Question

use the partial-quotients algorithm to compute 2614 ÷ 21. the quotient is box and the remainder is box.

Explanation:

Step1: Understand Partial - Quotients

The partial - quotients algorithm involves repeatedly subtracting multiples of the divisor from the dividend and keeping track of the number of times we subtract each multiple. We start with large multiples (like 100 times, 10 times the divisor) and then work our way down.

For \(2614\div21\):
First, we find how many times 21 can be subtracted from 2614 in large chunks. Let's start with 100 times 21: \(21\times100 = 2100\). Subtract this from 2614: \(2614 - 2100=514\). We have a partial quotient of 100.

Step2: Next Multiple

Now, take the remaining 514. Let's try 20 times 21: \(21\times20 = 420\). Subtract this from 514: \(514 - 420 = 94\). Now our partial quotients sum to \(100 + 20=120\).

Step3: Next Multiple

Take the remaining 94. Let's try 4 times 21: \(21\times4=84\). Subtract this from 94: \(94 - 84 = 10\). Now our partial quotients sum to \(120+4 = 124\).

Step4: Check Remainder

The remainder is 10, which is less than the divisor 21, so we stop. The total quotient is the sum of the partial quotients (\(100 + 20+4=124\)) and the remainder is 10.

Answer:

The quotient is \(124\) and the remainder is \(10\).