Explanation Consider a 4-hour clock. In a 4-hour clock, the elements belong to the set { 0 , 1 , 2 , 3 } . Multiplicative inverse of 2 in a 4-hour clock is a number x in the set { 0 , 1 , 2 , 3 } such that, 2 × x = 1 That is, when 2 x is divided by 4, the remainder should be 1. Notice that any multiple of two either leaves the remainder 0 or 2 when divided by 4. Thus, 2 has no multiplicative inverse in a 4-hour clock. Consider a 5-hour clock. In a 5-hour clock, the elements belong to the set { 0 , 1 , 2 , 3 , 4 } . Multiplicative inverse of 2 in a 5-hour clock is a number x in the set { 0 , 1 , 2 , 3 , 4 } such that, 2 × x = 1 That is, when 2 x is divided by 5, the remainder should be 1. Thus, 2 x will take the form 5 n + 1 . When n = 1 , 2 x = 6 x = 3 Thus, 2 has multiplicative inverse as 3 in a 5-hour clock. Similarly, in a 6-hour clock, the elements belong to the set { 0 , 1 , 2 , 3 , 4 , 5 } . Multiplicative inverse of 2 in a 6-hour clock is a number x in the set { 0 , 1 , 2 , 3 , 4 , 5 } such that, 2 × x = 1 . That is, when 2 x is divided by 6, the remainder should be 1. Notice that any multiple of two either leaves the remainder 0 or 2 or 4 when divided by 6. Thus, 2 has no multiplicative inverse in a 6-hour clock. Similar for a 7-hour clock, the elements belong to the set { 0 , 1 , 2 , 3 , 4 , 5 , 6 } . Multiplicative inverse of 2 in a 7-hour clock is a number x in the set { 0 , 1 , 2 , 3 , 4 , 5 , 6 } such that, 2 × x = 1 . That is, when 2 x is divided by 7, the remainder should be 1. Thus, 2 x will take the form 7 n + 1 . When n = 1 , 2 x = 8 x = 4 Thus, 2 has multiplicative inverse as 4 in a 7-hour clock. In a 8-hour clock, the elements belong to the set { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 } . Multiplicative inverse of 2 in a 8-hour clock is a number x in the set { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 } such that, 2 × x = 1 . That is, when 2 x is divided by 8, the remainder should be 1. Notice that any multiple of two either leaves the remainder 0 or 2 or 4 or 6 when divided by 8. Thus, 2 has no multiplicative inverse in a 8-hour clock. In a 9-hour clock, the elements belong to the set { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 }

Connect Math hosted by ALEKS Access Card 52 Weeks for Math in Our World

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ISBN: 9781259232848

Author: David Sobecki, Allan Bluman

Publisher: McGraw-Hill Education

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Chapter 15.2, Problem 118E

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To find: The multiplicative inverse, if there is one, for 2 in a 4-hour clock and repeat for 5-hour, 6-hour and 12-hour clock.

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Chapter 15.2, Problem 117E

Chapter 15.2, Problem 119E

Chapter 15 Solutions

Connect Math hosted by ALEKS Access Card 52 Weeks for Math in Our World

Ch. 15.1 - Use Table 15-1 to find the result of each...Ch. 15.1 - Which properties does the following system...Ch. 15.1 - Prob. 3TTO Ch. 15.1 - Prob. 4TTO Ch. 15.1 - Prob. 1E Ch. 15.1 - Prob. 2E Ch. 15.1 - Prob. 3E Ch. 15.1 - Prob. 4E Ch. 15.1 - Prob. 5E Ch. 15.1 - Prob. 6E

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The multiplicative inverse, if there is one, for 2 in a 4-hour clock and repeat for 5-hour, 6-hour and 12-hour clock.

Solution Summary: The author explains that the multiplicative inverse is obtained as Hours Multiplicative Inverse 4 None 5 3 6 None 7 4 8 None 11 6 12 None

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To find: The multiplicative inverse, if there is one, for 2 in a 4-hour clock and repeat for 5-hour, 6-hour and 12-hour clock.

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Chapter 15 Solutions