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

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:

$\frac{72}{5}$

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

$\frac{517}{19}$

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 $\small 11$ :

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

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 $\small 6$ :

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

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

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

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

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

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

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

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:

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

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

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

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

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

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

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

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:

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

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

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

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

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

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

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

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

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

$\frac{12}{5}$

$\frac{14}{5}$

$\frac{9}{5}$

$\frac{11}{5}$

$\frac{13}{5}$

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.

$2\tfrac{2}{5} = \frac{(5\cdot 2) +2}{5} = \frac{12}{5}$

Simplify:

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

$\small 12$

$\small 10$

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

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

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

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 $\small 7$ .

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

$\frac{76}{7}$

$\frac{360}{7}$

$\frac{355}{7}$

$\frac{76}{8}$

$\frac{502}{7}$

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

How to find out an improper fraction from a mixed fraction

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