## Divide by Two-Digit Divisors

The division algorithm for dividing by two-digit divisors is the same as that 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 will be no thousands or hundreds digit in the quotient. The first digit 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 make sure the remainder is less than the divisor. If the remainder is greater, an error has been made.

Think: 23 × n ≤ 113 so 4 is the greatest possible value of n.

Multiply 23 × 4.

Subtract 113 − 92. Compare to make 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 the 210 ones.

Think: 23 × n ≤ 218 so 9 is the greatest possible value of n.

Multiply 23 × 9.

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

Think: 23 × n ≤ 218 so 9 is the greatest possible value of n.

Multiply 23 × 9.

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

To check a division problem, 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 5.1:** Divide by Multiples of 10, 100, and 1,000