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SSAT Upper Level Math : Decimals with Fractions

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

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Example Questions

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

Express $\frac{8}{15}$ as a decimal.

Possible Answers:

$0.5\overline{8}$

0.5

$0.5\overline{3}$

0.52

$0.\overline{5}$

Correct answer:

$0.5\overline{3}$

Explanation:

Divide 8 by 15:

$\frac{8}{15} = 8 \div 15 = 0.5333...$

The 3 repeats, so the correct choice is $0.5\overline{3}$ .

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

Give the decimal equivalent of $\frac{11}{18}$ .

Possible Answers:

0.61

$0.6\overline{1}$

$0.\overline{611}$

$0.\overline{61}$

0.611

Correct answer:

$0.6\overline{1}$

Explanation:

Divide 11 by 18:

$\frac{11}{18} = 11 \div 18 = 0.61111...$

1重复无限,所以这可以重写as $0.6\overline{1}$ .

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

Give the decimal equivalent of $\frac{5}{27}$ .

Possible Answers:

$0.\overline{185}$

$0.18\overline{5}$

0.185

0.186

$0.1\overline{85}$

Correct answer:

$0.\overline{185}$

Explanation:

Divide 5 by 27:

$\frac{5}{27} = 5 \div 27 = 0.185185185...$

The group "185" repeats infinitely, so this can be written as $0.\overline{185}$ .

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

Give the decimal equivalent of $\frac{7}{36}$ .

Possible Answers:

0.195

0.194

$0.19\overline{4}$

0.19

$0.\overline{19}$

Correct answer:

$0.19\overline{4}$

Explanation:

Divide 7 by 36:

$\frac{7}{36} = 7 \div 36 = 0.19444444...$

The 4 repeats infinitely, so this can be rewritten as $0.19\overline{4}$ .

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

Write the value of this expression as a decimal:

$\frac{1}{3} + \frac{1}{4} + \frac{1}{2}$

Possible Answers:

$0.\overline{3}$

$0.91\overline{6}$

1.25

$0.\overline{923076}$

$1.08\overline{3}$

Correct answer:

$1.08\overline{3}$

Explanation:

Simplify the sum by taking the least common denominator, which is 12:

$\frac{1}{3} + \frac{1}{4} + \frac{1}{2}$

$= \frac{1\cdot 4}{3\cdot 4} + \frac{1\cdot 3}{4\cdot 3} + \frac{1\cdot 6}{2\cdot 6}$

$= \frac{ 4}{12} + \frac{3}{12} + \frac{6}{12} = \frac{13}{12}$

Divide 13 by 12:

$\frac{13}{12} = 1. 08333333... = 1.08\overline{3}$

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

Let $a = \frac{3}{5}$ , $b= \frac{2}{3}$ , $c = \frac{4}{7}$

Which of the following is closest to a + b + c ?

Possible Answers:

1.9

1.6

1.5

1.8

1.7

Correct answer:

1.8

Explanation:

a + b + c

$= \frac{3}{5}+ \frac{2}{3}+ \frac{4}{7}$

$= \frac{3 \times 21}{5 \times 21}+ \frac{2\times 35}{3 \times 35}+ \frac{4\times 15}{7 \times 15}$

$= \frac{63}{105}+ \frac{70}{105}+ \frac{60}{105} = \frac{193}{105}$

$= 193 \div 105 \approx 1.84$

The correct choice is 1.8.

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Example Question #7 :How To Find The Decimal Equivalent Of A Fraction

Let $a =3 \frac{3}{5}$ and $b=1 \frac{5}{6}$

Which of the following is closest to a - b ?

Possible Answers:

1.7

1.8

1.4

1.6

1.5

Correct answer:

1.8

Explanation:

$a - b = 3\frac{3}{5} - 1\frac{5}{6}$

$= \frac{18}{5} - \frac{11}{6}$

$= \frac{18\times 6 }{5 \times 6} - \frac{11\times 5}{6\times 5}$

$= \frac{108}{30} - \frac{55}{30}$

$= \frac{53}{30}$

$= 53 \div 30 \approx 1.77$

The correct choice is 1.8.

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Example Question #8 :How To Find The Decimal Equivalent Of A Fraction

Define an operation $\blacklozenge$ as follows:

For all real numbers a,b :

$a\blacklozenge b = a^{2} - b^{2}$

Which of the following is closest to $\frac{1}{2} \blacklozenge \frac{1}{3}$ ?

Possible Answers:

0.2

0.25

0.1

0.3

0.15

Correct answer:

0.15

Explanation:

$a\blacklozenge b = a^{2} - b^{2}$

$\frac{1}{2} \blacklozenge \frac{1}{3} =\left ( \frac{1}{2} \right ) ^{2} - \left ( \frac{1}{3} \right )^{2}= \frac{1}{4} - \frac{1}{9}= \frac{9}{36} - \frac{4}{36}= \frac{5}{36}$

$= 5 \div 36 = 0.13888...$

The correct choice is 0.15.

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Example Question #9 :How To Find The Decimal Equivalent Of A Fraction

Let $a =1 \frac{4}{9}$ , $b = 1\frac{3}{8}$ , and $c= \frac{1}{2}$ .

Which of the following is closest to a bc ?

Possible Answers:

1.4

1.1

1.3

1.2

Correct answer:

Explanation:

$a bc=1 \frac{4}{9} \times 1\frac{3}{8} \times \frac{1}{2}= \frac{13}{9} \times \frac{11}{8} \times \frac{1}{2}= \frac{143}{144}= 143 \div 144 \approx 0.99$

The correct response is 1.

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Example Question #10 :How To Find The Decimal Equivalent Of A Fraction

Simplify and express as a decimal:

$\frac{4\frac{2}{3}}{5\frac{3}{5}}$

Possible Answers:

0.875

0.8

$0.\overline{8}$

$0.8\overline{3}$

0.9

Correct answer:

$0.8\overline{3}$

Explanation:

$\frac{4\frac{2}{3}}{5\frac{3}{5}} = 4\frac{2}{3} \div 5\frac{3}{5} = \frac{14}{3} \div \frac{28}{5} = \frac{14}{3} \times \frac{5} {28} = \frac{1}{3} \times \frac{5} {2} = \frac{5}{6}$

$\frac{5}{6}= 5 \div 6 = 0.8333...$ ,

so the correct response is $0.8\overline{3}$ .

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SSAT Upper Level Math : Decimals with Fractions

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

All SSAT Upper Level Math Resources

Example Questions

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 #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

Example Question #7 :How To Find The Decimal Equivalent Of A Fraction

Example Question #8 :How To Find The Decimal Equivalent Of A Fraction

Example Question #9 :How To Find The Decimal Equivalent Of A Fraction

Example Question #10 :How To Find The Decimal Equivalent Of A Fraction

All SSAT Upper Level Math Resources

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