How to find the decimal equivalent of a fraction - SSAT Upper Level: Quantitative

Card 1 of 64

0

Didn't Know

0

Didn't Know

Knew It

0

1 of 2019 left

Question

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

Tap to reveal answer

Answer

Divide 5 by 27:

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

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

← Didn't Know|Knew It →

Question

Which of the following fractions is closest to 0.6?

Tap to reveal answer

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.

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

Answer

Divide 8 by 15:

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

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

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

Answer

Divide 11 by 18:

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

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

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

Answer

Divide 7 by 36:

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

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

← Didn't Know|Knew It →

Question

Write the value of this expression as a decimal:

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

Tap to reveal answer

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:

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

← Didn't Know|Knew It →

Question

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

Which of the following is closest to ?

Tap to reveal answer

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.

← Didn't Know|Knew It →

Question

Simplify and express as a decimal:

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

Tap to reveal answer

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 $0.8\overline{3}$ .

← Didn't Know|Knew It →

Question

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

Which of the following is closest to ?

Tap to reveal answer

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.

← Didn't Know|Knew It →

Question

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

Which of the following is closest to ?

Tap to reveal answer

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.

← Didn't Know|Knew It →

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 $\frac{1}{2} \blacklozenge \frac{1}{3}$ ?

Tap to reveal answer

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.

← Didn't Know|Knew It →

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 $\frac{1}{2} \blacklozenge \frac{1}{3}$ ?

Tap to reveal answer

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.

← Didn't Know|Knew It →

Question

Which of the following is a true statement?

Tap to reveal answer

Answer

Divide 7 by 13. The result is as follows:

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

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

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.

← Didn't Know|Knew It →

Question

Which of the following is a true statement?

Tap to reveal answer

Answer

Divide 19 by 27:

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

so

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

← Didn't Know|Knew It →

Question

Which of the following falls between 0.32 and 0.33?

Tap to reveal answer

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.

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

Answer

Divide 5 by 27:

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

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

← Didn't Know|Knew It →

Question

Which of the following fractions is closest to 0.6?

Tap to reveal answer

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.

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

Answer

Divide 8 by 15:

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

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

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

Answer

Divide 11 by 18:

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

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

← Didn't Know|Knew It →

0

Knew It