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ACT Math : Algebra

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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 #1021 : Algebra

Simplify the following expression:

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

Possible Answers:

$2$

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

$x^{2}+4$

$x^{2}-4$

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

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 #5 : How To Simplify A Fraction

Simplify:

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

Possible Answers:

None of the other answers

y-5y

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

1-5x

1-5y

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 #6 : How To Simplify A Fraction

Simplify the given fraction:

$\frac{120}{6000}$

Possible Answers:

$\frac{2}{25}$

$\frac{1}{5}$

$\frac{1}{100}$

$\frac{1}{20}$

$\frac{1}{50}$

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 #2512 : Act Math

Simplify: $\frac{18}{54}$

Possible Answers:

$\frac{1}{3}$

$\frac{3}{9}$

$\frac{2}{9}$

$\frac{9}{27}$

$\frac{2}{3}$

Correct answer:

$\frac{1}{3}$

Explanation:

is one third of , so $\frac{18}{54}$ in its simplest form is $\frac{1}{3}$ . To reach this answer, divide both and by .

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Example Question #1022 : Algebra

What is $\frac{6}{360}$ in its simplest form?

Possible Answers:

$\frac{1}{10}$

$\frac{1}{60}$

$\frac{1}{36}$

$\frac{6}{60}$

$\frac{1}{36}$

Correct answer:

$\frac{1}{60}$

Explanation:

To reach the answer, divide both the numerator and denominator by . After doing that, the answer is $\frac{1}{60}$ .

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Example Question #1023 : Algebra

Simplify: $\frac{8}{64}$

Possible Answers:

$\frac{4}{64}$

$\frac{1}{8}$

$\frac{8}{64}$

$\frac{4}{8}$

$\frac{2}{8}$

Correct answer:

$\frac{1}{8}$

Explanation:

To find the answer, divide both the numerator and the denominator by . The result is $\frac{1}{8}$ .

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ACT Math : Algebra

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #11 : Algebraic Fractions

Example Question #1021 : Algebra

Example Question #5 : How To Simplify A Fraction

Example Question #6 : How To Simplify A Fraction

Example Question #13 : Algebraic Fractions

Example Question #14 : Algebraic Fractions

Example Question #12 : How To Simplify A Fraction

Example Question #2512 : Act Math

Example Question #1022 : Algebra

Example Question #1023 : Algebra

All ACT Math Resources

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