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SAT Math : How to evaluate rational expressions

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Example Questions

Example Question #12 : Rational Expressions

If √(ab) = 8, and a²= b, what is a?

Possible Answers:

Correct answer:

Explanation:

If we plug in a² for b in the radical expression, we get √(a³) = 8. This can be rewritten as a^3/2 = 8. Thus, log_a8 = 3/2. Plugging in the answer choices gives 4 as the correct answer.

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Example Question #1 : Rational Expressions

Function_part1

Possible Answers:

–37/15

9/5

37/15

–11/5

–9/5

Correct answer:

–11/5

Explanation:

Fraction_part2

Fraction_part3

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Example Question #2 : Rational Expressions

If Jill walks $100\:\text{ft}$ in $20\:\sec$ , how long will it take Jill to walk $1500\:\text{ft}$ ?

Possible Answers:

$200\sec$

$100\sec$

$30\sec$

$400\sec$

$300\sec$

Correct answer:

$300\sec$

Explanation:

To solve this, we need to set a proportion.

$\frac{100\:\text{ft}}{20\sec}=\frac{1500\:\text{ft}}{x}$

Cross Multiply

$100\cdot x=1500\cdot 20$

$x=\frac{30000}{100}=300$

So it will take Jill $300 \sec$ to walk $1500\: \text{ft}$

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Example Question #3 : Rational Expressions

If $\frac{b+c}{c}=\frac{14}{15}$ , then which of the following must be also true?

Possible Answers:

$\frac{b}{c}=10$

$\frac{b}{c}=1$

$\frac{b}{c}=-\frac{1}{15}$

$\frac{b}{c}=\frac{7}{10}$

Correct answer:

$\frac{b}{c}=-\frac{1}{15}$

Explanation:

$\frac{b+c}{c}=\frac{14}{15}$

$\frac{b}{c}+\frac{c}{c}=\frac{14}{15}$

$\frac{b}{c}+1=\frac{14}{15}$

$\frac{b}{c}+1\ {\color{Red} -1}=\frac{14}{15}\ {\color{Red} -1}$

$\frac{b}{c}=\frac{14}{15}-\frac{15}{15}$

$\frac{b}{c}=-\frac{1}{15}$

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SAT Math : How to evaluate rational expressions

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #12 : Rational Expressions

Example Question #1 : Rational Expressions

Example Question #2 : Rational Expressions

Example Question #3 : Rational Expressions

All SAT Math Resources

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