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ACT Math : Arithmetic

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Example Questions

Example Question #311 : Arithmetic

Divide: $\frac{.5}{.25}$

Possible Answers:

$\frac{1}{4}$

$\frac{1}{5}$

$\frac{1}{2}$

Correct answer:

Explanation:

Eliminate the decimal place on the denominator by moving the decimal place 2 spaces to the right. Follow suit for the numerator. The decimal place should also move the same number of units to the right. Evaluate.

$\frac{.5}{.25}= \frac{.50}{.25} = \frac{50}{25} =2$

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Example Question #3 : How To Divide Decimals

Divide: $1.25\div 0.25$

Possible Answers:

0.5

0.6

0.06

Correct answer:

Explanation:

Rewrite $1.25\div 0.25$ so that both are in fraction form.

$1.25\div 0.25= \frac{5}{4} \div \frac{1}{4}$

Convert the division sign to multiplication, and take the reciprocal of the 2nd term.

$\frac{5}{4}\cdot \frac{4}{1} =5$

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Example Question #53 : Decimals

Order the following decimals from greatest to least:

0.999, 0.909, 0.990

Possible Answers:

0.909, 0.990, 0.999

0.909, 0.999, 0.990

0.999, 0.909, 0.990

0.990, 0.999, 0.909

0.999, 0.990, 0.909

Correct answer:

0.999, 0.990, 0.909

Explanation:

The greatest is 0.999 (999/1000), then 0.990 (990/1000), finally 0.909 (909/1000).

0.999 > 0.990 > 0.909

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Example Question #1 : Ordering

Place the following numbers in order from smallest to greatest:

$5.13,\ 5.11,\ 5.131,\ 5.111,\ 5.115$

Possible Answers:

$5.11,\ 5.111,\ 5.115,\ 5.13,\ 5.131$

$5.13,\ 5.131,\ 5.115,\ 5.111,\ 5.11$

$5.13,\ 5.111,\ 5.115,\ 5.11,\ 5.131$

$5.111,\ 5.115,\ 5.11,\ 5.13,\ 5.131$

$5.13,\ 5.115,\ 5.111,\ 5.11,\ 5.131$

Correct answer:

$5.11,\ 5.111,\ 5.115,\ 5.13,\ 5.131$

Explanation:

When comparing decimals, move left to right, comparing the size of the tenths, then the hundredths, then the thousandths, etc….

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Example Question #2 : How To Order Decimals From Least To Greatest Or From Greatest To Least

Arrange the following from least to greatest:

0.07, 14, 1.44, 0.007, 0.08, 0.9, 1.33

Possible Answers:

0.007, 0.07, 0.08, 0.9, 1.33, 1.44, 14

14, 1.33, 1.44, 0.08, 0.07, 0.9, 0.007

0.007, 0.08, 0.07, 0.9, 1.33, 1.44, 14

14, 1.44, 1.33, 0.9, 0.08, 0.07, 0.007

Correct answer:

0.007, 0.07, 0.08, 0.9, 1.33, 1.44, 14

Explanation:

From least to greatest:

0.007 ( $\frac{7}{1000}$ ), 0.07 ( $\frac{7}{100}$ ), 0.08 ( $\frac{8}{100}$ ), 0.9 ( $\frac{9}{10}$ ), 1.33 ( and $\frac{33}{100}$ ), 1.44 ( and $\frac{44}{100}$ ), 14

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Example Question #6 : How To Order Decimals From Least To Greatest Or From Greatest To Least

Put the following in order of least to greatest:

$0.28, \frac{6}{19}, \frac{29}{104}, 0.27,\frac{7}{26}$

Possible Answers:

None of the other answers

$\frac{7}{26}, \frac{29}{104}, 0.27, 0.28, \frac{6}{19}$

$0.27, \frac{7}{26}, \frac{29}{104}, 0.28, \frac{6}{19}$

$\frac{7}{26}, 0.27, 0.28, \frac{29}{104}, \frac{6}{19}$

$0.27, 0.28, \frac{7}{26}, \frac{29}{104}, \frac{6}{19}$

Correct answer:

None of the other answers

Explanation:

Begin by converting each fraction into a decimal:

$\frac{6}{19}\approx 0.3157$

$\frac{29}{104}\approx0.2788$

$\frac{7}{26}\approx0.269$

Now we can put the decimals in order:

0.269, 0.27, 0.2788, 0.28, 0.3157

or:

$\frac{7}{26}, 0.27, \frac{29}{104}, 0.28, \frac{6}{19}$

No answer choice matches this order, so our answer is "None of the other answers"

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Example Question #2 : Ordering

Order the following decimals from greatest to least:

0.052, 0.011, 0.340, 0.009, 0.101

Possible Answers:

0.009, 0.052, 0.340, 0.101, 0.011

0.340, 0.101, 0.052, 0.011, 0.009

0.011, 0.101, 0.340, 0.052, 0.009

0.101, 0.340, 0.011, 0.052, 0.009

0.340, 0.101, 0.011, 0.052, 0.009

Correct answer:

0.340, 0.101, 0.052, 0.011, 0.009

Explanation:

With decimals, the larger number has a value in the larger spot (anything with a nonzero value in the tenths, is larger than any number with a 0 in the tenths and a digit in the hundredths, and so on). Thus the correct ordering starts with the decimal with the largest digit in the tenth spot, or .340.

After that there is only one with a nonzero value in the tenths spot, so .101 comes next.

Then there are only two that have nonzero values in the hundreths spot, and since 5 is larger than 1 the next two are .052 and then .011.

Finally, the smallest number is the one with zeroes in the tenths and hundreths spot so .009 is the smallest.

Thus resulting in,

0.340, 0.101, 0.052, 0.011, 0.009

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Example Question #5 : Ordering

Order the following from least to greatest: $\textup{0.2, 0.34, 0.25, 1.8, 0.02}$

Possible Answers:

$\textup{0.34,1.8,0.02,0.25,0.2}$

1.8, 0.02, 0.2, 0.25, 0.34

$\textup{0.02, 0.2, 0.25, 0.34, 1.8}$

1.8, 0.34, 0.25, 0.2, 0.02

0.25, 0.2, 0.02, 0.34, 1.8

Correct answer:

$\textup{0.02, 0.2, 0.25, 0.34, 1.8}$

Explanation:

0.02 , equivalent to two-hundredths, is the least out of the collection.

0.2 , equivalent to twenty-hundredths, is the next highest.

0.25 , equivalent to twenty-five hundredths, is the next highest.

0.34 , equivalent to thirty-four hundredths, is the next highest.

Finally, the highest number is 1.8 , equivalent to one hundred and eighty hundredths.

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Example Question #1 : Fractions

Order the following fractions from least to greatest:

2/3, 3/4, 1/2

Possible Answers:

3/4, 2/3, 1/2

1/2, 2/3, 3/4

3/4, 1/2, 2/3

2/3, 3/4, 1/2

2/3, 1/2, 3/4

Correct answer:

1/2, 2/3, 3/4

Explanation:

1/2 is the least, then 2/3, then 3/4.

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Example Question #1 : Fractions

Place the following fractions in order from greatest to least.

$\frac{2}{5},\frac{4}{8},\frac{2}{10},\frac{3}{12}$

Possible Answers:

$\frac{2}{5}>\frac{2}{10}>\frac{3}{12}>\frac{4}{8}$

$\frac{4}{8}>\frac{3}{12}>\frac{2}{10}>\frac{2}{5}$

$\frac{4}{8}>\frac{2}{5}>\frac{3}{12}>\frac{2}{10}$

$\frac{2}{10}>\frac{3}{12}>\frac{2}{5}>\frac{4}{8}$

$\frac{3}{12}>\frac{4}{8}>\frac{2}{10}>\frac{2}{5}$

Correct answer:

$\frac{4}{8}>\frac{2}{5}>\frac{3}{12}>\frac{2}{10}$

Explanation:

This question can be most easily answered by converting the fractions into decimals first.

$\frac2{}{5}=0.40$

$\frac{4}{8}=0.50$

$\frac{3}{12}=0.25$

$\frac{2}{10}=0.20$

0.50>0.40>0.25>0.20

$\frac{4}{8}>\frac{2}{5}>\frac{3}{12}>\frac{2}{10}$

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ACT Math : Arithmetic

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #311 : Arithmetic

Example Question #3 : How To Divide Decimals

Example Question #53 : Decimals

Example Question #1 : Ordering

Example Question #2 : How To Order Decimals From Least To Greatest Or From Greatest To Least

Example Question #6 : How To Order Decimals From Least To Greatest Or From Greatest To Least

Example Question #2 : Ordering

Example Question #5 : Ordering

Example Question #1 : Fractions

Example Question #1 : Fractions

All ACT Math Resources

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