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GED Math : Decimals and Fractions

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Example Questions

Example Question #1 : Decimals And Fractions

Convert the following decimal into a fraction:

$\small 0.243=$

Possible Answers:

$\small \frac{2}{43}$

$\small \frac{243}{1000}$

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

$\small \frac{243}{100}$

Correct answer:

$\small \frac{243}{1000}$

Explanation:

The decimal, $\small 0.243$ , is read as two-hundred forty-three thousandths, which translates to:

$\small 243\ out\ of\ 1000\ or\ \frac{243}{1000}$

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Example Question #1 : Decimals And Fractions

Convert the following fraction to a decimal: $\small \frac{1}{8}$

Possible Answers:

$\small 0.08$

$\small 0.125$

$\small 0.18$

$\small 0.10$

Correct answer:

$\small 0.125$

Explanation:

$\small \frac{1}{8}=1\div8=1.000\div8=0.125$

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Example Question #2 : Decimals And Fractions

Multiply: $\frac{9}{5} \times \frac{4}{3}$

Possible Answers:

$\frac{8}{5}$

$\frac{12}{5}$

$\frac{32}{15}$

$\frac{16}{5}$

$\frac{28}{15}$

Correct answer:

$\frac{12}{5}$

Explanation:

Multiply numerators, then multiply denominators. We can cross-cancel the 9 and the 3 by dividing both by 3:

$\frac{9}{5} \times \frac{4}{3} =\frac{3}{5} \times \frac{4}{1}= \frac{3\times 4}{5\times 1}= \frac{12}{5}$

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Example Question #2 : Decimals And Fractions

Add the fractiions below.

$\frac{3}{4}+\frac{4}{6}$

Possible Answers:

$1\frac{5}{12}$

$\frac{1}{2}$

$1\frac{3}{7}$

$\frac{7}{12}$

$\frac{7}{10}$

Correct answer:

$1\frac{5}{12}$

Explanation:

To add fractions, you have to make sure that the fractions share a common denominator — that the denominator of both numbers is the same. Because these fractions do not have a common denonominator, you use the Lowest Common Multiple rule to find a common denominator.

For these fractions, the lowest common multiple is . 4*3=12 and 6*2=12 .

For the fractions to remain the same, you have to multiply the numerator and the denominator in $\frac{3}{4}$ by and the numerator and the denominator in $\frac{4}{6}$ by . Once you have found the common denominator and have multiplied the numerator and denominator for each fraction, you can add the fractions.

$\frac{3}{4}+\frac{4}{6}=\frac{9}{12}+\frac{8}{12}=\frac{17}{12}$

Because the numerator is larger than the denominator, you simplify the fraction to make it a mixed number.

$\frac{17}{12}=1\frac{5}{12}$

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Example Question #2 : Decimals And Fractions

Above is the menu for a coffee shop; there is no sales tax charged on purchases.

Hedwig wants to throw an informal party for herself and seventeen guests. She wants to serve a large espresso and a butter croissant to each attendee, including herself. As luck would have it, the shop is having a special - for every two croissants purchased, the third is free. How much change will Hedwig get back for a $100 bill?

Possible Answers:

$\$42.64$

$\$13.30$

$\$30.64$

$\$27.70$

Correct answer:

$\$13.30$

Explanation:

There will be eighteen people at the party, including Hedwig.

She will spend $\$3.29 \times 18 = \$59.22$ for the large espressos.

"Buy two get one free" means that only two-thirds of the eighteen croissants - twelve of them - will be bought at the regular price, and the remaining six will be free. She will therefore spend $\$2.29 \times 12 = \$27.48$ .

The total purchase price will be $\$59.22 + \$27.48= \$86.70$ .

The change from a $100 bill will be

$\$100.00 - \$86.70 = \$13.30$ .

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Example Question #1 : Decimals And Fractions

Divide:

$\frac{6}{5} \div \frac{24}{25}$

Do not use a calculator.

Possible Answers:

$\frac{4}{5}$

$\frac{5}{4}$

$\frac{144}{125}$

$\frac{125}{144}$

Correct answer:

$\frac{5}{4}$

Explanation:

$\frac{6}{5} \div \frac{24}{25} = \frac{6}{5} \times \frac{25}{24} = \frac{1}{1} \times \frac{5}{4} =\frac{5}{4}$

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Example Question #2 : Decimals And Fractions

Evaluate:

$\frac{5}{11} + \frac{7}{11} + \frac{9}{11} + \frac{3}{11}$

Do not use a calculator.

Possible Answers:

$2\frac{2}{11}$

$1\frac{9}{11}$

$2\frac{4}{11}$

Correct answer:

$2\frac{2}{11}$

Explanation:

$\frac{5}{11} + \frac{7}{11} + \frac{9}{11} + \frac{3}{11} = \frac{5+7+9+3}{11} = \frac{24}{11}$

which converts as follows:

$24 \div 11 = 2 \textrm{ R }2$ ,

$\frac{5}{11} + \frac{7}{11} + \frac{9}{11} + \frac{3}{11} = \frac{24}{11} = 2 \frac{2}{11}$

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Example Question #3 : Decimals And Fractions

Jim has a total of $13.85 in nickels, dimes, and quarters.

Suppose Jim has 47 nickels. How many dimes could he have?

Possible Answers:

Correct answer:

Explanation:

If Jim has 47 nickels, he has $47 \times \$ 0.05 = \$2.35$ in nickels. Since he has $13.85 total, he has a total of $\$ 13.85 - \$ 2.35 = \$11.50$ in dimes and quarters.

The number of dimes Jim has must leave an amount that can be made in quarters only - that is, a whole number multiple of $\$0.25$ . We try all four choices:

64 dimes: $64 \times $\0.10 = \$6.40$ in dimes

Amount in quarters: $\$11.50 - \$6.40 = \$5.10$

Divide this by $\$0.25$ :

$\$5.10 \div \$0.25 = 20.4$ , which is not a whole number.

65 dimes: $65 \times $\0.10 = \$6.50$ in dimes

Amount in quarters: $\$11.50 - \$6.50 = \$5.00$

Divide this by $\$0.25$ :

$\$5.00 \div \$0.25 = 20$ , which is a whole number.

66 dimes: $66 \times $\0.10 = \$6.60$ in dimes

Amount in quarters: $\$11.50 - \$6.60 = \$4.90$

Divide this by $\$0.25$ :

$\$4.90 \div \$0.25 = 19.6$ , which is not a whole number.

67 dimes: $67 \times $\0.10 = \$6.70$ in dimes

Amount in quarters: $\$11.50 - \$6.70 = \$4.80$

Divide this by $\$0.25$ :

$\$4.80 \div \$0.25 = 19.2$ , which is not a whole number.

65 dimes is the correct choice since it is the only one that allows for a whole number of quarters.

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Example Question #3 : Decimals And Fractions

Evaluate:

$-42 \div 0.07$

Do not use a calculator.

Possible Answers:

-0.006

-6,000

-0.0006

Correct answer:

Explanation:

To divide numbers of unlike sign, divide their absolute values and affix a negative symbol. That is,

$-42 \div 0.07 = - (42 \div 0.07)$

To divide a whole number by a decimal, move the decimal points in both numbers the same number of places until the divisor is a whole number.

Therefore, we move the (written or implied) decimal point in each two places:

$42. \div 0.07 \Rightarrow 4200. \div 7.$

This becomes a whole number division:

$4,200 \div 7 = 600$

Since we must affix a negative sign, the quotient is .

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Example Question #5 : Decimals And Fractions

Each student at an African-studies school is required to take one of three languages - Swahili, Hausa, or Yoruba. Assume that no student takes more than one language.

One-third of the students have chosen Swahili, and two-fifths of the other students have chosen Hausa. What fraction of the students have chosen Yoruba?

Possible Answers:

$\frac{3}{5}$

$\frac{4}{15}$

$\frac{2}{5}$

$\frac{1}{3}$

Correct answer:

$\frac{2}{5}$

Explanation:

$\frac{1}{3}$ of the students have chosen Swahili, so

$1 - \frac{1}{3} =\frac{3}{3} - \frac{1}{3} = \frac{2}{3}$

have chosen Hausa or Yoruba.

Since $\frac{2}{5}$ of these students have chosen Hausa,

$1 - \frac{2}{5} =\frac{5}{5} - \frac{2}{5} = \frac{3}{5}$

of them have chosen Yoruba.

This is three-fifths of two-thirds, so we multiply these fractions:

$\frac{2}{3} \times \frac{3}{5} = \frac{2}{1} \times \frac{1}{5} = \frac{2 \times 1}{1 \times 5} = \frac{2}{5}$

Two-fifths of the students are taking Yoruba.

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GED Math : Decimals and Fractions

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #1 : Decimals And Fractions

Example Question #1 : Decimals And Fractions

Example Question #2 : Decimals And Fractions

Example Question #2 : Decimals And Fractions

Example Question #2 : Decimals And Fractions

Example Question #1 : Decimals And Fractions

Example Question #2 : Decimals And Fractions

Example Question #3 : Decimals And Fractions

Example Question #3 : Decimals And Fractions

Example Question #5 : Decimals And Fractions

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