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order of operations, which we will say more about later.)

Let’s try another simple division problem.

Example 25. Find the quotient and remainder of the division 162 ÷ 42.

Solution. Putting the dividend and divisor into the long division form, wehave

42 16 2

Let’s estimate the number of subtractions that we’ll need to perform. 40 goes into 160 four times, so,
perhaps four is a good guess. But 4 × 42 = 168, which is too big (bigger than the dividend). So we
lower our estimate by 1. We get 3 × 42 = 126, which is less than the dividend, so this must be the
right choice.

3
42 16 2
−12 6

Subtracting, we obtain the remainder

3
42 16 2
−12 6
36

which is less than the divisor, as it should be. Thus, the quotient is 3 and the remainder is 36. As a
check, we verify that 3 × 42 + 36 = 162. (Multiplication before addition.)

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