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ACT Math : Arithmetic

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Example Questions

Example Question #141 : Fractions

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

Possible Answers:

$\frac{9}{5}$

$\frac{13}{5}$

$\frac{11}{5}$

$\frac{12}{5}$

$\frac{14}{5}$

Correct answer:

$\frac{12}{5}$

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.

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

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Example Question #5 : How To Find Out An Improper Fraction From A Mixed Fraction

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

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 $\small 11$ :

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

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Example Question #1531 : Act Math

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

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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Example Question #8 : Mixed / Improper Fractions

Simplify:

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

Possible Answers:

$\small 12$

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

$\small 10$

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

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

Correct answer:

$\small 12$

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 $\small 7$ .

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Example Question #5 : How To Find Out An Improper Fraction From A Mixed Fraction

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

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:

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

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

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

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:

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

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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 #11 : Mixed / Improper Fractions

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

Possible Answers:

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

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

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

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

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

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 #461 : Arithmetic

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

Possible Answers:

$4\frac{1}{4}$

$2\frac{1}{4}$

$5\frac{1}{2}$

$5\frac{3}{4}$

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 #13 : Mixed / Improper Fractions

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

Possible Answers:

$\frac{13}{3}$

$8\frac{2}{3}$

$6\frac{1}{3}$

$6\frac{3}{5}$

$\frac{3}{19}$

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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ACT Math : Arithmetic

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #141 : Fractions

Example Question #5 : How To Find Out An Improper Fraction From A Mixed Fraction

Example Question #1531 : Act Math

Example Question #8 : Mixed / Improper Fractions

Example Question #5 : How To Find Out An Improper Fraction From A Mixed Fraction

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

Example Question #1531 : Act Math

Example Question #11 : Mixed / Improper Fractions

Example Question #461 : Arithmetic

Example Question #13 : Mixed / Improper Fractions

All ACT Math Resources

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