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SAT Math : Algebraic Fractions

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Example Questions

Example Question #11 : Algebraic Fractions

Simplify:

(2x + 4)/(x + 2)

Possible Answers:

2x + 2

x + 1

x + 4

x + 2

Correct answer:

Explanation:

(2x + 4)/(x + 2)

To simplify you must first factor the top polynomial to 2(x + 2). You may then eliminate the identical (x + 2) from the top and bottom leaving 2.

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Example Question #12 : Algebraic Fractions

Simplify the following expression:

$\frac{2x^{4}-32}{2x^{2}-8}$

Possible Answers:

$x^{2}-4$

$(x+2)(x-2)$

$2$

$x^{2}+4$

$2(x^{2}-4)$

Correct answer:

$x^{2}+4$

Explanation:

Factor both the numerator and the denominator:

$\frac{2(x^{2}-4)(x^{2}+4)}{2(x^{2}-4)}$

After reducing the fraction, all that remains is:

$(x^{2}+4)$

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Example Question #2 : Algebraic Fractions

Simplify:

$\frac{x^{2}y-5x^{2}y^{2}}{x^{2}y}$

Possible Answers:

y-5y

$5+x^{2}y^{2}$

1-5x

1-5y

None of the other answers

Correct answer:

1-5y

Explanation:

With this problem the first thing to do is cancel out variables. The x²can all be divided by each other because they are present in each system. The equation will now look like this:

$\frac{y-5y^{2}}{y}$

Now we can see that the equation can all be divided by y, leaving the answer to be:

1-5y

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Example Question #14 : Algebraic Fractions

Simplify the given fraction:

$\frac{120}{6000}$

Possible Answers:

$\frac{1}{20}$

$\frac{1}{50}$

$\frac{2}{25}$

$\frac{1}{5}$

$\frac{1}{100}$

Correct answer:

$\frac{1}{50}$

Explanation:

120 goes into 6000 evenly 50 times, so we get 1/50 as our simplified fraction.

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Example Question #13 : Algebraic Fractions

Simplify the given fraction:

$\frac{125}{2000}$

Possible Answers:

$\frac{1}{16}$

$\frac{1}{8}$

$\frac{2}{16}$

$\frac{1}{32}$

$\frac{5}{16}$

Correct answer:

$\frac{1}{16}$

Explanation:

125 goes into 2000 evenly 16 times. 1/16 is the fraction in its simplest form.

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Example Question #14 : Algebraic Fractions

Simplify the following expression:

$\frac{4x^6}{8x^3}$

Possible Answers:

Correct answer:

Explanation:

Following this equation, you divide 4 by 8 to get 1/2. When a variable is raised to an exponent, and you are dividing, you subtract the exponents, so 6 – 3 = 3.

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Example Question #12 : How To Simplify A Fraction

Reduce the fraction:

$\frac{12}{96}$

Possible Answers:

$\frac{1}{8}$

$\frac{3}{24}$

$\frac{7}{12}$

$\frac{1}{4}$

$\frac{4}{16}$

Correct answer:

$\frac{1}{8}$

Explanation:

The numerator and denominator are both divisible by 12. Thus, we divide both by 12 to get our final answer.

If we instead divide by another common factor, we may need to complete the process again to make sure that we have completely reduced the fraction.

In mathematical words we get the following:

$\frac{12}{96}=\frac{1 \cdot 12}{8 \cdot 12}=\frac{1}{8}$

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Example Question #16 : Algebraic Fractions

Simplify the fraction: $\frac{18}{96}$

Possible Answers:

$\frac{3}{16}$

$\frac{3}{23}$

$\frac{6}{16}$

$\frac{9}{23}$

$\frac{6}{23}$

Correct answer:

$\frac{3}{16}$

Explanation:

Break up the fraction into common factors.

$18=3\times 6$

$96 = 16\times 6$

Rewrite the fraction.

$\frac{18}{96}=\frac{3\times 6}{16\times 6}$

Cancel the six.

The correct reduced fraction is $\frac{3}{16}$ .

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Example Question #17 : Algebraic Fractions

Simplify the fraction: $\frac{9}{96}$

Possible Answers:

$\frac{6}{19}$

$\frac{6}{23}$

$\frac{3}{32}$

$\frac{3}{23}$

$\frac{1}{16}$

Correct answer:

$\frac{3}{32}$

Explanation:

Break up the fraction into common factors.

$9=3\times 3$

$96 = 16\times 6$

Rewrite the fraction.

$\frac{9}{96}=\frac{3\times 3}{16\times 3 \times 2}$

Cancel the three on the numerator and denominator.

The fraction becomes:

$\frac{3}{16 \times 2}=\frac{3}{32}$

The correct reduced fraction is $\frac{3}{32}$ .

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Example Question #11 : Algebraic Fractions

Simplify the following fraction.

27a^5b^2c^8 / 3a^2b^4c^5

Possible Answers:

9a^3c^3 / b^2

9abc

9a^2c^2 / b^3

a^2b^5

3a^3c^3 / b^2

Correct answer:

9a^3c^3 / b^2

Explanation:

In order to simplify the fraction, you need to cancel out everything that the numerator and denominator share. Let's separate it into four sections: the numbers, the variable a, the variable b, and the variable c.

27 / 3 = 9

With the variable a, you have

a^5 / a^2

which simplifies to

a^3 in the numerator.

With the variable b, you have

b^2 / b^4

which simplifies to

b^2 in the denominator.

With the variable c, you have

c^8 / c^5

which simplifies to

c^3 in the numerator.

Once you combine everything, you get

9a^3c^3 / b^2

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SAT Math : Algebraic Fractions

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #11 : Algebraic Fractions

Example Question #12 : Algebraic Fractions

Example Question #2 : Algebraic Fractions

Example Question #14 : Algebraic Fractions

Example Question #13 : Algebraic Fractions

Example Question #14 : Algebraic Fractions

Example Question #12 : How To Simplify A Fraction

Example Question #16 : Algebraic Fractions

Example Question #17 : Algebraic Fractions

Example Question #11 : Algebraic Fractions

All SAT Math Resources

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