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SSAT Middle Level Math : Fractions

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Example Questions

Example Question #1301 : Numbers And Operations

Linda is having her friends over for a game night. If each person at the game night will drink $\frac{4}{5}$ $\displaystyle \frac{4}{5}$ of a liter of soda, and there will be $\displaystyle 7$ people at the game night, the number of liters of soda that Linda and her friends will drink is between the numbers:

Possible Answers:

$\displaystyle 6$ and $\displaystyle 7$

$\displaystyle 7$ and $\displaystyle 8$

$\displaystyle 8$ and $\displaystyle 9$

$\displaystyle 4$ and $\displaystyle 5$

$\displaystyle 5$ and $\displaystyle 6$

Correct answer:

$\displaystyle 5$ and $\displaystyle 6$

Explanation:

$\frac{7}{1}\times\frac{4}{5}=\frac{28}{5}$ $\displaystyle \frac{7}{1}\times\frac{4}{5}=\frac{28}{5}$

$\frac{28}{5}=5\frac{3}{5}$ $\displaystyle \frac{28}{5}=5\frac{3}{5}$ because $\displaystyle 5$ can go into $\displaystyle 25$ five times, with $\displaystyle 3$ left over.

$5\frac{3}{5}$ $\displaystyle 5\frac{3}{5}$ is between the whole numbers $\displaystyle 5$ and $\displaystyle 6$.

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

Write the decimal equivalent of $\frac{3}{400}$ $\displaystyle \frac{3}{400}$.

Possible Answers:

0.0075 $\displaystyle 0.0075$

0.006 $\displaystyle 0.006$

0.00625 $\displaystyle 0.00625$

0.00675 $\displaystyle 0.00675$

0.009 $\displaystyle 0.009$

Correct answer:

0.0075 $\displaystyle 0.0075$

Explanation:

$\frac{3}{400} = 3 \div 400 = 0.0075$ $\displaystyle \frac{3}{400} = 3 \div 400 = 0.0075$

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

Express 0.014 as a fraction in lowest terms.

Possible Answers:

$\frac{14}{1,000}$ $\displaystyle \frac{14}{1,000}$

$\frac{7}{200}$ $\displaystyle \frac{7}{200}$

$\frac{7}{2,000}$ $\displaystyle \frac{7}{2,000}$

$\frac{7}{50}$ $\displaystyle \frac{7}{50}$

$\frac{7}{500}$ $\displaystyle \frac{7}{500}$

Correct answer:

$\frac{7}{500}$ $\displaystyle \frac{7}{500}$

Explanation:

The fraction has its last nonzero digit in the thousandths place, so write the number, without the decimal point, over 1,000. Then reduce.

$\frac{14}{1,000} =\frac{14\div 2}{1,000\div 2} = \frac{7}{500}$ $\displaystyle \frac{14}{1,000} =\frac{14\div 2}{1,000\div 2} = \frac{7}{500}$

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

Express $\frac{3}{400}$ $\displaystyle \frac{3}{400}$ as a decimal.

Possible Answers:

0.006 $\displaystyle 0.006$

0.00675 $\displaystyle 0.00675$

0.009 $\displaystyle 0.009$

0.0075 $\displaystyle 0.0075$

0.00625 $\displaystyle 0.00625$

Correct answer:

0.0075 $\displaystyle 0.0075$

Explanation:

$\frac{3}{400} = 3 \div 400 = 0.0075$ $\displaystyle \frac{3}{400} = 3 \div 400 = 0.0075$

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

Which of the following is NOT equal to $0.5 \bullet 20$ $\displaystyle 0.5 \bullet 20$?

Possible Answers:

$\frac{1}{5} \bullet 50$ $\displaystyle \frac{1}{5} \bullet 50$

$\frac{1}{4} \bullet 40$ $\displaystyle \frac{1}{4} \bullet 40$

$\frac{2}{3} \bullet 15$ $\displaystyle \frac{2}{3} \bullet 15$

$\frac{3}{4} \bullet 16$ $\displaystyle \frac{3}{4} \bullet 16$

$2 \bullet 5$ $\displaystyle 2 \bullet 5$

Correct answer:

$\frac{3}{4} \bullet 16$ $\displaystyle \frac{3}{4} \bullet 16$

Explanation:

All of the answer choices multiply to give you 10 except

$\frac{3}{4} \bullet 16$ $\displaystyle \frac{3}{4} \bullet 16$

so that is the correct answer.

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

What fractions equals 0.5 $\displaystyle 0.5$?

Possible Answers:

$\frac{8}{16}$ $\displaystyle \frac{8}{16}$

$\frac{8}{12}$ $\displaystyle \frac{8}{12}$

$\frac{8}{4}$ $\displaystyle \frac{8}{4}$

$\frac{8}{32}$ $\displaystyle \frac{8}{32}$

$\frac{8}{2}$ $\displaystyle \frac{8}{2}$

Correct answer:

$\frac{8}{16}$ $\displaystyle \frac{8}{16}$

Explanation:

0.5 $\displaystyle 0.5$ is equal to $\frac{1}{2}$ $\displaystyle \frac{1}{2}$.

Thus we are looking for a fraction that reduces to $\frac{1}{2}$ $\displaystyle \frac{1}{2}$.

$\frac{8}{12}$ $\displaystyle \frac{8}{12}$ reduces to $\frac{2}{3}$ $\displaystyle \frac{2}{3}$ (divide numerator and denominator by 4).

$\frac{8}{4}$ $\displaystyle \frac{8}{4}$ reduces to 2 (divide numerator and denominator by 4).

$\frac{8}{2}$ $\displaystyle \frac{8}{2}$ reduces to 4 (divide numerator and denominator by 2).

$\frac{8}{32}$ $\displaystyle \frac{8}{32}$ reduces $\frac{1}{4}$ $\displaystyle \frac{1}{4}$ (divide numerator and denominator by 4).

$\frac{8}{16}$ $\displaystyle \frac{8}{16}$ is the only one that reduces to $\frac{1}{2}$ $\displaystyle \frac{1}{2}$ (divide numerator and denominator by 8).

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Example Question #3 : How To Find The Decimal Equivalent Of A Fraction

Write as a decimal:

$\frac{5}{9}$ $\displaystyle \frac{5}{9}$

Possible Answers:

$0.5\overline{4}$ $\displaystyle 0.5\overline{4}$

$0.\overline{54}$ $\displaystyle 0.\overline{54}$

$0.\overline{5}$ $\displaystyle 0.\overline{5}$

0.5 $\displaystyle 0.5$

$0.\overline{45}$ $\displaystyle 0.\overline{45}$

Correct answer:

$0.\overline{5}$ $\displaystyle 0.\overline{5}$

Explanation:

$5 \div 9 = 0.5555...$ $\displaystyle 5 \div 9 = 0.5555...$

That is, the digit 5 will repeat infinitely. This can be written as $0.\overline{5}$ $\displaystyle 0.\overline{5}$.

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Example Question #4 : How To Find The Decimal Equivalent Of A Fraction

Write as a decimal:

$\frac{9}{11}$ $\displaystyle \frac{9}{11}$

Possible Answers:

$0.\overline{81}$ $\displaystyle 0.\overline{81}$

0.9 $\displaystyle 0.9$

$0.8\overline{1}$ $\displaystyle 0.8\overline{1}$

0.81 $\displaystyle 0.81$

$0.\overline{8}$ $\displaystyle 0.\overline{8}$

Correct answer:

$0.\overline{81}$ $\displaystyle 0.\overline{81}$

Explanation:

$9 \div 11 = 0.81818181...$ $\displaystyle 9 \div 11 = 0.81818181...$

That is, the group "81" will repeat infinitely. This quotient can be written as $0.\overline{81}$ $\displaystyle 0.\overline{81}$.

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Example Question #5 : How To Find The Decimal Equivalent Of A Fraction

Rewrite as a decimal:

$\frac{7}{12}$ $\displaystyle \frac{7}{12}$

Possible Answers:

$0.58\overline{3}$ $\displaystyle 0.58\overline{3}$

$0.5\overline{3}$ $\displaystyle 0.5\overline{3}$

0.58 $\displaystyle 0.58$

0.575 $\displaystyle 0.575$

$0.\overline{53}$ $\displaystyle 0.\overline{53}$

Correct answer:

$0.58\overline{3}$ $\displaystyle 0.58\overline{3}$

Explanation:

$7 \div 12 = 0.583333...$ $\displaystyle 7 \div 12 = 0.583333...$

That is, after 5 and 8, the digit 3 will repeat infinitely. This can be rewritten as $0.58\overline{3}$ $\displaystyle 0.58\overline{3}$.

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Example Question #6 : How To Find The Decimal Equivalent Of A Fraction

Write as a decimal:

$\frac{5}{18}$ $\displaystyle \frac{5}{18}$

Possible Answers:

0.27 $\displaystyle 0.27$

0.2727 $\displaystyle 0.2727$

$0.\overline{27}$ $\displaystyle 0.\overline{27}$

$0.2\overline{7}$ $\displaystyle 0.2\overline{7}$

$0.\overline{277}$ $\displaystyle 0.\overline{277}$

Correct answer:

$0.2\overline{7}$ $\displaystyle 0.2\overline{7}$

Explanation:

$5 \div 18 = 0.27777...$ $\displaystyle 5 \div 18 = 0.27777...$

That is, after the 2, the digit 7 repeats infinitely. This can be rewritten as $0.2\overline{7}$ $\displaystyle 0.2\overline{7}$.

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SSAT Middle Level Math : Fractions

Study concepts, example questions & explanations for SSAT Middle Level Math

All SSAT Middle Level Math Resources

Example Questions

Example Question #1301 : Numbers And Operations

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

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

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

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

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

Example Question #3 : How To Find The Decimal Equivalent Of A Fraction

Example Question #4 : How To Find The Decimal Equivalent Of A Fraction

Example Question #5 : How To Find The Decimal Equivalent Of A Fraction

Example Question #6 : How To Find The Decimal Equivalent Of A Fraction

All SSAT Middle Level Math Resources

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