How to find the decimal equivalent of a fraction - SSAT Upper Level Quantitative (Math)

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Question

Which of the following fractions is closest to 0.6?

Answer

For each fraction, divide each numerator by its denominator to get its decimal representation, then subtract to find its difference from 0.6.

$\frac{4}{7} \approx 0.5714 ; 0.6 - 0.5714 =0.0286$

$\frac{5}{8}=0.625; 0.625-0.6 = 0.025$

$\frac{9}{16} = 0.5625; 0.6-0.5625=0.0375$

$\frac{2}{3}\approx 0.6667; 0.6667-0.6=0.0667$

$\frac{13}{20} = 0.65; 0.65-0.6=0.05$

$\frac{5}{8}$ is the closest to 0.6 of the five.

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Question

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

Answer

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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Question

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

Answer

Divide 11 by 18:

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

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

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Question

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

Answer

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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Question

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

Answer

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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Question

Write the value of this expression as a decimal:

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

Answer

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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Question

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

Which of the following is closest to ?

Answer

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

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

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

$= 193 \div 105 \approx 1.84$

The correct choice is 1.8.

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Question

Simplify and express as a decimal:

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

Answer

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

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

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

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Question

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

Which of the following is closest to ?

Answer

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

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

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

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

$= \frac{53}{30}$

$= 53 \div 30 \approx 1.77$

The correct choice is 1.8.

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Question

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

Which of the following is closest to ?

Answer

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

The correct response is 1.

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Question

Define an operation $\blacklozenge$ as follows:

For all real numbers :

$a\blacklozenge b = \frac{ab}{a+b}$

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

Answer

$a\blacklozenge b = \frac{ab}{a+b}$

$\frac{1}{2} \blacklozenge \frac{1}{3}=\frac{\frac{1}{2} \times \frac{1}{3}}{\frac{1}{2} +\frac{1}{3}}=\frac{\frac{1}{6} }{\frac{5}{6} } = \frac{1}{6} \div \frac{5}{6} = \frac{1}{6} \times \frac{6} {5} = \frac{1}{1} \times \frac{1} {5} = \frac{1}{5}$

$\frac{1}{5} = 1 \div 5 = 0.2$ ,

is the correct response.

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Question

Define an operation $\blacklozenge$ as follows:

For all real numbers :

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

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

Answer

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

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

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

The correct choice is 0.15.

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Question

Which of the following is a true statement?

Answer

Divide 7 by 13. The result is as follows:

The correct choice is that $0.53 < \frac{7}{13} < 0.54$ .

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Question

Which of the following is closest to the sum of two thirds and four fifths?

Answer

$\frac{2}{3} + \frac{4}{5} = \frac{2 \cdot 5}{3\cdot 5} + \frac{3\cdot 4}{3\cdot 5} = \frac{10}{15} + \frac{12}{15} =\frac{22}{15}$

Divide 22 by 15:

Of the five choices, the closest is 1.45.

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Question

Which of the following is a true statement?

Answer

Divide 19 by 27:

$0.70 < \frac{19}{27}< 0.71$ ,

so

$-0.71< -\frac{19}{27}< -0.70$ .

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Question

Which of the following falls between 0.32 and 0.33?

Answer

Since all of the fractions have 77 as a denominator, one way to solve this problem is to let be the numerator of the correct fraction. Therefore, the equivalent problem is to find integer such that

$0.32 < \frac{N}{77} < 0.33$

Multiply each expression by :

$0.32 \cdot 77 < \frac{N}{77} \cdot 77 < 0.33 \cdot 77$

Therefore, , making $\frac{25}{77}$ the correct choice.

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