SSAT Upper Level Math : Rational Numbers

Study concepts, example questions & explanations for SSAT Upper Level Math

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Example Questions

Example Question #12 : How To Find Decimal Fractions

Convert to a fraction. 

Possible Answers:

Correct answer:

Explanation:

First, lets convert the exponent into a fraction. Any negative exponent means it's the reciprocal of the positive exponent. So  means . Now lets multiply it with the . This means  or  or .

Example Question #12 : How To Find Decimal Fractions

Convert  into a fraction. 

Possible Answers:

Correct answer:

Explanation:

Let  be .  

Lets multiply  by . Now we have:

 

Lets subtract this equation with the first one and we get:

 We do this because we want to get rid of the repeating decimals and now we have a simple equation, isolate  and we arrive at the final answer. 

Example Question #283 : Fractions

Convert  into a fraction.

Possible Answers:

Correct answer:

Explanation:

Let  be  

Lets multiply  by . I chose , because there is a set of  numbers that make the repeating decimal. To determine the value to multiply the repeating decimal, we do  to the power of number in a set before it repeats.

Now we have:

 

Lets subtract this equation with the first one and we get:

 We do this because we want to get rid of the repeating decimals and now we have a simple equation, isolate  and we arrive at the final answer. 

Example Question #1 : Simplifying Fractions

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?

Possible Answers:

Correct answer:

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 : Simplifying Fractions

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

Possible Answers:

Correct answer:

Explanation:

Add the numerator and the denominator: 

The correct response is therefore .

Example Question #3 : Simplifying Fractions

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) 

Possible Answers:

Correct answer:

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 #2 : Simplifying Fractions

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

Possible Answers:

Correct answer:

Explanation:

Multiply the numerator and the denominator: 

The product is a three-digit number.

Example Question #1413 : Ssat Upper Level Quantitative (Math)

Put the fraction in the simplest form.

Possible Answers:

Correct answer:

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 #1 : How To Simplify A Fraction

Put the fraction in simplest form.

Possible Answers:

Correct answer:

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 #281 : Rational Numbers

Put the fraction in simplest form.

Possible Answers:

Correct answer:

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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