23, 529/23 Round to a one-digit arithmetic fact. Estimate the quotient.
Compare the quotient to the estimate
Evaluate the expression using mental math and the division algorithm.

The given expression for the division is 23,529/23

Evaluating the expression using mental math gives;

23,529/23 = (23,000 + 230 + 230 + 23 × 3)/23 = 1000 + 10 + 10 + 3 = 1,023

Evaluating the expression using the division algorithm states as follows;

When an integer a is divided by another integer n, then we can find the numbers q and r such that a = b·q + r and a/b = q + r/b, where, b > 0, and 0 ≤ r ≤ b

Where;

q = The quotient

r = The reminder

Therefore, we have;

23,529 = 23×q + r

Given that 23 × 1029 = 25,529, we have

23,529 = 23 × 1029 + 0

Therefore, q = 1029, and r = 0

Step-by-step explanation: