# SSAT Upper Level Math : Mixed / Improper Fractions

## Example Questions

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

Which of the following is one more than  ?

Explanation:

Rewrite  as follows:

, so .

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

Which of the following is three times  ?

Explanation:

Since ,

### Example Question #3 : Mixed / Improper Fractions

Which of the following is 80% of  ?

Explanation:

80% of a number is equal to  multiplied by that number, so 80% of  is

Since

.

### Example Question #2 : Mixed / Improper Fractions

Which of the following is  increased by 25%?

The correct answer is not among the other responses.

Explanation:

A number increased by 25% is 125%, or , multiplied by the number.  increased by 25% is therefore

, so

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

Decrease  by 12.5%. What is the result?

Explanation:

Decreasing a number by 12.5% is the same as taking 87.5% of a number, or multiplying it by

.

, so

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

Change to a mixed number

Explanation:

To convert from a fraction to a mixed number we must find out how many times the denominator goes into the numerator using division and the remainder becomes the new fraction.

### Example Question #6 : Mixed / Improper Fractions

Write  as a mixed fraction.

Explanation:

Divide the numerator by the denominator.

Now, the whole number part will be . Write the remainder on top of the denominator to get the fraction.

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

If  is rewritten as an improper fraction, what will its numerator be?

Explanation:

The numerator of the improper form of a mixed fraction is the original numerator added to the product of the integer and the original denominator:

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

Rewrite   as an improper fraction in lowest terms, and call  the sum of its numerator and its denominator. Which of the following is a true statement?

Explanation:

, in lowest terms, is , so  is rewritten as .

The numerator of the improper form of a mixed fraction is the original numerator added to the product of the integer and the original denominator. The new denominator is the same as the old one. Therefore,

,

Add the numerator and the denominator: .

The correct response is .

### Example Question #211 : Rational Numbers

Rewrite  as an improper fraction in lowest terms. If we assign to  the numerator of this fraction, which of the following will be a true statement?

Explanation:

in lowest terms is , so first, rewrite  as .

The numerator of the improper form of a mixed fraction is the original numerator added to the product of the integer and the original denominator:

The correct response is .

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