How to find the reciprocal of a fraction - SSAT Upper Level Quantitative

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Give the reciprocal of 0.75.

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The reciprocal of a number is the quotient of 1 and the number.

Divide 1 by 0.75 by moving the decimal point to the right in each number two places:

$1 \div 0.75 = 100 \div 75 = 1 $\frac{25}{75}$ = 1 $\frac{1}{3}$$

Give the reciprocal of 0.8.

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The reciprocal of a number is the quotient of 1 and that number. Divide 1 by 0.8 by moving the decimal point to the right in each number one place:

$1 \div 0.8 = 10 \div 8 = 1.25$

Add the reciprocals of , , and . What is the sum?

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The reciprocals of 4, 6, and 8 are, respectively, $\frac{1}{4}$, $\frac{1}{6}$, $\frac{1}{8}$ . Their sum is

$\frac{1}{4}$+\frac{1}{6}$+ $\frac{1}{8}$

First we find the least common denominator between all three fractions.

$= $\frac{1}{4}$\bigg($\frac{6}{6}$\bigg) + $\frac{1}{6}$\bigg($\frac{4}{4}$\bigg) +\frac{1}{8}$\bigg($\frac{3}{3}$\bigg)$

$=\frac{6}{24}$+\frac{4}{24}$+\frac{3}{24}$ = $\frac{13}{24}$$

Subtract the reciprocal of 11 from the reciprocal of 13. What is the result?

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The reciprocals of 11 and 13 are, respectively, $\frac{1}{11}$ and $\frac{1}{13}$ . The requested difference is

$\frac{1}{13}$-$\frac{1}{11}$ = $\frac{1\cdot 11}{13 \cdot 11}$-$\frac{1\cdot 13}{11 \cdot 13}$ = $\frac{1 1}{143 }$-$\frac{ 13}{143}$ =-$\frac{2}{143}$

This answer is not among the given choices.

Add the reciprocals of 0.3 and 0.7. What is their sum?

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$0.3 = $\frac{3}{10}$$ , so its reciprocal is $\frac{10}{3}$ .

$0.7= $\frac{7}{10}$$ , so its reciprocal is $\frac{10}{7}$ .

Add them:

$\frac{10}{3}$ + $\frac{10}{7}$ = $\frac{10 \cdot 7 }{3 \cdot 7}$ + $\frac{10\cdot 3}{7\cdot 3}$ = $\frac{70}{21}$+\frac{30}{21}$ = $\frac{100}{21}$

$100 \div 21 = 4 \textup{ R }16$ , so

$\frac{100}{21}$= 4$\frac{16}{21}$

Subtract the reciprocal of 1.5 from the reciprocal of 0.125. What is the result?

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$1.5 = $\frac{15}{10}$ = $\frac{3}{2}$$ , so its reciprocal is $\frac{2}{3}$ .

$0.125 = $\frac{125}{1,000}$ = $\frac{1}{8}$$ , so its reciprocal is 8.

The requested difference is $8-$\frac{2}{3}$ = 7$\frac{1}{3}$$

Let be the reciprocal of 0.22. Which of the following is true of ?

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$0.22 = $\frac{22}{100}$$ , so its reciprocal is $N= $\frac{100}{22}$$ .

Since $100 \div 22 = 4\textup{ R }12$ ,

$N= $\frac{100}{22}$ = 4 $\frac{12}{22}$=4$\frac{6}{11}$$

Therefore, .

Let be the reciprocal of 1.77. Which of the following is true of ?

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$1.77= $\frac{177}{100}$$ , so its reciprocal is $N= $\frac{100}{177}$$ .

If 100 is divided by 177, the decimal equivalent is seen to be so

.

Give the reciprocal of 0.75.

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The reciprocal of a number is the quotient of 1 and the number.

Divide 1 by 0.75 by moving the decimal point to the right in each number two places:

$1 \div 0.75 = 100 \div 75 = 1 $\frac{25}{75}$ = 1 $\frac{1}{3}$$

Give the reciprocal of 0.8.

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The reciprocal of a number is the quotient of 1 and that number. Divide 1 by 0.8 by moving the decimal point to the right in each number one place:

$1 \div 0.8 = 10 \div 8 = 1.25$

Add the reciprocals of , , and . What is the sum?

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The reciprocals of 4, 6, and 8 are, respectively, $\frac{1}{4}$, $\frac{1}{6}$, $\frac{1}{8}$ . Their sum is

$\frac{1}{4}$+\frac{1}{6}$+ $\frac{1}{8}$

First we find the least common denominator between all three fractions.

$= $\frac{1}{4}$\bigg($\frac{6}{6}$\bigg) + $\frac{1}{6}$\bigg($\frac{4}{4}$\bigg) +\frac{1}{8}$\bigg($\frac{3}{3}$\bigg)$

$=\frac{6}{24}$+\frac{4}{24}$+\frac{3}{24}$ = $\frac{13}{24}$$

Subtract the reciprocal of 11 from the reciprocal of 13. What is the result?

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The reciprocals of 11 and 13 are, respectively, $\frac{1}{11}$ and $\frac{1}{13}$ . The requested difference is

$\frac{1}{13}$-$\frac{1}{11}$ = $\frac{1\cdot 11}{13 \cdot 11}$-$\frac{1\cdot 13}{11 \cdot 13}$ = $\frac{1 1}{143 }$-$\frac{ 13}{143}$ =-$\frac{2}{143}$

This answer is not among the given choices.

Add the reciprocals of 0.3 and 0.7. What is their sum?

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$0.3 = $\frac{3}{10}$$ , so its reciprocal is $\frac{10}{3}$ .

$0.7= $\frac{7}{10}$$ , so its reciprocal is $\frac{10}{7}$ .

Add them:

$\frac{10}{3}$ + $\frac{10}{7}$ = $\frac{10 \cdot 7 }{3 \cdot 7}$ + $\frac{10\cdot 3}{7\cdot 3}$ = $\frac{70}{21}$+\frac{30}{21}$ = $\frac{100}{21}$

$100 \div 21 = 4 \textup{ R }16$ , so

$\frac{100}{21}$= 4$\frac{16}{21}$

Subtract the reciprocal of 1.5 from the reciprocal of 0.125. What is the result?

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$1.5 = $\frac{15}{10}$ = $\frac{3}{2}$$ , so its reciprocal is $\frac{2}{3}$ .

$0.125 = $\frac{125}{1,000}$ = $\frac{1}{8}$$ , so its reciprocal is 8.

The requested difference is $8-$\frac{2}{3}$ = 7$\frac{1}{3}$$

Let be the reciprocal of 0.22. Which of the following is true of ?

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$0.22 = $\frac{22}{100}$$ , so its reciprocal is $N= $\frac{100}{22}$$ .

Since $100 \div 22 = 4\textup{ R }12$ ,

$N= $\frac{100}{22}$ = 4 $\frac{12}{22}$=4$\frac{6}{11}$$

Therefore, .

Let be the reciprocal of 1.77. Which of the following is true of ?

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$1.77= $\frac{177}{100}$$ , so its reciprocal is $N= $\frac{100}{177}$$ .

If 100 is divided by 177, the decimal equivalent is seen to be so

.

Give the reciprocal of 0.8.

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The reciprocal of a number is the quotient of 1 and that number. Divide 1 by 0.8 by moving the decimal point to the right in each number one place:

$1 \div 0.8 = 10 \div 8 = 1.25$

Give the reciprocal of 0.75.

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The reciprocal of a number is the quotient of 1 and the number.

Divide 1 by 0.75 by moving the decimal point to the right in each number two places:

$1 \div 0.75 = 100 \div 75 = 1 $\frac{25}{75}$ = 1 $\frac{1}{3}$$

Add the reciprocals of , , and . What is the sum?

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The reciprocals of 4, 6, and 8 are, respectively, $\frac{1}{4}$, $\frac{1}{6}$, $\frac{1}{8}$ . Their sum is

$\frac{1}{4}$+\frac{1}{6}$+ $\frac{1}{8}$

First we find the least common denominator between all three fractions.

$= $\frac{1}{4}$\bigg($\frac{6}{6}$\bigg) + $\frac{1}{6}$\bigg($\frac{4}{4}$\bigg) +\frac{1}{8}$\bigg($\frac{3}{3}$\bigg)$

$=\frac{6}{24}$+\frac{4}{24}$+\frac{3}{24}$ = $\frac{13}{24}$$

Subtract the reciprocal of 11 from the reciprocal of 13. What is the result?

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The reciprocals of 11 and 13 are, respectively, $\frac{1}{11}$ and $\frac{1}{13}$ . The requested difference is

$\frac{1}{13}$-$\frac{1}{11}$ = $\frac{1\cdot 11}{13 \cdot 11}$-$\frac{1\cdot 13}{11 \cdot 13}$ = $\frac{1 1}{143 }$-$\frac{ 13}{143}$ =-$\frac{2}{143}$

This answer is not among the given choices.