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ACT Math : ACT Math

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 : How To Find Decimal Fractions

Simplify:

$0.35+\frac{0.75}{0.2}-0.4*\frac{0.5}{0.1}$

Possible Answers:

$\frac{21}{10}$

$\frac{30}{7}$

$\frac{213}{10}$

$\frac{25}{4}$

Correct answer:

$\frac{21}{10}$

Explanation:

Begin by multiplying all of your decimal fractions by $\frac{100}{100}$ :

$0.35+\frac{0.75}{0.2}*\frac{100}{100}-0.4*\frac{0.5}{0.1}*\frac{100}{100}$

Simplify:

$0.35+\frac{75}{20}-0.4*\frac{50}{10}=0.35+\frac{15}{4}-0.4*5$

Now perform the multiplication:

$0.35+\frac{15}{4}-2$

The easiest thing to do next is to subtract from 0.35 :

$0.35+\frac{15}{4}-2=\frac{15}{4}-1.65$

Next, convert 1.65 into the fraction $\frac{165}{100}$ :

$\frac{15}{4}-\frac{165}{100}$

Now, the common denominator can be 100 :

$\frac{15}{4}*\frac{25}{25}-\frac{165}{100}=\frac{375}{100}-\frac{165}{100}$

Simplify:

$\frac{375}{100}-\frac{165}{100}=\frac{210}{100}=\frac{21}{10}$

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Example Question #2 : Decimals

Convert 0.825 into a fraction.

Possible Answers:

$\frac{5}{7}$

$\frac{29}{40}$

$\frac{4}{5}$

$\frac{3}{5}$

$\frac{33}{40}$

Correct answer:

$\frac{33}{40}$

Explanation:

0.825 in fraction form is $\frac{825}{1000}$ . Simplifying the fraction equals $\frac{33}{40}$ .

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Example Question #1 : Decimals

What is 0.48x equivalent to?

Possible Answers:

48x

$\frac{24}{50}x$

$\frac{48}{x}$

$\frac{24}{100}x$

$\frac{24}{48}x$

Correct answer:

$\frac{24}{50}x$

Explanation:

We need to convert 0.48 into a fraction.

To do this, write down $\frac{0.48}{1}$

Now, because the decimal goes to the hundreth place, multiply the numerator and denominator of the fraction by 100.

$\frac{0.48\times100}{1\times100}=\frac{48}{100}$

Now, simplify the fraction.

$\frac{48}{100}=\frac{24}{50}$

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Example Question #2 : How To Find The Fractional Equivalent Of A Decimal

A tub of food contains 0.5 pounds of vegetables, 1.75 pounds of lard, and pounds of sausage. What is its total weight as an improper fraction?

Possible Answers:

$\frac{17}{4}$

$\frac{91}{8}$

$\frac{83}{4}$

$\frac{69}{4}$

$\frac{18}{4}$

Correct answer:

$\frac{69}{4}$

Explanation:

To begin with, it is easiest just to add these decimals together using your calculator:

0.5+1.75+15=17.25

Now, this is the same thing as:

17 + 0.25

We can rewrite this:

$17 + \frac{1}{4}$

To find this, you need to give the two numbers a common denominator:

$17 + \frac{1}{4} = \frac{68}{4}+\frac{1}{4}=\frac{69}{4}$

This is your answer.

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Example Question #1 : How To Find The Fractional Equivalent Of A Decimal

What is the fractional equivalent of 0.33 ?

Possible Answers:

$\frac{3}{10}$

$\frac{33}{100}$

$\frac{333}{1000}$

$\frac{1}{3}$

Correct answer:

$\frac{33}{100}$

Explanation:

In decimal form 0.33 is said 33 hundredths.

This is equal to

$\frac{33}{100}$ .

This fraction cannot be reduced any further therefore it is in its final answer form.

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Example Question #1 : How To Find The Fractional Equivalent Of A Decimal

Write 0.45 as a fraction.

Possible Answers:

$\frac{11}{20}$

$\frac{5}{9}$

$\frac{3}{4}$

$\frac{9}{20}$

$\frac{2}{5}$

Correct answer:

$\frac{9}{20}$

Explanation:

.45 is equivalent to 45 out of 100, or $\frac{45}{100}$ .

Divide both the numerator and denominator by 5 to simplify the fraction:

$\frac{9}{20}$

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Example Question #261 : Arithmetic

Convert this decimal to a fraction in reduced form:

$\large 0.3\overline{6}$

Possible Answers:

$\frac{9}{25}$

$\frac{11}{30}$

$\frac{4}{11}$

$\frac{12}{37}$

Correct answer:

$\frac{11}{30}$

Explanation:

To figure out what fraction this decimal corresponds to, we have to get rid of the repeating part, otherwise we would be dealing with an infinite recursion and we don't have the tools to deal with that yet. Instead, we will set the decimal equal to and multiply it by 10, and also multiply it by 100.

$x = 0.3\overline{6}{}$

$10x=3.\overline{6}{}$

$100x = 36.\overline{6}{}$

Notice that in 10x and 100x we have the same repeating decimal part. So if we subtract them, it disappears:

100x-10x=33.0{}

Now all that remains is to do the algebra.

90x=33{}

$x=\frac{33}{90} = \frac{11}{30}{}$

$\frac{11}{30}{}$ is our final answer.

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Example Question #1 : How To Find The Fractional Equivalent Of A Decimal

What is the fractional equivalent of 3.14 ?

Possible Answers:

$\frac{51}{16}$

$\frac{22}{7}$

$\frac{157}{50}$

$\textup{None of these}$

$\frac{71}{23}$

Correct answer:

$\frac{157}{50}$

Explanation:

To find the fractional equivalent of a decimal, set the decimal as a fraction over , then multiply top and bottom by one power of for each digit after the decimal. In this case, we have two digits after the decimal, so we multiply top and bottom by 100 :

$3.14 = \frac{3.14}{1} = \frac{314}{100}$

Now, start simplifying.

$\frac{314}{100} = \frac{157}{50}$

Since we cannot reduce further, $3.14 = \frac{157}{50}$ .

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Example Question #1 : Basic Squaring / Square Roots

Find the square of 0.12 .

Possible Answers:

0.0144

14.4

1.44

0.144

Correct answer:

0.0144

Explanation:

Squaring a decimal is identical to multiplying decimals.

Drop the decimal, multiply the number by its self, and then add up the decimal points in the original problem and put it back into your answer.

$0.12^2=0.12\cdot0.12$ (note: 4 decimal places)

$12\cdot12=144\rightarrow 0.0144$

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Example Question #1 : Basic Squaring / Square Roots

What is $\small 0.1^{3}$ ?

Possible Answers:

0.3

0.01

0.1

100

0.001

Correct answer:

0.001

Explanation:

You can solve this on your calculator, or think about it as a fraction $\left( \small \frac{1}{10}\right)$ to make the problem easier to do by hand. $\small 0.1^{3}=0.1\times 0.1\times 0.1=0.001$ .

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ACT Math : ACT Math

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : How To Find Decimal Fractions

Example Question #2 : Decimals

Example Question #1 : Decimals

Example Question #2 : How To Find The Fractional Equivalent Of A Decimal

Example Question #1 : How To Find The Fractional Equivalent Of A Decimal

Example Question #1 : How To Find The Fractional Equivalent Of A Decimal

Example Question #261 : Arithmetic

Example Question #1 : How To Find The Fractional Equivalent Of A Decimal

Example Question #1 : Basic Squaring / Square Roots

Example Question #1 : Basic Squaring / Square Roots

All ACT Math Resources

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