How to simplify a fraction

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SSAT Upper Level Quantitative › How to simplify a fraction

Questions 1 - 10
1

Put the fraction in simplest form.

Explanation

To simplify a fraction, divide both the numerator and the denominator by the same numbers until there is no number that can divide them both without resulting in a remainder.

2

Put the fraction in simplest form.

Explanation

To simplify a fraction, divide both the numerator and the denominator by the same numbers until there is no number that can divide them both without resulting in a remainder.

3

Put the fraction in simplest form.

Explanation

To simplify a fraction, divide both the numerator and the denominator by the same numbers until there is no number that can divide them both without resulting in a remainder.

4

Put the fraction in simplest form.

Explanation

To simplify a fraction, divide both the numerator and the denominator by the same numbers until there is no number that can divide them both without resulting in a remainder.

5

Fill in the blank with the missing fraction.

Explanation

In this problem we are making equivalent fractions. In order to make equivalent fractions you have to multiply the numerator and the denominator by the same number.

6

Consider a fraction , where the numerator is unknown. How many of the following values of would yield a fraction not in lowest terms?

I)

II)

III)

IV)

Explanation

The prime factorization of is , so the fraction is reducible if and only if is a multiple of 5 or 13.

We can immediately tell that 115 is the only multiple of 5, so we test the other numbers to see if there is a multiple of 13. We soon see that

, so 116 and 118 cannot be multples of 13.

115 and 117 are the only values of that yield reducible fractions, so the correct response is two.

7

Put the fraction in simplest form.

Explanation

To simplify a fraction, divide both the numerator and the denominator by the same numbers until there is no number that can divide them both without resulting in a remainder.

8

Rewrite the mixed fraction as an improper fraction in lowest terms, and call the product of the numerator and the denominator of the simplified improper fraction. How many digits does have?

Explanation

, so simplifies to .

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,

Multiply the numerator and the denominator: ,

a three-digit number.

9

Reduce to lowest terms, call the sum of the numerator and the denominator. Which statement is true of ?

Explanation

Add the numerator and the denominator:

The correct response is therefore .

10

Put the fraction in simplest form.

Explanation

To simplify a fraction, divide both the numerator and the denominator by the same numbers until there is no number that can divide them both without resulting in a remainder.

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