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

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Question

Give the reciprocal of 0.8.

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Answer

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:

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

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Question

Give the reciprocal of 0.75.

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Answer

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:

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

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Question

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

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Answer

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.

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

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

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Question

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

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Answer

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.

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Question

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

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Answer

$0.3 = \frac{3}{10}$ , 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

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

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Question

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

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Answer

$1.5 = \frac{15}{10} = \frac{3}{2}$ , 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 $8-\frac{2}{3} = 7\frac{1}{3}$

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Question

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

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Answer

$0.22 = \frac{22}{100}$ , 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, .

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Question

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

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Answer

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

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

.

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Question

Give the reciprocal of 0.8.

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Answer

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:

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

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Question

Give the reciprocal of 0.75.

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Answer

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:

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

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Question

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

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Answer

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.

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

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

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Question

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

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Answer

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.

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Question

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

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Answer

$0.3 = \frac{3}{10}$ , 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

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

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Question

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

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Answer

$1.5 = \frac{15}{10} = \frac{3}{2}$ , 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 $8-\frac{2}{3} = 7\frac{1}{3}$

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Question

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

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Answer

$0.22 = \frac{22}{100}$ , 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, .

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Question

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

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Answer

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

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

.

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Question

Give the reciprocal of 0.75.

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Answer

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:

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

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Question

Give the reciprocal of 0.8.

Tap to reveal answer

Answer

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:

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

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Question

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

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Answer

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.

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

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

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Question

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

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Answer

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.

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

Give the reciprocal of 0.8.

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:

Give the reciprocal of 0.75.

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:

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

The reciprocals of 4, 6, and 8 are, respectively, . Their sum is First we find the least common denominator between all three fractions.

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

The reciprocals of 11 and 13 are, respectively, and . The requested difference is This answer is not among the given choices.

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

, so its reciprocal is . , so its reciprocal is . Add them: , so

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

, so its reciprocal is . , so its reciprocal is 8. The requested difference is

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

, so its reciprocal is . Since , Therefore, .

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

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

Give the reciprocal of 0.8.

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:

Give the reciprocal of 0.75.

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:

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

The reciprocals of 4, 6, and 8 are, respectively, . Their sum is First we find the least common denominator between all three fractions.

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

The reciprocals of 11 and 13 are, respectively, and . The requested difference is This answer is not among the given choices.

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

, so its reciprocal is . , so its reciprocal is . Add them: , so

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

, so its reciprocal is . , so its reciprocal is 8. The requested difference is

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

, so its reciprocal is . Since , Therefore, .

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

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

Give the reciprocal of 0.75.

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:

Give the reciprocal of 0.8.

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:

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

The reciprocals of 4, 6, and 8 are, respectively, . Their sum is First we find the least common denominator between all three fractions.

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

The reciprocals of 11 and 13 are, respectively, and . The requested difference is This answer is not among the given choices.

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:

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

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:

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

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.

$1.5 = \frac{15}{10} = \frac{3}{2}$ , 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 $8-\frac{2}{3} = 7\frac{1}{3}$

$0.22 = \frac{22}{100}$ , 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, .

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

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

.

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:

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

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:

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

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.

$1.5 = \frac{15}{10} = \frac{3}{2}$ , 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 $8-\frac{2}{3} = 7\frac{1}{3}$

$0.22 = \frac{22}{100}$ , 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, .

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

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

.

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:

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

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:

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

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.