SAT Math : Algebraic Fractions

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #51 : Algebraic Fractions

The numerator of a fraction is the sum of 4 and 5 times the denominator. If you divide the fraction by 2, the numerator is 3 times the denominator. Find the simplified version of the fraction.

Possible Answers:

Correct answer:

Explanation:

Let numerator = N and denominator = D.

According to the first statement, 

N = (D x 5) + 4.

According to the second statement, N / 2 = 3 * D. 

Let's multiply the second equation by –2 and add itthe first equation:

–N = –6D

+[N = (D x 5) + 4]

=

–6D + (D x 5) + 4 = 0

–1D + 4 = 0

D = 4

Thus, N = 24.

Therefore, N/D = 24/4 = 6.

Example Question #11 : How To Solve For A Variable As Part Of A Fraction

Solve for x:

Possible Answers:

Correct answer:

Explanation:

In order to solve for x, you must cross multiply the ratio first. They will be equal to each other. 

, you then can add 3x to both sides and 402 to both sides as well. You are left with:

 divide both sides by 9 to get the final answer:

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