GMAT Math : Understanding fractions

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Example Question #21 : Understanding Fractions

Simplify the following into a single fraction: $\frac{x}{y}+\frac{ab}{cd}$

Possible Answers:

$\frac{ycd}{xab}$

Not enough information provided.

$\frac{xab}{ycd}$

$\frac{ycd}{xcd+yab}$

$\frac{xcd+yab}{ycd}$

Correct answer:

$\frac{xcd+yab}{ycd}$

Explanation:

In order to simplify $\frac{x}{y}+\frac{ab}{cd}$ , combine the terms by finding the common denominator:

$\frac{x}{y}+\frac{ab}{cd}$

$=\frac{x(cd)}{y(cd)}+\frac{(y)ab}{(y)cd}$

$=\frac{xcd+yab}{ycd}$

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Example Question #21 : Understanding Fractions

Simplify the following expression: $\frac{5}{6}+\frac{7}{11}+\frac{4}{3}$

Possible Answers:

$\frac{182}{64}$

$\frac{184}{62}$

$\frac{185}{66}$

$\frac{181}{61}$

$\frac{183}{69}$

Correct answer:

$\frac{185}{66}$

Explanation:

In order to simplify the expression, we start by finding the common denominator of each term in $\frac{5}{6}+\frac{7}{11}+\frac{4}{3}$ :

In this case the common denominator is 66.

$\frac{5}{6}\left(\frac{11}{11} \right )+\frac{7}{11}\left(\frac{6}{6} \right )+\frac{4}{3}\left(\frac{22}{22} \right )$

$=\frac{55}{66}+\frac{42}{66}+\frac{88}{66}$

$=\frac{55+42+88}{66}$

$=\frac{185}{66}$

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Example Question #23 : Understanding Fractions

Clara wants to make sixteen batches of her world famous Icky Sticky Ooey Gooey Chocolate Bomb Brownies. Each batch of brownies requires $\frac{3}{4}$ cups of flour, $1\frac{1}{2}$ cups of sugar, and $1\frac{3}{4}$ cups of bittersweet chocolate.

She has 14 cups of flour, 22 cups of sugar, and 25 cups of bittersweet chocolate on hand; assuming other ingredients are not an issue, can Clara make sixteen batches of brownies?

Possible Answers:

No, because she does not have enough flour, sugar, or chocolate

No, because she does not have enough sugar or flour

No, because she does not have enough flour or chocolate

Yes

No, because she does not have enough sugar or chocolate

Correct answer:

No, because she does not have enough sugar or chocolate

Explanation:

To make sixteen batches of brownies, Clara will require:

$\frac{3}{4} \times 16 = 12$ cups of flour; since Clara has 14 cups on hand, she has sufficient flour.

$1\frac{1}{2} \times 16 = 24$ cups of sugar; since Clara has 22 cups on hand, she needs more sugar.

$1\frac{3}{4} \times 16 = 28$ cups of bittersweet chocolate; since Clara has 25 cups on hand, she needs more bittersweet chocolate.

The correct choice is that she cannot make them, since she does not have enough sugar or chocolate.

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Example Question #24 : Understanding Fractions

Suzanne wants to make fifteen batches of her world famous Icky Sticky Ooey Gooey Oatmeal Peanut Butter Cookies. Each batch of cookies requires $1\frac{1}{2}$ cups of flour, $1\frac{1}{4}$ cups of sugar, and $1\frac{3}{4}$ cups of oatmeal, among other ingredients.

She has 20 cups of flour, 24 cups of sugar, and 30 cups of oatmeal on hand; assuming other ingredients are not an issue, can Suzanne make fifteen batches of brownies?

Possible Answers:

No, because she does not have enough flour

No, because she does not have enough sugar

Yes

No, because she does not have enough oatmeal

No, because she does not have enough flour, sugar, or oatmeal

Correct answer:

No, because she does not have enough flour

Explanation:

To make fifteen batches of cookies, Suzanne will require:

$1\frac{1}{2} \times 15 = 22 \frac{1}{2}$ cups of flour; since Suzanne has 20 cups on hand, she needs more flour.

$1\frac{1}{4} \times 15 = 18 \frac{3}{4}$ cups of sugar; since Suzanne has 24 cups on hand, she has sufficient sugar.

$1\frac{3}{4} \times 15 = 26 \frac{1}{4}$ cups of oatmeal; since Suzanne has 30 cups on hand, she has sufficient oatmeal.

The correct choice is that she cannot make them, since she does not have enough flour.

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Example Question #25 : Understanding Fractions

Three fifths of a number is twenty greater than one tenth of the same number. What is that number?

Possible Answers:

The correct answer is not among the other responses.

Correct answer:

Explanation:

If the number is , then the relation can be written as

$\frac{1}{10}N + 20 = \frac{3}{5} N$

$10 \cdot \left ( \frac{1}{10}N + 20 \right )= 10 \cdot \frac{3}{5} N$

N + 200 = 6N

200 = 5N

N = 40

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Example Question #26 : Understanding Fractions

Add three fourths of a number to one eighth of a number to get 56. What is the number?

Possible Answers:

The correct answer is not given among the other responses.

Correct answer:

Explanation:

If the number is , then the relation can be written as

$\frac{3}{4}N + \frac{1}{8}N = 56$

$\frac{6}{8}N + \frac{1}{8}N = 56$

$\frac{7}{8}N = 56$

$\frac{8} {7} \cdot \frac{7}{8} N =\frac{8} {7}\cdot 56$

N =64

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Example Question #27 : Understanding Fractions

Divide two sevenths of a number by one half to get 40. What is the number?

Possible Answers:

280

140

$91\frac{3}{7}$

$22\frac{6}{7}$

Correct answer:

Explanation:

If the number is , then the relation can be written as

$\frac{2}{7} N \div \frac{1}{2} = 40$

$\frac{2}{7} N \cdot \frac{2} {1}= 40$

$\frac{4}{7} N = 40$

$\frac{7} {4}\cdot \frac{4}{7}N = \frac{7} {4}\cdot40$

N = 70

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Example Question #28 : Understanding Fractions

Compute the following:

$(\frac{4}{5}\div \frac{20}{15} ) +\frac{16}{45}$

Possible Answers:

$\small \small \frac{4}{15}$

$\small 3 \frac{16}{45}$

$\small \frac{43}{45}$

$\small \small \frac{4}{5}$

$\small \small \frac{41}{45}$

Correct answer:

$\small \frac{43}{45}$

Explanation:

Consider that dividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction. So, you can rewrite the presented expression:

$(\frac{4}{5}\div \frac{20}{15} ) +\frac{16}{45}$

like this:

$(\frac{4}{5}\ast \frac{15}{20} ) +\frac{16}{45}$

Now you can multiply across the numerators and denominators of the two fractions to find their product:

$\frac{60}{100} +\frac{16}{45}$

Each of these fractions can be reduced. Let's reduce the first fraction:

$\frac{3}{5}+\frac{16}{45}$

Now we can multiply the first fraction by $\frac{9}9{}$ to create a common denominator:

$(\frac{3}{5}\cdot\frac{9}{9})+\frac{16}{45}$

$\frac{27}{45}+\frac{16}{45}$

At this point, we can add the fractions together. Since the result cannot be simplified, it is the correct answer.

$\frac{43}{45}$

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Example Question #21 : Understanding Fractions

Which of the following is equal to $\frac{2}{3}$ ?

Possible Answers:

$\frac{5}{6}+\frac{2}{9}$

$\frac{4}{3}-\frac{1}{6}$

$\frac{7}{6}-\frac{4}{6}$

$\frac{8}{3}-\frac{5}{3}$

$\frac{15}{9}-1$

Correct answer:

$\frac{15}{9}-1$

Explanation:

Testing out all of the answer choices, the only solution that is equal to $\frac{2}{3}$ is $\frac{15}{9}-1=\frac{15}{9}-\frac{9}{9}=\frac{6}{9}=\frac{2}{3}$

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Example Question #21 : Understanding Fractions

Simplify the following expression: $\frac{5}{9}\div\frac{4}{3}$

Possible Answers:

$\frac{2}{3}$

$\frac{5}{12}$

$\frac{7}{12}$

$\frac{1}{3}$

$\frac{1}{2}$

Correct answer:

$\frac{5}{12}$

Explanation:

In order to simplify $\frac{5}{9}\div\frac{4}{3}$ , we must remember that dividing by a fraction is the same as multiplying by its reciprocal. Therefore:

$\frac{5}{9}\div\frac{4}{3}$

$=\frac{5}{9}\times \frac{3}{4}$

$=\frac{15}{36}$

$=\frac{5}{12}$

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GMAT Math : Understanding fractions

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #21 : Understanding Fractions

Example Question #21 : Understanding Fractions

Example Question #23 : Understanding Fractions

Example Question #24 : Understanding Fractions

Example Question #25 : Understanding Fractions

Example Question #26 : Understanding Fractions

Example Question #27 : Understanding Fractions

Example Question #28 : Understanding Fractions

Example Question #21 : Understanding Fractions

Example Question #21 : Understanding Fractions

All GMAT Math Resources

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