# GRE Math : How to find out a mixed fraction from an improper fraction

## Example Questions

### Example Question #1 : How To Find Out A Mixed Fraction From An Improper Fraction

and  are positive integers.

is a multiple of .

Quantity A:

Quantity B:

The two quantities are equal.

Quantity B is greater.

The relationship cannot be determined.

Quantity A is greater.

The relationship cannot be determined.

Explanation:

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.

### Example Question #1 : Mixed / Improper Fractions

Which of the following is the mixed fraction equivalent to ?

Explanation:

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.

### Example Question #2 : How To Find Out A Mixed Fraction From An Improper Fraction

Which of the following is equivalent to ?

Explanation:

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 .

### Example Question #2 : How To Find Out A Mixed Fraction From An Improper Fraction

Quantity A:

Quantity B:

Which of the following is true?

The relationship of the two quantities cannot be determined based on the information provided.

Quantity A is larger.

The two quantities are equal

Quantity B is larger.