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ACT Math : Decimals with Fractions

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Example Questions

Example Question #1 : Decimals

When 5/11 is written as a decimal, what is the 100th digit to the right of the decimal point?

Possible Answers:

Correct answer:

Explanation:

When 5 is divided by 11, the decimal is 0.45 repeating, with a 5 in the hundreths place. The key here is to recognize that 100 is an even number, and the 5 in 0.45 is two places to the right of the decimal point (2 also being an even number).

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Example Question #1 : Decimals With Fractions

Find the sum of the following:

$5\frac{1}{8}+6\frac{3}{16}?$

Possible Answers:

11.1875

11.3125

11.25

11.625

11.125

Correct answer:

11.3125

Explanation:

To get the decimal from a fraction, divide the numerator by the denominator

$\frac{1}{8}=0.125$

$5\frac{1}{8}=5.125$

$\frac{3}{16}=0.1875$

$6\frac{3}{16}=6.1875$

5.125+6.1875=11.3125

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Example Question #1 : Decimals With Fractions

Find the sum to the nearest hundredth:

$13\frac{3}{8} + 12\frac{17}{40} ?$

Possible Answers:

27.4

25.8

28.9

26.3

24.3

Correct answer:

25.8

Explanation:

1. Convert the fractions to decimals by division:

$\frac{3}{8}=0.375$

$\frac{17}{40}=0.425$

2. Add the corresponding whole numbers to the decimals:

13+0.375=13.375

12+0.425=12.425

3. Add the two decimals:

13.375 + 12.425 = 25.8

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

If $\frac{1}{3} < x < 0.76$ , can equal which of the following?

Possible Answers:

$\frac{1}{4}$

$\frac{5}{16}$

None of the other answer choices are correct

$\frac{2}{5}$

$\frac{4}{12}$

Correct answer:

$\frac{2}{5}$

Explanation:

Convert all of the fractions to decimals. Thus, x is contained within the range of 0.33 < x < 0.76. The answers choices become 1/4 = 0.25, 4/12 = 0.33, 2/5 = 0.4, and 5/16 = 0.3125, respectively. Therefore, the only answer which is within the desired range is 2/5.

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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:

$\frac{30}{7}$

$\frac{25}{4}$

$\frac{21}{10}$

$\frac{213}{10}$

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 #1 : Decimals With Fractions

Convert 0.825 into a fraction.

Possible Answers:

$\frac{4}{5}$

$\frac{33}{40}$

$\frac{3}{5}$

$\frac{5}{7}$

$\frac{29}{40}$

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 #2 : Decimals With Fractions

What is 0.48x equivalent to?

Possible Answers:

$\frac{24}{50}x$

$\frac{24}{48}x$

48x

$\frac{48}{x}$

$\frac{24}{100}x$

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 #1 : Decimals With Fractions

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:

$\frac{83}{4}$

$\frac{91}{8}$

$\frac{18}{4}$

$\frac{69}{4}$

$\frac{17}{4}$

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 : Decimals With Fractions

What is the fractional equivalent of 0.33 ?

Possible Answers:

$\frac{3}{10}$

$\frac{333}{1000}$

$\frac{1}{3}$

$\frac{33}{100}$

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 #2 : Decimals With Fractions

Write 0.45 as a fraction.

Possible Answers:

$\frac{11}{20}$

$\frac{3}{4}$

$\frac{5}{9}$

$\frac{2}{5}$

$\frac{9}{20}$

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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ACT Math : Decimals with Fractions

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : Decimals

Example Question #1 : Decimals With Fractions

Example Question #1 : Decimals With Fractions

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

Example Question #1 : How To Find Decimal Fractions

Example Question #1 : Decimals With Fractions

Example Question #2 : Decimals With Fractions

Example Question #1 : Decimals With Fractions

Example Question #1 : Decimals With Fractions

Example Question #2 : Decimals With Fractions

All ACT Math Resources

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