# GRE Math : Mixed / Improper Fractions

## 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 relationship cannot be determined.

The two quantities are equal.

Quantity B is greater.

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 two quantities are equal

Quantity A is larger.

Quantity B is larger.

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

The two quantities are equal

Explanation:

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.

### Example Question #61 : Fractions

Write as an improper fraction.

Explanation:

To find the improper fraction value, we must effectively add together 71 and 5/7. To do this, we will give 71 a denominator of 7; therefore, we are transforming 71/1 to x/7.  The shortest way to do this is to multiply by 7/7 (which really is 1); therefore, 71 = 71 * (7/7) = 497/7.

Now add them: (497 + 5)/7 = 502/7

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

Which of the following improper fractions is equivalent to ?

Explanation:

To find an improper fraction, you need to multiply the whole number that you have by the denominator of the associated fraction.  For our problem, this means that you will multiply  by , getting .  Next, you add this to the numerator of your fraction, giving you , or .  Finally, you place this over your original denominator, giving you:

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

Which of the following improper fractions is equivalent to ?