SAT Math : How to multiply rational expressions

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #1 : How To Multiply Rational Expressions

Simplify (4x)/(x– 4) * (x + 2)/(x– 2x)

Possible Answers:

x/(x + 2)

4/(x + 2)2

4/(x – 2)2

(4x+ 8x)/(x+ 8x)

x/(x – 2)2

Correct answer:

4/(x – 2)2


Factor first.  The numerators will not factor, but the first denominator factors to (x – 2)(x + 2) and the second denomintaor factors to x(x – 2).  Multiplying fractions does not require common denominators, so now look for common factors to divide out.  There is a factor of x and a factor of (x + 2) that both divide out, leaving 4 in the numerator and two factors of (x – 2) in the denominator.

Example Question #6 : Rational Expressions

what is 6/8 X 20/3

Possible Answers:
Correct answer: 5

6/8 X 20/3 first step is to reduce 6/8 -> 3/4 (Divide top and bottom by 2)

3/4 X 20/3 (cross-cancel the threes and the 20 reduces to 5 and the 4 reduces to 1)

1/1 X 5/1 = 5

Example Question #7 : Rational Expressions

Evaluate and simplify the following product:

Possible Answers:

Correct answer:


The procedure for multplying together two rational expressions is the same as multiplying together any two fractions: find the product of the numerators and the product of the denominators separately, and then simplify the resulting quotient as far as possible, as shown:

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