# SSAT Upper Level Math : Simplifying Fractions

## Example Questions

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### Example Question #1 : How To Simplify A Fraction

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.

### Example Question #2 : How To Simplify A Fraction

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 .

### Example Question #3 : How To Simplify A Fraction

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.

### Example Question #1 : How To Simplify A Fraction

Reduce the fraction  to lowest terms, and call  the product of the numerator and the denominator of the simplified fraction. Give the value of .

Explanation:

Multiply the numerator and the denominator:

The product is a three-digit number.

### Example Question #5 : How To Simplify A Fraction

Put the fraction in the simplest form.

Explanation:

To put a fraction in simplest form, keep dividing the numerator and denominator by the same number until you cannot go any further.

### Example Question #6 : How To Simplify A Fraction

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.

### Example Question #7 : How To Simplify A Fraction

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.

### Example Question #1 : How To Simplify A Fraction

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.

### Example Question #9 : How To Simplify A Fraction

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.

### Example Question #1 : How To Simplify A Fraction

Put the fraction in simplest form.