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GMAT Math : Fractions

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Example Question #152 : Algebra

What value must take in order for the following expression to be greater than zero?

$\frac{3}{k}-\frac{5}{7}$

Possible Answers:

Correct answer:

Explanation:

is such that:

$\frac{3}{k}-\frac{5}{7}>0$

Add $\frac{5}{7}$ to each side of the inequality:

$\frac{3}{k}>\frac{5}{7}$

Multiply each side of the inequality by :

$\frac{21}{k}>5$

Multiply each side of the inequality by :

21>5k

Divide each side of the inequality by :

$k< \frac{21}{5}$

You can now change the fraction on the right side of the inequality to decimal form.

$k<\frac{21}{5}=\frac{20}{5}+\frac{1}{5}= 4.2$

The correct answer is , since k has to be less than 4.2 for the expression to be greater than zero.

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Example Question #361 : Arithmetic

$\frac{2}{3}+\frac{3}{4}+\frac{5}{6}=$

Possible Answers:

$\frac{9}{4}$

$\frac{14}{3}$

$\frac{11}{6}$

$\frac{7}3{}$

$\frac{27}{4}$

Correct answer:

$\frac{9}{4}$

Explanation:

In order to add these fractions, we must first find a common denominator for all three. Looking at our three different denominators, we can see that their lowest common denominator is 12. Therefore, we need to rewrite each fraction with a denominator of 12:

$\frac{2}{3}+\frac{3}{4}+\frac{5}{6}=\frac{2(4)}{3(4)}+\frac{3(3)}{4(3)}+\frac{5(2)}{6(2)}=\frac{8}{12}+\frac{9}{12}+\frac{10}{12}$

Now that the fractions all have a common denominator, we can simply add them together and then simplify the result, recognizing that 27 and 12 have a common factor of 3:

$\frac{8}{12}+\frac{9}{12}+\frac{10}{12}=\frac{27}{12}=\frac{9}{4}$

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Example Question #11 : Fractions

Which of the following is less than $\frac{5}{8}$ ?

Possible Answers:

$\frac{7}{6}$

$\frac{1}{2}$

$\frac{3}{4}$

$\frac{5}{6}$

$\frac{2}{3}$

Correct answer:

$\frac{1}{2}$

Explanation:

In order to determine which fractions are less than $\frac{5}{8}$ , it's best to convert them to decimals and compare:

$\frac{5}{8}=0.625$

$\frac{1}{2}=0.5$

$\frac{3}{4}=0.75$

$\frac{2}{3}=0.67$

$\frac{5}{6}=0.83$

$\frac{7}{6}=1.167$

Therefore, $\frac{1}2{}$ is the only choice that is less than $\frac{5}{8}$ .

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Example Question #362 : Arithmetic

Define an operation $\ast$ as follows:

For all real numbers a ,b ,

$a \ast b = \frac{1}{4}a + b^{2}$

Evaluate $\frac{2}{3} \ast \frac{1}{3}$ .

Possible Answers:

$\frac{5}{18}$

$\frac{2}{15}$

$\frac{1}{4}$

None of the other responses is correct.

$\frac{1}{16}$

Correct answer:

$\frac{5}{18}$

Explanation:

$a \ast b = \frac{1}{4}a + b^{2}$

$\frac{2}{3} \ast \frac{1}{3}= \frac{1}{4} \cdot \frac{2}{3} + \left (\frac{1}{3} \right ) ^{2}$

$= \frac{2}{12} + \frac{1}{9}$

$= \frac{1}{6} + \frac{1}{9}$

$= \frac{3}{18} + \frac{2}{18}$

$= \frac{5}{18}$

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Example Question #12 : Fractions

Casius has $\tiny \frac{1}{6}$ of a liter of water. Olivar has $\tiny \frac{4}{7}$ of the amount Casius has. How many liters of water does Olivar have?

Possible Answers:

$\tiny \frac{2}{21}$

$\tiny \tiny \frac{1}{4}$

$\tiny \tiny \frac{6}{7}$

$\tiny \frac{7}{24}$

$\tiny \tiny \frac{7}{6}$

Correct answer:

$\tiny \frac{2}{21}$

Explanation:

This question tests your ability to read word problems and multiply fractions. Because we know that Olivar has $\frac{4}{7}$ of what Casius has, we can see that we need to multiply. Perform the following operation to find the answer.

$\frac{1}{6}*\frac{4}{7}=\frac{4}{42}=\frac{2}{21}$

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Example Question #11 : Fractions

Define an operation $\ast$ as follows:

For all real numbers a ,b ,

$a \ast b = 2a \div b$

Evaluate $5\frac{1}{6} \ast 3\frac{1}{3}$ , and round to the nearest whole number.

Possible Answers:

Correct answer:

Explanation:

$a \ast b = 2a \div b$

$5\frac{1}{6} \ast 3\frac{1}{3} = 2 \left ( 5\frac{1}{6} \right ) \div 3\frac{1}{3}$

$= 2 \left ( \frac{31}{6} \right ) \div \frac{10}{3}$

$= \frac{31}{3} \div \frac{10}{3}$

$= \frac{31}{3} \cdot \frac{3}{10}$

$= \frac{31} {10}$

$=3 \frac{1} {10}$

This rounds to 3.

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Example Question #11 : Fractions

Seven thirds of eighteen seventieths is what?

Possible Answers:

Seven sixths

Five thirds

Seven fifths

Three sevenths

Three fifths

Correct answer:

Three fifths

Explanation:

Seven thirds of eighteen seventieths is

$\frac{7}{3} \times \frac{18 }{70} = \frac{7}{3} \times \frac{9}{35} = \frac{1}{1} \times \frac{3}{5}= \frac{3}{5}$

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Example Question #14 : Fractions

One orange yields $\frac{1}{3}$ cup of juice; one gallon is equal to 16 cups. How many oranges are needed to yield one half gallon of orange juice?

Possible Answers:

Correct answer:

Explanation:

One half gallon comprises 8 cups. To find the number of oranges needed, divide:

$8 \div \frac{1}{3} = 24$

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Example Question #11 : Fractions

Raise $\frac{15}{75}$ to the fourth power and express the result in lowest terms.

Possible Answers:

$\frac{1}{216}$

$\frac{1}{125}$

$\frac{1}{1,296}$

$\frac{1}{256}$

$\frac{1}{625}$

Correct answer:

$\frac{1}{625}$

Explanation:

$\frac{15}{75}$ reduces to $\frac{15 \div 15}{75 \div 15} = \frac{1}{5}$ . Raise this to the fourth power:

$\left ( \frac{1}{5} \right )^{4} = \frac{1}{5^{4}} = \frac{1}{625}$

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Example Question #18 : Fractions

Evaluate: $\left (\frac{3}{7} \right )^{4} + \left (-\frac{3}{7} \right )^{4}$

Possible Answers:

$\frac{1,296}{2,401}$

$\frac{162}{2,401}$

$-\frac{162}{2,401}$

$-\frac{1,296}{2,401}$

Correct answer:

$\frac{162}{2,401}$

Explanation:

$\left (\frac{3}{7} \right )^{4} = \frac{3^{4} }{7^{4} } = \frac{81 }{2,401}$

$\left (-\frac{3}{7} \right )^{4} =\left (\frac{3}{7} \right )^{4} = \frac{81 }{2,401}$

$\left (\frac{3}{7} \right )^{4} + \left (-\frac{3}{7} \right )^{4}=\frac{81 }{2,401}+\frac{81 }{2,401}=\frac{162}{2,401}$

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GMAT Math : Fractions

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #152 : Algebra

Example Question #361 : Arithmetic

Example Question #11 : Fractions

Example Question #362 : Arithmetic

Example Question #12 : Fractions

Example Question #11 : Fractions

Example Question #11 : Fractions

Example Question #14 : Fractions

Example Question #11 : Fractions

Example Question #18 : Fractions

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