GRE Math : How to divide fractions

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Example Questions

Example Question #51 : Fractions

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.

The two quantities are equal.

Quantity B is greater.

The relationship cannot be determined.

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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GRE Math : How to divide fractions

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #51 : Fractions

Example Question #52 : Fractions

Example Question #53 : Fractions

Example Question #54 : Fractions

All GRE Math Resources

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