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ACT Math : Mixed / Improper Fractions

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Example Questions

Example Question #1531 : Act Math

Which of the following is equivalent to $\small \frac{52}{6}$ ?

Possible Answers:

$\small 8\frac{1}{3}$

$\small 8\frac{2}{3}$

$\small 9\frac{1}{6}$

$\small \small 8\frac{5}{6}$

$\small 8\frac{1}{2}$

Correct answer:

$\small 8\frac{2}{3}$

Explanation:

Use your calculator to your advantage. You know that $\small \frac{52}{6}$ is $\small 8.66666666666667$ . This means that the mixed fraction equivalent must be of the form:

$\small \small \small 8\frac{x}{6}$

Now, you find the fractional portion by multiplying $\small 0.66666666666667$ by $\small \small 6$ , which when rounded gives you $\small 4$ . (The quickest way to get $\small 0.66666666666667$ in your calculator is to subtract $\small 8$ from $\small 8.66666666666667$ .) Thus, your answer is:

$\small \small 8\frac{4}{6}$ , which should be reduced to $\small 8\frac{2}{3}$ .

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

Convert $\dpi{100} \small \frac{21}{4}$ to a mixed number.

Possible Answers:

$\dpi{100} \small 4\frac{1}{4}$

$\dpi{100} \small \frac{4}{5}$

$\dpi{100} \small 5\frac{1}{2}$

$\dpi{100} \small 5\frac{1}{4}$

$\dpi{100} \small 20\frac{1}{4}$

Correct answer:

$\dpi{100} \small 5\frac{1}{4}$

Explanation:

4 goes into 21 five times. 5 becomes your whole number. There is a remainder of 1 and your denominator remains the same, so your fraction is $\dpi{100} \small \frac{1}{4}$ .

$\dpi{100} \small 5\frac{1}{4}$

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Example Question #11 : Mixed / Improper Fractions

What is $\frac{23}{4}$ written as a mixed number?

Possible Answers:

$5\frac{3}{4}$

$5\frac{1}{2}$

$4\frac{1}{4}$

$2\frac{1}{4}$

Correct answer:

$5\frac{3}{4}$

Explanation:

goes into five times with a remainder of

The denominator does not change.

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Example Question #2 : Mixed / Improper Fractions

Which of the following is the mixed fraction equivalent to $\frac{19}{3}$ ?

Possible Answers:

$6\frac{3}{5}$

$6\frac{1}{3}$

$\frac{13}{3}$

$8\frac{2}{3}$

$\frac{3}{19}$

Correct answer:

$6\frac{1}{3}$

Explanation:

To begin, notice that using your calculator, you can find:

$\frac{19}{3} = 6.33333...$

Now, the closest even multiple of that is less than is . Therefore, you know that your number is:

$\frac{19}{3}=\frac{18}{3}+\frac{1}{3}$

This is the same as:

$6+\frac{1}{3}$ , or simply, $6\frac{1}{3}$ . This is your mixed fraction.

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Example Question #4 : Mixed / Improper Fractions

Which of the following is equivalent to $\frac{82}{4}$ ?

Possible Answers:

$15\frac{1}{2}$

$20\frac{1}{4}$

$15\frac{3}{4}$

$20\frac{3}{8}$

$20\frac{1}{2}$

Correct answer:

$20\frac{1}{2}$

Explanation:

Although there are many ways to convert improper fractions into mixed fractions, the easiest way is to use your calculator to your advantage. Begin by dividing by . This gives you 20.5 . Therefore, you can eliminate all the options that have do not have for their first portion. Next, multiply 0.5 by the denominator (), and get . This means that you have and $\frac{2}{4}$ , or $\frac{1}{2}$ . Thus, your answer is $20\frac{1}{2}$ .

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Example Question #12 : Mixed / Improper Fractions

What does $\small \small \small \small \frac{32}{14}+\frac{6}{7}$ equal, expressed as a mixed number?

Possible Answers:

$\small 1\tfrac{17}{21}$

$\small 2\tfrac{2}{7}$

$3\tfrac{1}{7}$

$\small 1\tfrac{5}{14}$

$\small 1\tfrac{4}{7}$

Correct answer:

$3\tfrac{1}{7}$

Explanation:

Simplify the two fractions, then find a common denominator, then solve. $\small \small \frac{32}{14}+\frac{6}{7}=\frac{16}{7}+\frac{6}{7}=\frac{22}{7}=3\tfrac{1}{7}$

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Example Question #4 : How To Find Out A Mixed Fraction From An Improper Fraction

Convert the improper fraction $\frac{27}{6}$ to a mixed number. Reduce all fractions if possible.

Possible Answers:

$5\frac{1}{6}$

$1\frac{6}{21}$

$\frac{6}{27}$

$4\frac{1}{2}$

$4\frac{3}{6}$

Correct answer:

$4\frac{1}{2}$

Explanation:

To convert a mixed number into a fraction, first divide the denominator into the numerator and record the remainder:

$27/6 = 4 \:\textup{remainder} \: 3$ .

the result is the mixed number, with the remainder being put as the numerator over the old denominator:
$\frac{27}{6} = 4 \frac{3}{6} = 4 \frac{1}{2}$ when we reduce.

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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 #1531 : Act Math

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

Example Question #11 : Mixed / Improper Fractions

Example Question #2 : Mixed / Improper Fractions

Example Question #4 : Mixed / Improper Fractions

Example Question #12 : Mixed / Improper Fractions

Example Question #4 : How To Find Out A Mixed Fraction From An Improper Fraction

All ACT Math Resources

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