GMAT Math : Understanding fractions

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Example Question #31 : Understanding Fractions

When positive integer is divided by 16, the remainder is 15. What is the remainder when is divided by 8 ?

Possible Answers:

Correct answer:

Explanation:

We can set up the following equation from what we are told in the question: n = 16q + 15 where is the quotient, then we divide by 8: $\frac{16q+7}{8}$ or $2q+\frac{7}{8}$ . From there we can see that $\frac{7}{8}$ will yield a remainder of , which is our final answer.

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Example Question #32 : Understanding Fractions

Simplify the following expression: $\frac{3}{4}-\frac{5}{8}+\frac{3}{16}$

Possible Answers:

$\frac{3}{2}$

$\frac{5}{16}$

$\frac{5}{8}$

$\frac{4}{3}$

$\frac{1}{2}$

Correct answer:

$\frac{5}{16}$

Explanation:

In order to simplify the expression $\frac{3}{4}-\frac{5}{8}+\frac{3}{16}$ , let's first change the terms to reflect a common denominator:

$\frac{3\times 4}{4\times 4}-\frac{5\times 2}{8\times 2}+\frac{3}{16}$

$=\frac{12}{16}-\frac{10}{16}+\frac{3}{16}$

$=\frac{12-10+3}{16}$

$=\frac{5}{16}$

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Example Question #33 : Understanding Fractions

When positive integer is divided by 12, the remainder is 7. What is the remainder when is divided by 3?

Possible Answers:

Correct answer:

Explanation:

The remainder cannot be greater or equal to the divisor, so we can already eliminate 3, 4 and 5. Then, we can set up an equation with the given information. We know that when is divided by 12, the remainder is 7 : n= 12q + 7 , where is the quotient. So, let's try to divide by 3 and we get : $\frac{12q+7}{3}$ or $4q + \frac{7}{3}$ . Therefore, the remainder must be one, since when 7 is divided by 3, the remainder is .

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Example Question #34 : Understanding Fractions

and are positive integers and $\frac{a}{b}= 36.24$ . What is the remainder?

Possible Answers:

Correct answer:

Explanation:

We are told that $\frac{a}{b}=36+0.24$ . In other words, the remainder can be expressed as follows:

$\frac{r}{b}=0.24$ or $\frac{r}{b}= \frac{24}{100}$

If we simplify, we get $\frac{r}{b}= \frac{6}{25}$ .

Therefore, we can see that is a multiple of . The only possible multiple of in the answer choice is .

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Example Question #31 : Understanding Fractions

What is $\frac{(5-2)!}{(3-3)!}$ ?

Possible Answers:

Does not exist

Correct answer:

Explanation:

Here we can be tempted to answer that the answer does not exist since there can be no division by 0; however, (3-3)!=0!=1 , or in other words, the factorial of 0 is 1. Therefore, the final answer is given by or .

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Example Question #36 : Understanding Fractions

$\frac{3}{8}$ of a number, , is . What is ?

Possible Answers:

Correct answer:

Explanation:

We can solve this problem by setting up our equation and solving for the number, :

$\frac{3}{8}n=24$

3n=(8)(24)

3n=192

n=64

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Example Question #37 : Understanding Fractions

$\frac{5}{16}$ of a number, , is 125 . What is the value of ?

Possible Answers:

400

200

$39 \frac{1}{6}$

625

Correct answer:

400

Explanation:

$\frac{5}{16}n=125$

5n=(125)(16)

5n=2000

n=400

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Example Question #32 : Understanding Fractions

Solve:

$\frac{3}{8} + \frac{2}{9} =$

Possible Answers:

$\frac{6}{72}$

$\frac{5}{8}$

$\frac{43}{72}$

$\frac{5}{9}$

$\frac{5}{17}$

Correct answer:

$\frac{43}{72}$

Explanation:

In order to add the two fractions, we must find the lowest common denominator. To do this, we simply multiply each fraction by the denominator of the opposite over itself:

$\frac{9}{9}\cdot\frac{3}{8} + \frac{8}{8}\cdot \frac{2}{9} = \frac{27}{72} + \frac{16}{72} = \frac{43}{72}$

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Example Question #39 : Understanding Fractions

Simplify the following into a single fraction.

$\frac{a}{b} + \frac{6a}{7c}$

Possible Answers:

$\frac{7a}{7c+b}$

$\frac{a}{7bc}$

None of the other answers.

$\frac{a(7c+6b)}{7bc}$

$\frac{a}{bc}$

Correct answer:

$\frac{a(7c+6b)}{7bc}$

Explanation:

To simply, we must first find the common denominator of the two fractions. That would be $b \times 7c$ or 7bc

Hence we multiply the first fraction by $\frac{7c}{7c}$ and the second fraction by $\frac{b}{b}$ , and we will have.

$\frac{7ac}{7bc} + \frac{6ab}{7bc}$ .

Now that the denominators match, we can add the fractions. The denominator stays the same after this, only the numerators add together.

$\frac{7ac+6ab}{7bc}$

Then factor out an from the numerator to get the final answer.

$\frac{a(7c+6b)}{7bc}$

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GMAT Math : Understanding fractions

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #31 : Understanding Fractions

Example Question #32 : Understanding Fractions

Example Question #33 : Understanding Fractions

Example Question #34 : Understanding Fractions

Example Question #31 : Understanding Fractions

Example Question #36 : Understanding Fractions

Example Question #37 : Understanding Fractions

Example Question #32 : Understanding Fractions

Example Question #39 : Understanding Fractions

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