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ACT Math : Mixed / Improper Fractions

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Example Questions

Example Question #453 : Arithmetic

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

$4\frac{7}{9}$

Possible Answers:

$\frac{13}{7}$

$\frac{43}{9}$

$\frac{11}{9}$

$\frac{37}{7}$

$\frac{28}{9}$

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:

$\frac{76}{7}$

$\frac{76}{8}$

$\frac{502}{7}$

$\frac{360}{7}$

$\frac{355}{7}$

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 : Mixed / Improper Fractions

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

Possible Answers:

$\frac{24}{5}$

$\frac{72}{5}$

$\frac{16}{5}$

$\frac{84}{3}$

$\frac{70}{5}$

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 : Mixed / Improper Fractions

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

Possible Answers:

$\frac{31}{19}$

$\frac{49}{19}$

$\frac{517}{19}$

$\frac{481}{19}$

$\frac{813}{17}$

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 #1 : Mixed / Improper Fractions

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

Possible Answers:

$\frac{14}{5}$

$\frac{11}{5}$

$\frac{9}{5}$

$\frac{12}{5}$

$\frac{13}{5}$

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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Example Question #5 : How To Find Out An Improper Fraction From A Mixed Fraction

Which of the following is equivalent to $\small 5\frac{7}{11}$ ?

Possible Answers:

$\small \frac{71}{11}$

$\small \frac{21}{3}$

$\small \frac{62}{11}$

$\small \frac{53}{11}$

$\small \frac{12}{11}$

Correct answer:

$\small \frac{62}{11}$

Explanation:

Remember that to convert mixed fractions, you can treat it like an addition. Thus

$\small 5\frac{7}{11} = 5 + \frac{7}{11}$

You then find the common denominator of the two which is $\small 11$ :

$\small 5 + \frac{7}{11} = \frac{55 + 7}{11} = \frac{62}{11}$

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Example Question #7 : Mixed / Improper Fractions

Which of the following is equivalent to $\small 4 \frac{5}{6}$ ?

Possible Answers:

$\small \frac{29}{6}$

$\small \frac{11}{2}$

$\small \frac{25}{6}$

$\small \frac{11}{6}$

$\small \frac{23}{6}$

Correct answer:

$\small \frac{29}{6}$

Explanation:

Remember that to convert mixed fractions, you can treat it like an addition. Thus

$\small 4 \frac{5}{6} = 4 +\frac{5}{6}$

You then find the common denominator of the two which is $\small 6$ :

$\small \frac{24 + 5}{6} = \frac{29}{6}$

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Example Question #8 : Mixed / Improper Fractions

Simplify:

$\small 4 \frac{2}{3} + 7\frac{1}{3}$

Possible Answers:

$\small 12$

$\small \frac{34}{3}$

$\small 10$

$\small \frac{13}{3}$

$\small \frac{14}{3}$

Correct answer:

$\small 12$

Explanation:

Remember that to convert mixed fractions, you can treat it like an addition. Thus

$\small 4 = \frac{2}{3} + 7\frac{1}{3} = 4 + \frac{2}{3} + 7 + \frac{1}{3}$

Now, using the common denominator of $\small 3$ , you know:

$\small 4 + \frac{2}{3} + 7 + \frac{1}{3} = \frac{12+2+21+1}{3} = \frac{36}{3} = 12$

Another way to do this is to notice that $\small \frac{2}{3} + \frac{1}{3} = 1$ . Then you just add these values to $\small 4$ and $\small 7$ .

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Example Question #5 : How To Find Out An Improper Fraction From A Mixed Fraction

Which of the following is equivalent to $\small \frac{55}{7}$ ?

Possible Answers:

$\small 8\frac{1}{7}$

$\small 6\frac{4}{7}$

$\small \small 7\frac{6}{7}$

$\small \small \small 7\frac{3}{7}$

$\small 7\frac{1}{7}$

Correct answer:

$\small \small 7\frac{6}{7}$

Explanation:

Use your calculator to your advantage. You know that $\small \frac{55}{7}$ is $\small \small 7.85714285714286$ . This means that the mixed fraction equivalent must be of the form:

$\small 7\frac{x}{7}$

Now, you find the fractional portion by multiplying $\small 0.85714285714286$ by $\small 7$ , which when rounded gives you $\small 6$ . (The quickest way to get $\small 0.85714285714286$ in your calculator is to subtract $\small 7$ from $\small \small 7.85714285714286$ .) Thus, your answer is:

$\small \small 7\frac{6}{7}$

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

Which of the following is equivalent to $\small \frac{71}{6}$ ?

Possible Answers:

$\small 11\frac{5}{6}$

$\small \small 11\frac{2}{3}$

$\small \small \small 11\frac{1}{6}$

$\small \small 12\frac{1}{3}$

$\small \small 11\frac{1}{2}$

Correct answer:

$\small 11\frac{5}{6}$

Explanation:

Use your calculator to your advantage. You know that $\small \frac{71}{6}$ is $\small 11.83333333333333$ . This means that the mixed fraction equivalent must be of the form:

$\small \small 11\frac{x}{6}$

Now, you find the fractional portion by multiplying $\small \small 0.83333333333333$ by $\small \small 6$ , which when rounded gives you $\small \small 5$ . (The quickest way to get $\small \small 0.83333333333333$ in your calculator is to subtract $\small \small 11$ from $\small 11.83333333333333$ .) Thus, your answer is:

$\small 11\frac{5}{6}$

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ACT Math : Mixed / Improper Fractions

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #453 : Arithmetic

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

Example Question #2 : Mixed / Improper Fractions

Example Question #3 : Mixed / Improper Fractions

Example Question #1 : Mixed / Improper Fractions

Example Question #5 : How To Find Out An Improper Fraction From A Mixed Fraction

Example Question #7 : Mixed / Improper Fractions

Example Question #8 : Mixed / Improper Fractions

Example Question #5 : 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

All ACT Math Resources

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