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ACT Math : How to find out a mixed fraction from an improper fraction

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Example Questions

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:

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

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

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

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

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

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

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

Possible Answers:

$5\frac{1}{2}$ $\displaystyle 5\frac{1}{2}$

$4\frac{1}{4}$ $\displaystyle 4\frac{1}{4}$

$5\frac{3}{4}$ $\displaystyle 5\frac{3}{4}$

$2\frac{1}{4}$ $\displaystyle 2\frac{1}{4}$

Correct answer:

$5\frac{3}{4}$ $\displaystyle 5\frac{3}{4}$

Explanation:

$\displaystyle 4$ goes into $\displaystyle 23$ five times with a remainder of $\displaystyle 3$

The denominator does not change.

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

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

Possible Answers:

$\frac{13}{3}$ $\displaystyle \frac{13}{3}$

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

$6\frac{3}{5}$ $\displaystyle 6\frac{3}{5}$

$6\frac{1}{3}$ $\displaystyle 6\frac{1}{3}$

$\frac{3}{19}$ $\displaystyle \frac{3}{19}$

Correct answer:

$6\frac{1}{3}$ $\displaystyle 6\frac{1}{3}$

Explanation:

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

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

Now, the closest even multiple of $\displaystyle 3$ that is less than $\displaystyle 19$ is $\displaystyle 18$ . Therefore, you know that your number is:

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

This is the same as:

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

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Example Question #1 : Mixed / Improper Fractions

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

Possible Answers:

$20\frac{1}{2}$ $\displaystyle 20\frac{1}{2}$

$15\frac{3}{4}$ $\displaystyle 15\frac{3}{4}$

$20\frac{3}{8}$ $\displaystyle 20\frac{3}{8}$

$15\frac{1}{2}$ $\displaystyle 15\frac{1}{2}$

$20\frac{1}{4}$ $\displaystyle 20\frac{1}{4}$

Correct answer:

$20\frac{1}{2}$ $\displaystyle 20\frac{1}{2}$

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 $\displaystyle 82$ by $\displaystyle 4$ . This gives you 20.5 $\displaystyle 20.5$ . Therefore, you can eliminate all the options that have do not have $\displaystyle 20$ for their first portion. Next, multiply 0.5 $\displaystyle 0.5$ by the denominator ( $\displaystyle 4$ ), and get $\displaystyle 2$ . This means that you have $\displaystyle 20$ and $\frac{2}{4}$ $\displaystyle \frac{2}{4}$ , or $\frac{1}{2}$ $\displaystyle \frac{1}{2}$ . Thus, your answer is $20\frac{1}{2}$ $\displaystyle 20\frac{1}{2}$ .

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

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

Possible Answers:

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

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

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

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

$3\tfrac{1}{7}$ $\displaystyle 3\tfrac{1}{7}$

Correct answer:

$3\tfrac{1}{7}$ $\displaystyle 3\tfrac{1}{7}$

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

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

Possible Answers:

$5\frac{1}{6}$ $\displaystyle 5\frac{1}{6}$

$\frac{6}{27}$ $\displaystyle \frac{6}{27}$

$4\frac{1}{2}$ $\displaystyle 4\frac{1}{2}$

$1\frac{6}{21}$ $\displaystyle 1\frac{6}{21}$

$4\frac{3}{6}$ $\displaystyle 4\frac{3}{6}$

Correct answer:

$4\frac{1}{2}$ $\displaystyle 4\frac{1}{2}$

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:
$\frac{27}{6} = 4 \frac{3}{6} = 4 \frac{1}{2}$ $\displaystyle \frac{27}{6} = 4 \frac{3}{6} = 4 \frac{1}{2}$ when we reduce.

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ACT Math : How to find out a mixed fraction from an improper fraction

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

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

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

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

Example Question #1 : Mixed / Improper Fractions

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

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

All ACT Math Resources

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