Mixed / Improper Fractions - ACT Math

Card 0 of 17

Question

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

Answer

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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Question

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

Answer

goes into five times with a remainder of

The denominator does not change.

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Question

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

Answer

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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Question

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

Answer

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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Question

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

Answer

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 . Therefore, you can eliminate all the options that have do not have for their first portion. Next, multiply 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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Question

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

Answer

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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Question

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

Answer

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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Question

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

$4\frac{7}{9}$

Answer

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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Question

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

Answer

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 , or . Finally, you place this over your original denominator, giving you:

$\frac{72}{5}$

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Question

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

Answer

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 , or . Finally, you place this over your original denominator, giving you:

$\frac{517}{19}$

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Question

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

Answer

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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Question

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

Answer

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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Question

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

Answer

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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Question

Simplify:

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

Answer

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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Question

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

Answer

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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Question

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

Answer

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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Question

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

Answer

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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