Question

Find the quotient q and remainder r in the division algorithm with divisor b=13 and dividend, a equal to each of the following: (a) 110 (b) 311 (c) -4 (d) -39 (e) -110

Answer 1

When dividing a dividend by a divisor of 13, the quotient and remainder can be found using the division algorithm. For the given dividends, the quotients and remainders are as follows: (a) Quotient: 8, Remainder: 6; (b) Quotient: 23, Remainder: 10; (c) Quotient: 0, Remainder: -4; (d) Quotient: -3, Remainder: -0; (e) Quotient: -9, Remainder: -7.

Step-by-step explanation:

The division algorithm is used to find the quotient and remainder when dividing a dividend by a divisor. Given a divisor of 13 and dividends of 110, 311, -4, -39, and -110, let's find the quotients and remainders in each case:

1. (a) Dividend: 110, Quotient (q): 8, Remainder (r): 6
2. (b) Dividend: 311, Quotient (q): 23, Remainder (r): 10
3. (c) Dividend: -4, Quotient (q): 0, Remainder (r): -4
4. (d) Dividend: -39, Quotient (q): -3, Remainder (r): -0
5. (e) Dividend: -110, Quotient (q): -9, Remainder (r): -7