How to find out a mixed fraction from an improper fraction - GRE Quantitative Reasoning

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Question

and are positive integers.

is a multiple of .

Quantity A:

Quantity B:

Answer

Recall that the exponent of the denominator is sutracted from the exponent of the numerator.

Therefore Quantity A is equivalent to x5–y, and because we would then be comparing an arithmetic operation to a geometric operation, it does not matter whether y is a multiple of 5. The two quantities cannot be compared.

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Question

Which of the following is the mixed fraction equivalent to ?

Answer

To begin, notice that using your calculator, you can find:

Now, the closest even multiple of that is less than is . Therefore, you know that your number is:

This is the same as:

, or simply, . This is your mixed fraction.

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Question

Which of the following is equivalent to ?

Answer

Although there are many ways to convert improper fractions into mixed fractions, the easiest way is to use your calculator to your advantage. Begin by dividing by . This gives you . Therefore, you can eliminate all the options that have do not have for their first portion. Next, multiply by the denominator (), and get . This means that you have and , or . Thus, your answer is .

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Question

Quantity A:

Quantity B:

Which of the following is true?

Answer

Though there are several ways you could solve this, let's convert the improper fraction into a mixed one so we can compare them. Start by dividing by . This gives you

Now, since we know that the two numbers have the same whole-number value, we need to compare their decimal portions. Compare to . The latter is indeed Therefore, the two values are equal.

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