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What are the quotient and remainder whena) 19 is divided

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen ISBN: 9780073383095 37

Solution for problem 9E Chapter 4.1

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

Discrete Mathematics and Its Applications | 7th Edition

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Problem 9E

What are the quotient and remainder whena) 19 is divided by 7?________________b) -111 is divided by 11?________________c) 789 is divided by 23?________________d) 1001 is divided by 13?________________e) 0 is divided by 19?________________f) 3 is divided by 5?________________g) - 1 is divided by 3?________________h) 4 is divided by 1?

Step-by-Step Solution:
Step 1 of 3

Solution:Step-1: Division algorithm:If and , then there are unique integers q and r , with , such that Here d is called the divisor. a is called the dividend. q is called the quotient. r is called the remainder.Note that the remainder is non negative , and less than the divisor. Step-2: a)In this problem we need to find the quotient and remainder when 19 is divided by 7. We know that 19 is a prime number. When 19 is divided by 7 means 19 = 7(2) +5 , where 2 is the quotient and 5 is the remainder. Therefore , when 19 is divided by 7 , the quotient is 2 and the remainder is 5 Step-3: b)In this problem we need to find the quotient and remainder when -111 is divided by 11. When -111 is divided by 11 means -111 = 11(-11) +10 ,where -11 is the quotient and 10 is the remainder. Therefore , when -111 is divided by 11 , the quotient is (-11) and the remainder is 10.Step-4: c)In this problem we need to find the quotient and remainder when 789 is divided by 23. We know that 789 is not a prime number. When 789 is divided by 23 means 789 = 23(34) +7 , where 34 is the quotient and 7 is the remainder. Therefore , when 789 is divided by 23 , the quotient is 34 and the remainder is 7Step-5: d)In this problem we need to find the quotient and remainder when 1001 is divided by 13. We know that 1001 is not a prime number. When 1001 is divided by 13 means 1001 = 13(77) +0 , where 77 is the quotient and 0 is the remainder Therefore , when 1001 is divided by 13 , the quotient is 77 and the remainder is 0.Step-6:e)In this problem we need to find the quotient and remainder when 0 is divided by 19. When 0 is divided by 19 means 0 = 19(0) +0 , where 0 is the quotient and 0 is the remainder Therefore , when 0 is divided by 19 , the quotient is 0 and the remainder is 0.Step-7:f)In this problem we need to find the quotient and remainder when 3 is divided by 5. We know that 3 is a prime number. When 3 is divided by 5 means 3 = 5(0) +3 , where 0 is the quotient and 3 is the remainder Therefore , when 3 is divided by 5 , the quotient is 0 and the remainder is 3.Step-8:g)In this problem we need to find the quotient and remainder when -1 is divided by 3. When -1 is divided by 3 means -1 = 3(-1) +2 , where -1 is the quotient and 2 is the remainder Therefore , when -1 is divided by 3 , the quotient is -1 and the remainder is 2.Step-9:h)In this problem we need to find the quotient and remainder when 4 is divided by 1. When 4 is divided by 1 means 4 = 1(4) +0 , where 4 is the quotient and 0 is the remainder Therefore , when 4 is divided by 1 , the quotient is 4 and the remainder is 0.

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Chapter 4.1, Problem 9E is Solved
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Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

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