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ACT Math : Arithmetic

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Example Questions

Example Question #3 : Lowest Common Denominator

Find the lowest common denominator of these four fractions:

$\frac{1}{3},\frac{1}{4},\frac{1}{12},\frac{1}{15}$

Possible Answers:

Correct answer:

Explanation:

All of the denominators must be able to divide into the same number. First, see if the three smaller numbers (3, 4, 12) divide into the largest number (15)—NO. Then check the multiples of the largest number to see if the lower numbers divide into it:

15 * 2 = 30 (NO)

15 * 3 = 45 (NO)

15 * 4 = 60 (YES!)

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Example Question #1 : How To Find The Lowest / Least Common Denominator

Solve the following: $\frac{7}{6}+\frac{3}{8}-\frac{10}{12}$

Possible Answers:

$\frac{5}{6}$

$\frac{2}{3}$

$\frac{3}{4}$

$\frac{17}{24}$

$\frac{11}{12}$

Correct answer:

$\frac{17}{24}$

Explanation:

Finding the common denomenator of yields a result of $\frac{17}{24}$

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Example Question #1 : Lowest Common Denominator

Find the least common denominator for the following fractions:

$\frac{1}{3},\frac{5}{12},\frac{7}{10}$

Possible Answers:

360

120

Correct answer:

Explanation:

The least common multiple of 3, 10, and 12 is 60. 60 is divisible by all three numbers (60/3 = 20, 60/10 = 6, and 60/12 = 5). Therefore, you could convert these fractions to 20/60, 25/60, and 42/60.

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Example Question #1 : Simplifying Fractions

Simplify the following fraction:

$\frac{24}{256}$

Possible Answers:

$\frac{8}{32}$

$\frac{6}{64}$

$\frac{3}{64}$

$\frac{3}{32}$

$\frac{12}{128}$

Correct answer:

$\frac{3}{32}$

Explanation:

Find the largest number that divides into both and 256

$\frac{24}{8}=3$

$\frac{256}{8}=32$

$\frac{24}{256}=\frac{3}{32}$

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Example Question #2 : How To Simplify A Fraction

Simplify the following fraction until the numerator and denominator share no factors.

$\frac{616}{210}$

Possible Answers:

$\frac{212}{245}$

$\frac{308}{105}$

$\frac{44}{15}$

$\frac{66}{47}$

Correct answer:

$\frac{44}{15}$

Explanation:

To simplify a fraction you need to find all the factors that the numerator and denominator have in common. You can see that both share 2 so when you divide both by 2 you get

$\frac{308}{105}$

this is close to the answer but it asks for no common factors, it is hard to see but both of these share 7 as a common factor. When you divide both by 7 you get

$\frac{44}{15}$

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Example Question #501 : Arithmetic

Which of the following is the least common denominator for the expression below?

$\frac{1}{d\times e^2\times f}-\frac{1}{d\times f^2}-\frac{1}{d^2\times f}$

Possible Answers:

$d\times f$

$d^2\times e\times f^2$

$d^2\times e^2\times f^2$

$d\times e\times f$

$d^5\times e^2\times f^4$

Correct answer:

$d^2\times e^2\times f^2$

Explanation:

Finding the least common denominator in rational expressions follows the same procedue as finding the least common denominator in fractions.

The least common denominator for this rational exresspion will use all terms with the highest exponents of each.

The first fraction has e^2 as the highest term, the second fraction has f^2 as the highest term, and the third fraction has d^2 as the highest term. Now we combine these and get the least common denominator to be:

$d^2 \times e^2 \times f^2$

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Example Question #501 : Arithmetic

Simplify the following fraction:
$\frac{96}{108}$

Possible Answers:

$\frac{32}{36}$

$\frac{48}{54}$

$\frac{8}{9}$

$\frac{16}{18}$

$\textup{The fraction is already in simplest form}$

Correct answer:

$\frac{8}{9}$

Explanation:

To simplify a fraction, find the gcf (gcd) of the numerator and denominator and divide both by the gcf (gcd). the gcf of and 108 is so:

$\frac{96/12}{108/12}=\frac{8}{9}$

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Example Question #4 : How To Simplify A Fraction

Simplify the following fraction:

$\small \frac{420}{5390}$

Possible Answers:

$\small \frac{44}{79}$

$\small \frac{42}{539}$

$\small \frac{21}{44}$

$\small \frac{84}{1078}$

$\small \frac{6}{77}$

Correct answer:

$\small \frac{6}{77}$

Explanation:

The first and easiest simplification for this fraction is to divide numerator and denominator by $\small 10$ . This gives you:

$\small \frac{42}{539}$

Next, notice that the two fractions do not both contain factors of $\small 3$ . This is because the denominator's digits, when added up come to $\small 17$ , which is not divisible by $\small 3$ . This means $\small 539$ is not divisible by $\small 3$ . Now, $\small 42$ is $\small 2*3*7$ . There is no shared $\small 2$ between these numbers. However, if you try, you will see that they are both divisible by $\small 7$ , which gives you:

$\small \frac{6}{77}$

This is simplest form.

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Example Question #3 : How To Simplify A Fraction

Simplify the following fraction:

$\small \frac{315}{825}$

Possible Answers:

$\small \frac{105}{275}$

$\small \small \small \frac{21}{55}$

$\small \frac{3}{5}$

$\small \frac{7}{11}$

$\small \small \frac{63}{165}$

Correct answer:

$\small \small \small \frac{21}{55}$

Explanation:

First, begin by noticing that both numerator and denominator contain a $\small 5$ . Dividing this out gives you:

$\small \small \frac{63}{165}$

Now, $\small 1+6+5=12$ and $\small 6+3=9$ . Since each of these are true, we know that both numerator and denominator contain a $\small 3$ . Dividing this out, you get:

$\small \small \small \frac{21}{55}$

This is the simplest possible form of the fraction.

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Example Question #5 : How To Simplify A Fraction

Maria owns an art studio and spent $\$1850$ in supplies. She sells her paintings for $\$150$ each. How many paintings does Maria need to sell until she makes a profit?

Possible Answers:

Correct answer:

Explanation:

Divide the total money spent by the cost of each painting.

$\frac{\$1850}{\$150}=12.33333$

Therefore, to make a profit, she needs to sell more than this amount. Since she can't sell a portion of a painting, the answer has to be the next nearest whole number ().

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ACT Math : Arithmetic

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #3 : Lowest Common Denominator

Example Question #1 : How To Find The Lowest / Least Common Denominator

Example Question #1 : Lowest Common Denominator

Example Question #1 : Simplifying Fractions

Example Question #2 : How To Simplify A Fraction

Example Question #501 : Arithmetic

Example Question #501 : Arithmetic

Example Question #4 : How To Simplify A Fraction

Example Question #3 : How To Simplify A Fraction

Example Question #5 : How To Simplify A Fraction

All ACT Math Resources

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