Mixed / Improper Fractions

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ACT Math › Mixed / Improper Fractions

Questions 1 - 10

1

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

$\frac{517}{19}$

$\frac{31}{19}$

$\frac{481}{19}$

$\frac{813}{17}$

$\frac{49}{19}$

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 . Next, you add this to the numerator of your fraction, giving you , or . Finally, you place this over your original denominator, giving you:

$\frac{517}{19}$

2

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

$\frac{517}{19}$

$\frac{31}{19}$

$\frac{481}{19}$

$\frac{813}{17}$

$\frac{49}{19}$

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 . Next, you add this to the numerator of your fraction, giving you , or . Finally, you place this over your original denominator, giving you:

$\frac{517}{19}$

3

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

$\frac{72}{5}$

$\frac{16}{5}$

$\frac{70}{5}$

$\frac{84}{3}$

$\frac{24}{5}$

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

$\frac{72}{5}$

4

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

$\frac{72}{5}$

$\frac{16}{5}$

$\frac{70}{5}$

$\frac{84}{3}$

$\frac{24}{5}$

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

$\frac{72}{5}$

5

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

$6\frac{1}{3}$

$6\frac{3}{5}$

$\frac{3}{19}$

$\frac{13}{3}$

$8\frac{2}{3}$

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.

6

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

$6\frac{1}{3}$

$6\frac{3}{5}$

$\frac{3}{19}$

$\frac{13}{3}$

$8\frac{2}{3}$

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.

7

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

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

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

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

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

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

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 $\small 11$ :

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

8

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

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

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

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

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

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

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 $\small 11$ :

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

9

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

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

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

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

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

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

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 $\small 6$ :

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

10

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

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

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

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

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

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

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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