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ACT Math : Algebraic Fractions

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Example Questions

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 #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 #11 : Algebraic Fractions

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

Possible Answers:

$\frac{6}{60}$

$\frac{1}{36}$

$\frac{1}{10}$

$\frac{1}{60}$

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 #12 : Algebraic Fractions

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

Possible Answers:

$\frac{4}{8}$

$\frac{8}{64}$

$\frac{1}{8}$

$\frac{4}{64}$

$\frac{2}{8}$

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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Example Question #1 : How To Evaluate A Fraction

Evaluate the following equation when x=5 and round your answer to the nearest hundredth.

$\frac{x^{3}-2x^{2}-3x+5}{5x+3}$

Possible Answers:

4.33

5.00

2.32

-1.94

5.28

Correct answer:

2.32

Explanation:

$\frac{x^{3}-2x^{2}-3x+5}{5x+3}$

1. Plug in wherever there is an in the above equation.

$\frac{5^{3}-(2)(5^{2})-(3)(5)+5}{(5)(5)+3}$

2. Perform the above operations.

$\frac{5^{3}-(2)(25)-(3)(5)+5}{(5)(5)+3}$

$\frac{125-50-15+5}{25+3}$

$\frac{65}{28}=2.32$

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Example Question #13 : Algebraic Fractions

Mary walked to school at an average speed of 2 miles per hour and jogged back along the same route at an average speed of 6 miles per hour. If her total traveling time was 1 hour, what was the total number of miles in the round trip?

Possible Answers:

Correct answer:

Explanation:

Since Mary traveled 3 times as quickly coming from school as she did going to school (6 miles per hour compared to 2 miles per hour), we know that Mary spent only a third of the time coming from school as she did going. If x represents the number of hours it took to get to school, then x/3 represents the number of hours it took her to return.

Knowing that the total trip took 1 hour, we have:

x + x/3 = 1

3x/3 + 1x/3 = 1

4x/3 = 1

x = 3/4

So we know it took Mary 3/4 of an hour to travel to school (and the remaining 1/4 of an hour to get back).

Remembering that distance = rate * time, the distance Mary traveled on her way to school was (2 miles per hour) * (3/4 of an hour) = 3/2 miles. Furthermore, since she took the same route coming back, she must have traveled 3/2 of a mile to return as well.

Therefore, the the total number of miles in Mary's round trip is 3/2 miles + 3/2 miles = 6/2 miles = 3 miles.

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Example Question #21 : Algebraic Fractions

If $w=\frac{1}{8}$ then which of the following is equal to $w^\frac{2}{3}$ ?

Possible Answers:

$\frac{1}{4}$

$\frac{1}{64}$

$\frac{1}{32}$

$\frac{1}{2}$

$\frac{1}{16}$

Correct answer:

$\frac{1}{4}$

Explanation:

To raise $\frac{1}{8}$ to the exponent $\frac{2}{3}$ , square $\frac{1}{8}$ and then take the cube root.

$w^\frac{2}{3}=\sqrt[3]{w^2}$

$(\frac{1}{8})^\frac{2}{3}=\sqrt[3]{(\frac{1}{8})^2}=\sqrt[3]{\frac{1}{64}}$

$\sqrt[3]{\frac{1}{64}}=\frac{1}{4}$

$(\frac{1}{8})^{\frac{2}{3}}=\frac{1}{4}$

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ACT Math : Algebraic Fractions

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

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 #2512 : Act Math

Example Question #11 : Algebraic Fractions

Example Question #12 : Algebraic Fractions

Example Question #1 : How To Evaluate A Fraction

Example Question #13 : Algebraic Fractions

Example Question #21 : Algebraic Fractions

All ACT Math Resources

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