The integers q and r , with 0 ≤ r < | b | , such that a = b q + r in each of the following cases. (a) a = 12 , 345 ; b = − 39 (b) a = − 27 , 361 ; b = − 977 (c) a = − 102 , 497 ; b = − 1473 (d) a = 98 , 764 ; b = 4789 (e) a = − 41 , 391 ; b = − 755 (f) a = 555 , 555 , 123 ; b = 111 , 111 , 111 (g) a = 81 , 538 , 416 , 000 ; b = 38 , 754

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Answer 1

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Chapter 4.1, Problem 6E

To determine

The integers q and r, with 0≤r<|b|, such that a=bq+r in each of the following cases.

(a) a=12,345;b=−39

(b) a=−27,361;b=−977

(c) a=−102,497;b=−1473

(d) a=98,764;b=4789

(e) a=−41,391;b=−755

(f) a=555,555,123;b=111,111,111

(g) a=81,538,416,000;b=38,754

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Answer 2

Question

Chapter 4.1, Problem 6E

To determine

The integers q and r, with 0≤r<|b|, such that a=bq+r in each of the following cases.

(a) a=12,345;b=−39

(b) a=−27,361;b=−977

(c) a=−102,497;b=−1473

(d) a=98,764;b=4789

(e) a=−41,391;b=−755

(f) a=555,555,123;b=111,111,111

(g) a=81,538,416,000;b=38,754

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Answer 3

Question

Chapter 4.1, Problem 6E

To determine

The integers q and r, with 0≤r<|b|, such that a=bq+r in each of the following cases.

(a) a=12,345;b=−39

(b) a=−27,361;b=−977

(c) a=−102,497;b=−1473

(d) a=98,764;b=4789

(e) a=−41,391;b=−755

(f) a=555,555,123;b=111,111,111

(g) a=81,538,416,000;b=38,754

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Answer 4

Question

Chapter 4.1, Problem 6E

To determine

The integers q and r, with 0≤r<|b|, such that a=bq+r in each of the following cases.

(a) a=12,345;b=−39

(b) a=−27,361;b=−977

(c) a=−102,497;b=−1473

(d) a=98,764;b=4789

(e) a=−41,391;b=−755

(f) a=555,555,123;b=111,111,111

(g) a=81,538,416,000;b=38,754

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Answer 5

Chapter 4.1, Problem 6E

To determine

The integers q and r, with 0≤r<|b|, such that a=bq+r in each of the following cases.

(a) a=12,345;b=−39

(b) a=−27,361;b=−977

(c) a=−102,497;b=−1473

(d) a=98,764;b=4789

(e) a=−41,391;b=−755

(f) a=555,555,123;b=111,111,111

(g) a=81,538,416,000;b=38,754

Answer 6

Chapter 4.1, Problem 6E

To determine

The integers q and r, with 0≤r<|b|, such that a=bq+r in each of the following cases.

(a) a=12,345;b=−39

(b) a=−27,361;b=−977

(c) a=−102,497;b=−1473

(d) a=98,764;b=4789

(e) a=−41,391;b=−755

(f) a=555,555,123;b=111,111,111

(g) a=81,538,416,000;b=38,754

Answer 7

Chapter 4.1, Problem 6E

To determine

The integers q and r, with 0≤r<|b|, such that a=bq+r in each of the following cases.

(a) a=12,345;b=−39

(b) a=−27,361;b=−977

(c) a=−102,497;b=−1473

(d) a=98,764;b=4789

(e) a=−41,391;b=−755

(f) a=555,555,123;b=111,111,111

(g) a=81,538,416,000;b=38,754

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. 4.1 - 227 Ch. 4.1 - The Well-Ordering Principle states that any...Ch. 4.1 - Prob. 3TFQ Ch. 4.1 - Prob. 4TFQ Ch. 4.1 - Prob. 5TFQ Ch. 4.1 - Prob. 6TFQ Ch. 4.1 - Prob. 7TFQ Ch. 4.1 - Prob. 8TFQ Ch. 4.1 - Prob. 9TFQ Ch. 4.1 - Prob. 10TFQ

Solution Summary: The author explains how to determine the integers q and r, using the division algorithm.

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The integers q and r, with 0≤r<|b|, such that a=bq+r in each of the following cases.

(a) a=12,345;b=−39

(b) a=−27,361;b=−977

(c) a=−102,497;b=−1473

(d) a=98,764;b=4789

(e) a=−41,391;b=−755

(f) a=555,555,123;b=111,111,111

(g) a=81,538,416,000;b=38,754

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Chapter 4 Solutions

Solution Summary: The author explains how to determine the integers q and r, using the division algorithm.

Concept explainers

Videos

The integers q and r, with 0≤r<|b|, such that a=bq+r in each of the following cases. (a) a=12,345;b=−39 (b) a=−27,361;b=−977 (c) a=−102,497;b=−1473 (d) a=98,764;b=4789 (e) a=−41,391;b=−755 (f) a=555,555,123;b=111,111,111 (g) a=81,538,416,000;b=38,754

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Chapter 4 Solutions

The integers q and r, with 0≤r<|b|, such that a=bq+r in each of the following cases.

(a) a=12,345;b=−39

(b) a=−27,361;b=−977

(c) a=−102,497;b=−1473

(d) a=98,764;b=4789

(e) a=−41,391;b=−755

(f) a=555,555,123;b=111,111,111

(g) a=81,538,416,000;b=38,754