of fuel.

Car B can travel 25 miles per gallon of fuel.

Quantity A: The fuel efficiency of car A

Quantity B: The fuel efficiency of car B

Possible Answers:

Quantity A is greater.

Quantity B is greater.

The relationship cannot be determined.

The two quantities are equal.

Correct answer:

Quantity B is greater.

Explanation:

Let's make the two quantities look the same.

Quantity A: 120 miles / 5 gallons = 24 miles / gallon

Quantity B: 25 miles / gallon

Quantity B is greater.

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Example Question #52 : Fractions

Quantity A:

The -value of the equation $y = \frac{3}{4}x-2$ when $y = \frac{-1}{3}$

Quantity B:

$\frac{3}{4}$

Possible Answers:

The relationship cannot be determined from the information given.

Both quantities are equal

Quantity A is greater.

Quantity B is greater.

Correct answer:

Quantity A is greater.

Explanation:

In order to solve quantitative comparison problems, you must first deduce whether or not the problem is actually solvable. Since this consists of finding the solution to an -coordinate on a line where nothing too complicated occurs, it will be possible.

Thus, your next step is to solve the problem.

Since $y = \frac{3}{4}x-2$ and $y = \frac{-1}{3}$ , you can plug in the -value and solve for :

$y = \frac{3}{4}x-2$

Plug in y:

$\frac{-1}{3} = \frac{3}{4}x-2$

Add 2 to both sides:

$\frac{5}{3} = \frac{3}{4}x$

Divide by 3/4. To divide, first take the reciprocal of 3/4 (aka, flip it) to get 4/3, then multiply that by 5/3:

$\frac{20}{9} = x$

Make the improper fraction a mixed number:

$2\tfrac{2}{9}$

Now that you have what x equals, you can compare it to Quantity B.

Since $2\tfrac{2}{9}$ is bigger than 2, the answer is that Quantity A is greater

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Example Question #53 : Fractions

What is equivalent to $\frac{\frac{1}{5}}{\frac{4}{15}}$ ?

Possible Answers:

$\frac{5}{4}$

$\frac{4}{75}$

$\frac{6}{5}$

$\frac{4}{5}$

$\frac{3}{4}$

Correct answer:

$\frac{3}{4}$

Explanation:

Remember that when you divide by a fraction, you multiply by the reciprocal of that fraction. Therefore, this division really is:

$\frac{1}{5}\cdot \frac{15}{4}$

At this point, it is merely a matter of simplification and finishing the multiplication:

$\frac{1}{5}\cdot\frac{15}{4}=\frac{15}{20}=\frac{3}{4}$

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Example Question #54 : Fractions

Which of the following is equivalent to $\frac{7}{\frac{4}{5}}$ ?

Possible Answers:

$\frac{35}{4}$

$\frac{28}{5}$

$\frac{5}{28}$

$\frac{11}{5}$

$\frac{4}{35}$

Correct answer:

$\frac{35}{4}$

Explanation:

To begin with, most students find it easy to remember that...

$\frac{7}{\frac{4}{5}}=\frac{\frac{7}{1}}{\frac{4}{5}}$

From this, you can apply the rule of division of fractions. That is, multiply by the reciprocal:

Therefore,

$\frac{\frac{7}{1}}{\frac{4}{5}} = \frac{7}{1} \cdot \frac{5}{4}=\frac{35}{4}$

Since nothing needs to be reduced, this is your answer.

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Example Question #1 : How To Find The Reciprocal Of A Fraction

Carpenter A takes 45 hours to build a table. Carpenter B takes 30 hours. When they work together, how long will it take them to build a table?

Possible Answers:

$10\ hrs$

$25\ hrs$

$20\ hrs$

$18\ hrs$

$15\ hrs$

Correct answer:

$18\ hrs$

Explanation:

Write their respective rates as fractions:

Carpenter A: $\dpi{100} \small \frac{1\ table}{45\ hours}$

Carpenter B: $\dpi{100} \small \frac{1\ table}{30\ hours}$

Add them together to find their combined rate. First find a common denominator. The smallest multiple of both 45 and 30 is 90:

$\dpi{100} \small \frac{2}{90}+\frac{3}{90}=\frac{5}{90}=\frac{1\ table}{18\ hours}$

Therefore, they take 18 hours to build a table together.

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Example Question #1 : How To Find The Reciprocal Of A Fraction

What is the sum of the reciprocal of , the reciprocal of , the reciprocal of , and xyz ?

Possible Answers:

$\frac{xy+xz+yz+x^2y^2z^2}{xyz}$

$\frac{x^2+y^2+z^2+xyz}{xyz}$

$\frac{xy+xz+yz+xyz+x^2y^2z^2}{xyz}$

None of the other answers

$\frac{x+y+z+xyz}{xyz}$

Correct answer:

$\frac{xy+xz+yz+x^2y^2z^2}{xyz}$

Explanation:

Begin by finding the reciprocal of , the reciprocal of , and the reciprocal of :

$\frac{1}{x}$ , $\frac{1}{y}$ , $\frac{1}{z}$

In order to add the four terms together, we will need to find a common denominator. Find the common denominator by multiplying the three different terms in the denominator (x, y, and z). Our common denominator will be xyz . Put each term into terms of this common denominator:

$\frac{1}{x}*\frac{yz}{yz}=\frac{yz}{xyz}$

$\frac{1}{y}*\frac{xz}{xz}=\frac{xz}{xyz}$

$\frac{1}{z}*\frac{xy}{xy}=\frac{xy}{xyz}$

$xyz*\frac{xyz}{xyz}=\frac{x^2y^2z^2}{xyz}$

Now, add each term together:

$\frac{xy}{xyz}+\frac{xz}{xyz}+\frac{yz}{xyz}+\frac{x^2y^2z^2}{xyz}=\frac{xy+xz+yz+x^2y^2z^2}{xyz}$

Look for the answer choice that matches this.

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Example Question #1 : Reciprocals

Find the reciprocal of the following expression:

$\frac{2x^2 + 3x + 4}{3b}$

Possible Answers:

$\frac{2x^2 + 3x + 4}{3b}$

$\frac{3b}{3b}$

$\frac{2x^2 + 3x + 4}{2x^2 + 3x + 4}$

$\frac{3b}{2x^2 +3x + 4}$

$\frac{3b}{2x^2 + 2x + 2}$

Correct answer:

$\frac{3b}{2x^2 +3x + 4}$

Explanation:

To find the reciprocal of a rational expression--any rational expression--all you need to do is flip the numerator and the denominator.

Therefore, the correct answer is:

$\frac{3b}{2x^2 +3x + 4}$

You can check this by multiplying the two expressions together and ensuring that your answer is .

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Example Question #4 : How To Find The Reciprocal Of A Fraction

Find the reciprocal of the following expression:

$22\frac{1}{2}$

Possible Answers:

$\frac{33}{22}$

$\frac{1}{22}$

$\frac{22}{33}$

$\frac{45}{2}$

$\frac{2}{45}$

Correct answer:

$\frac{2}{45}$

Explanation:

To find the reciprocal of any fraction, you merely need to invert the numerator and denominator.

In this case, first you have to convert the mixed number into a fraction:

$22\frac{1}{2} = \frac{2\cdot 22}{2}+\frac{1}{2}=\frac{44}{2} + \frac{1}{2} = \frac{45}{2}$

Therefore, the answer is:

$\frac{2}{45}$

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Example Question #51 : Fractions

What is the least common denominator of 150 and 175 ?

Possible Answers:

1050

26250

Correct answer:

1050

Explanation:

To find the least common denominator of two numbers, it is easiest first to factor them into prime factors:

$150=25\cdot6=5^2\cdot2\cdot3=2\cdot3\cdot5^2$

$175=5^2\cdot7$

Now, you need to compare each number and choose the case in which the prime factor has the highest power. Therefore, since and are found only in 150 , you will select those. You can take "either" 5^2 . Finally, the in 175 is the largest factor of . Your LCD is found by multiplying all of these together:

$2\cdot3\cdot5^2\cdot7 = 1050$

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Example Question #2 : How To Find The Lowest / Least Common Denominator

Simplify:

$\frac{4}{35}+\frac{7}{30}$

Possible Answers:

$\frac{814}{105}$

$\frac{91}{5}$

$\frac{73}{210}$

$\frac{9141}{1050}$

$\frac{81}{11}$

Correct answer:

$\frac{73}{210}$

Explanation:

To begin to solve this, you need to find the least common denominator of and . The easiest way to do this is to begin by factoring them into prime factors:

$35=5\cdot7$

$30=2\cdot3\cdot5$

The LCD is found by selecting the largest power for each factor across the two values. Therefore, you will take ,, and from and the from the . Your LCD is therefore:

$2\cdot3\cdot5\cdot7=210$ .

Now, apply this to your fractions:

$\frac{4}{35}\cdot\frac{6}{6}+\frac{7}{30}\cdot\frac{7}{7}=\frac{24}{210}+\frac{49}{210}=\frac{73}{210}$

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GRE Math : Fractions

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #461 : Arithmetic

Example Question #52 : Fractions

Example Question #53 : Fractions

Example Question #54 : Fractions

Example Question #1 : How To Find The Reciprocal Of A Fraction

Example Question #1 : How To Find The Reciprocal Of A Fraction

Example Question #1 : Reciprocals

Example Question #4 : How To Find The Reciprocal Of A Fraction

Example Question #51 : Fractions

Example Question #2 : How To Find The Lowest / Least Common Denominator

All GRE Math Resources

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