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Example Questions

Example Question #131 : Fractions

A flight from Boston to Los Angeles lasts about 6 hours. The time zone difference is such that it is 3 hours later in Boston. If the flight leaves Boston at 8:00 AM, what will be the local time in Los Angeles when the plane arrives?

Possible Answers:

5:00 PM

1:00 PM

3:00 PM

11:00 AM

2:00 PM

Correct answer:

11:00 AM

Explanation:

The plane will land in Los Angeles at 2:00 PM Boston time (8:00 AM + 6 hours = 2:00 PM).

Going west, subtract the time zone difference. Going east, add the time zone difference.

So, 2:00 PM Boston time becomes 11:00 AM local time in Los Angeles (2:00 PM – 3 hours = 11:00 AM).

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Example Question #1521 : Act Math

How many rational numbers are between 1 and 2?

Possible Answers:

Just one

Two: 1 and 2

None

Infinitely many

Correct answer:

Infinitely many

Explanation:

The definition of a rational number is an integer or a fraction. We can take the fractions 3/2, 4/3, 5/4, 6/5, 7/6, 8/7,...and continue in this way to realize there are infinitely many rational numbers.

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Example Question #1 : Compound Fractions

John's shadow is six feet long, and Mary's shadow is five feet long. If John is four feet tall, which of the following is closest to Mary's height in inches?

Possible Answers:

$33\ inches$

$48\ inches$

$12\ inches$

$60\ inches$

$40\ inches$

Correct answer:

$40\ inches$

Explanation:

First we set up a proportion. Mary's shadow (5 feet) to John's shadow (6 feet) is equal to Mary's height (x feet) to John's height (4 feet), i.e. 5 / 6 = x / 4.

Solve for x by first cross-mulitplying: 20 = 6x.

Divide both sides by 6: x = 20 / 6 feet

Multiply by 12 to find this height in inches: 20 * 12 / 6 = 20 * 2 = 40 inches

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Example Question #2 : Compound Fractions

When two resistors ( $R_{1}$ and $R_{2}$ ) are added together in a parallel circuit to create an equivalent single resistor, the equivalent resistor ( $R_{eq}$ ) has a resistance defined by the following equation:

$\frac{1}{R_{eq}}= \frac{1}{R_{1}}+\frac{1}{R_{2}}$

If $R_{1}=10$ and $R_{2}=20$ , what does $R_{eq}$ equal?

Possible Answers:

None of the other answers

$\frac{20}{3}$

$\frac{3}{20}$

Correct answer:

$\frac{20}{3}$

Explanation:

Plugging $R_{1}=10$ and R_2=20 into the equation gives:

$\frac{1}{R_{eq}}=\frac{1}{10}+\frac{1}{20}$

Create a common denominator by multiplying $\frac{1}{10}$ by in the numerator and denominator:

$\frac{1}{R_{eq}}=\frac{2}{20}+\frac{1}{20}$

$\frac{1}{R_{eq}}=\frac{3}{20}$

Finally:

$R_{eq} = \frac{20}{3}$

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Example Question #3 : Compound Fractions

What does $\small \frac{\frac{2}{3}\times \frac{1}{4}}{\frac{2}{9}+\frac{1}{3}}$ equal?

Possible Answers:

$\frac{11}{17}$

$\frac{5}{54}$

$\frac{18}{35}$

$\frac{3}{10}$

$\frac{1}{2}$

Correct answer:

$\frac{3}{10}$

Explanation:

Simplify the numerator first: $\small \frac{2}{3}\times \frac{1}{4}=\frac{2}{12}=\frac{1}{6}$ .

Then, simplify the denominator: $\frac{2}{9}+\frac{1}{3}=\frac{2}{9}+\frac{3}{9}=\frac{5}{9}$ .

Next, you have to do $\frac{1}{6}\div \frac{5}{9}$ , which is the same as $\small \small \frac{1}{6}\times \frac{9}{5}=\frac{9}{30}=\frac{3}{10}$ , when solved for and simplified.

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Example Question #1 : How To Find Out An Improper Fraction From A Mixed Fraction

Turn the following from a mixed number to an improper fraction:

$4\frac{7}{9}$

Possible Answers:

$\frac{28}{9}$

$\frac{43}{9}$

$\frac{37}{7}$

$\frac{11}{9}$

$\frac{13}{7}$

Correct answer:

$\frac{43}{9}$

Explanation:

To turn a mixed number into an improper fraction you must recognize the following:

$4\frac{7}{9}=4+\frac{7}{9}$

now we need to add 4 and seven ninths, to do that you multiply by a good form of 1

$4+\frac{7}{9}=\frac{9}{9}\cdot4+\frac{7}{9}=\frac{36}{9}+\frac{7}{9}$

now with the common denominator you can add the fractions to get

$\frac{43}{9}$

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Example Question #1 : How To Find Out An Improper Fraction From A Mixed Fraction

Write $71\frac{5}{7}$ as an improper fraction.

Possible Answers:

$\frac{502}{7}$

$\frac{355}{7}$

$\frac{360}{7}$

$\frac{76}{7}$

$\frac{76}{8}$

Correct answer:

$\frac{502}{7}$

Explanation:

To find the improper fraction value, we must effectively add together 71 and ⁵/₇. To do this, we will give 71 a denominator of 7; therefore, we are transforming ⁷¹/₁ to ^x/₇. The shortest way to do this is to multiply by ⁷/₇ (which really is 1); therefore, 71 = 71 * (⁷/₇) = ⁴⁹⁷/₇.

Now add them: ^{(497 + 5)}/₇ = ⁵⁰²/₇

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Example Question #2 : How To Find Out An Improper Fraction From A Mixed Fraction

Which of the following improper fractions is equivalent to $14\frac{2}{5}$ ?

Possible Answers:

$\frac{72}{5}$

$\frac{84}{3}$

$\frac{70}{5}$

$\frac{24}{5}$

$\frac{16}{5}$

Correct answer:

$\frac{72}{5}$

Explanation:

To find an improper fraction, you need to multiply the whole number that you have by the denominator of the associated fraction. For our problem, this means that you will multiply by , getting . Next, you add this to the numerator of your fraction, giving you 70+2 , or . Finally, you place this over your original denominator, giving you:

$\frac{72}{5}$

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Example Question #3 : How To Find Out An Improper Fraction From A Mixed Fraction

Which of the following improper fractions is equivalent to $27\frac{4}{19}$ ?

Possible Answers:

$\frac{49}{19}$

$\frac{813}{17}$

$\frac{517}{19}$

$\frac{31}{19}$

$\frac{481}{19}$

Correct answer:

$\frac{517}{19}$

Explanation:

To find an improper fraction, you need to multiply the whole number that you have by the denominator of the associated fraction. For our problem, this means that you will multiply by , getting 513 . Next, you add this to the numerator of your fraction, giving you 513+4 , or 517 . Finally, you place this over your original denominator, giving you:

$\frac{517}{19}$

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Example Question #2 : How To Find Out An Improper Fraction From A Mixed Fraction

Convert $2\tfrac{2}{5}$ to an improper fraction.

Possible Answers:

$\frac{9}{5}$

$\frac{12}{5}$

$\frac{14}{5}$

$\frac{13}{5}$

$\frac{11}{5}$

Correct answer:

$\frac{12}{5}$

Explanation:

To determine the numerator of the improper fraction, multiply the denominator with the whole number. Then add this with the numerator. The denominator will remain the same.

$2\tfrac{2}{5} = \frac{(5\cdot 2) +2}{5} = \frac{12}{5}$

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ACT Math : ACT Math

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #131 : Fractions

Example Question #1521 : Act Math

Example Question #1 : Compound Fractions

Example Question #2 : Compound Fractions

Example Question #3 : Compound Fractions

Example Question #1 : How To Find Out An Improper Fraction From A Mixed Fraction

Example Question #1 : How To Find Out An Improper Fraction From A Mixed Fraction

Example Question #2 : How To Find Out An Improper Fraction From A Mixed Fraction

Example Question #3 : How To Find Out An Improper Fraction From A Mixed Fraction

Example Question #2 : How To Find Out An Improper Fraction From A Mixed Fraction

All ACT Math Resources

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