Question

perform each of the following divisions using both the repeated-subtraction and the standard algorithm. a. 18÷585b. 22÷561c. 97÷1000a. The division problem 18÷585 has a quotient of ____ and a remainder of ___. b. The division problem of 22÷ 561 has a quotient of _____ and a remainder of ___.c. The division problem of 97÷1000 has a quotient of ____ and a remainder of ___

Answer 1

(a)

Repeat-subtraction is a method of subtracting an equal number of items from a larger group. In this case, we have to form 18 groups and subtract 18 items from 585 until we get zero or closer.

585-18 = 567

567-18 = 549

549-18 = 531

531-18 = 513

513-18 = 495

495-18 = 477

477-18 = 459

459-18 = 441

411-18 = 423

423-18 = 405

405-18 = 387

387-18 = 369

369-18 = 351

351-18 = 333

333-18 = 315

315-18 = 297

297-18 = 279

279-18 = 261

261-18 = 243

243-18 = 225

225-18 = 207

207-18 = 189

189-18 = 171

171-18 = 153

153-18 = 135

135-18 = 117

117-18 = 99

99-18 = 81

81-18 = 63

63-18 = 45

45-18 = 27

27-18 = 9

As you can observe, we can form 32 groups, which means the quotient is 32, and the remainder is 9.

Now, we divide use the standard algorithm

Now, we repeat the process for b and c.

(b)

Subtracting 22 from 561, we get 25 formed groups in total using the repeated-subtraction method. Then, using the standard method, we get

So, the remainder is 11 and the quotient is 25.

(c)

Subtracting 97 from 1000, we get 10 groups. Then,