## Divide by Two-Digit Divisors

The division algorithm for dividing by two-digit divisors is the same as for one-digit divisors. Students must develop skill in estimating the first digit in the dividend, including making adjustments when the first estimate is too great or too small.

Example: Divide 1,138 by 23.

Look at the dividend. Since 11 < 23, there are not enough thousands or hundreds to divide. The first digit in the quotient will be in the tens place.
Think: 23 × n ≤ 113, so 4 is the greatest possible value of n.

Multiply 23 × 4.

Subtract 113 − 92. Compare to be sure the remainder is less than the divisor. If the remainder is greater, an error has been made.

Rename the remainder of 21 tens as 210 ones. Bring down the 8 ones in the dividend and add to get 218 ones.
Think: 23 × n ≤ 218, so 9 is the greatest possible value of n.

Multiply 23 × 9.

Subtract 218 − 207. Compare to be sure the remainder is less than the divisor. If the remainder is greater, an error has been made.

To check the division, multiply the quotient by the divisor and add the remainder. The result should be equal to the dividend.

Since division problems with zeros in the quotient cause some students difficulty, extra practice with such computations should be provided.

Teaching Model 11.6: Adjust the Quotient