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SSAT Upper Level Math : Decimals with Fractions

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Example Questions

Example Question #1 : Decimals With Fractions

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

Possible Answers:

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

$0.5\overline{8}$ $\displaystyle 0.5\overline{8}$

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

0.5 $\displaystyle 0.5$

0.52 $\displaystyle 0.52$

Correct answer:

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

Explanation:

Divide 8 by 15:

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

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

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Example Question #2 : Decimals With Fractions

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

Possible Answers:

$0.\overline{611}$ $\displaystyle 0.\overline{611}$

0.611 $\displaystyle 0.611$

0.61 $\displaystyle 0.61$

$0.\overline{61}$ $\displaystyle 0.\overline{61}$

$0.6\overline{1}$ $\displaystyle 0.6\overline{1}$

Correct answer:

$0.6\overline{1}$ $\displaystyle 0.6\overline{1}$

Explanation:

Divide 11 by 18:

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

The 1 repeats infinitely, so this can be rewritten as $0.6\overline{1}$ $\displaystyle 0.6\overline{1}$ .

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Example Question #3 : Decimals With Fractions

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

Possible Answers:

0.185 $\displaystyle 0.185$

$0.1\overline{85}$ $\displaystyle 0.1\overline{85}$

$0.18\overline{5}$ $\displaystyle 0.18\overline{5}$

0.186 $\displaystyle 0.186$

$0.\overline{185}$ $\displaystyle 0.\overline{185}$

Correct answer:

$0.\overline{185}$ $\displaystyle 0.\overline{185}$

Explanation:

Divide 5 by 27:

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

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

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Example Question #4 : Decimals With Fractions

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

Possible Answers:

$0.\overline{19}$ $\displaystyle 0.\overline{19}$

0.195 $\displaystyle 0.195$

$0.19\overline{4}$ $\displaystyle 0.19\overline{4}$

0.194 $\displaystyle 0.194$

0.19 $\displaystyle 0.19$

Correct answer:

$0.19\overline{4}$ $\displaystyle 0.19\overline{4}$

Explanation:

Divide 7 by 36:

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

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

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Example Question #5 : Decimals With Fractions

Write the value of this expression as a decimal:

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

Possible Answers:

$1.08\overline{3}$ $\displaystyle 1.08\overline{3}$

$0.91\overline{6}$ $\displaystyle 0.91\overline{6}$

$0.\overline{923076}$ $\displaystyle 0.\overline{923076}$

1.25 $\displaystyle 1.25$

$0.\overline{3}$ $\displaystyle 0.\overline{3}$

Correct answer:

$1.08\overline{3}$ $\displaystyle 1.08\overline{3}$

Explanation:

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

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

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

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

Divide 13 by 12:

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

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Example Question #6 : Decimals With Fractions

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

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

Possible Answers:

1.9 $\displaystyle 1.9$

1.6 $\displaystyle 1.6$

1.5 $\displaystyle 1.5$

1.7 $\displaystyle 1.7$

1.8 $\displaystyle 1.8$

Correct answer:

1.8 $\displaystyle 1.8$

Explanation:

$\displaystyle a + b + c$

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

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

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

$= 193 \div 105 \approx 1.84$ $\displaystyle = 193 \div 105 \approx 1.84$

The correct choice is 1.8.

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Example Question #7 : Decimals With Fractions

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

Which of the following is closest to a - b $\displaystyle a - b$ ?

Possible Answers:

1.6 $\displaystyle 1.6$

1.4 $\displaystyle 1.4$

1.5 $\displaystyle 1.5$

1.7 $\displaystyle 1.7$

1.8 $\displaystyle 1.8$

Correct answer:

1.8 $\displaystyle 1.8$

Explanation:

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

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

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

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

$= \frac{53}{30}$ $\displaystyle = \frac{53}{30}$

$= 53 \div 30 \approx 1.77$ $\displaystyle = 53 \div 30 \approx 1.77$

The correct choice is 1.8.

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Example Question #241 : Rational Numbers

Define an operation $\blacklozenge$ $\displaystyle \blacklozenge$ as follows:

For all real numbers a,b $\displaystyle a,b$ :

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

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

Possible Answers:

0.3 $\displaystyle 0.3$

0.2 $\displaystyle 0.2$

0.1 $\displaystyle 0.1$

0.15 $\displaystyle 0.15$

0.25 $\displaystyle 0.25$

Correct answer:

0.15 $\displaystyle 0.15$

Explanation:

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

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

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

The correct choice is 0.15.

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Example Question #1371 : Ssat Upper Level Quantitative (Math)

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

Which of the following is closest to a bc $\displaystyle a bc$ ?

Possible Answers:

$\displaystyle 1$

1.3 $\displaystyle 1.3$

1.4 $\displaystyle 1.4$

1.2 $\displaystyle 1.2$

1.1 $\displaystyle 1.1$

Correct answer:

$\displaystyle 1$

Explanation:

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

The correct response is 1.

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Example Question #7 : Decimals With Fractions

Simplify and express as a decimal:

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

Possible Answers:

$0.8\overline{3}$ $\displaystyle 0.8\overline{3}$

0.875 $\displaystyle 0.875$

0.8 $\displaystyle 0.8$

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

0.9 $\displaystyle 0.9$

Correct answer:

$0.8\overline{3}$ $\displaystyle 0.8\overline{3}$

Explanation:

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

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

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

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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 : Decimals With Fractions

Example Question #2 : Decimals With Fractions

Example Question #3 : Decimals With Fractions

Example Question #4 : Decimals With Fractions

Example Question #5 : Decimals With Fractions

Example Question #6 : Decimals With Fractions

Example Question #7 : Decimals With Fractions

Example Question #241 : Rational Numbers

Example Question #1371 : Ssat Upper Level Quantitative (Math)

Example Question #7 : Decimals With Fractions

All SSAT Upper Level Math Resources

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