Divide multi-digit numbers by 2-digit divisors

Whole-number division with typically up to four-digit dividends and two-digit divisors is understood through place value: the dividend is decomposed into groups, and each quotient digit represents how many groups of the divisor fit at that place. The quotient and remainder satisfy $\text{dividend}=\text{divisor}\times\text{quotient}+\text{remainder}$ , with the remainder less than the divisor; estimation checks the quotient’s size and the remainder is interpreted as a quantity, not appended as another digit. The scope is whole-number quotients and remainders, excluding decimal division and more general rational divisors.

Detailed Explanation: Divide multi-digit numbers by 2-digit divisors

To divide by a two-digit divisor, use place value and divide one part of the dividend at a time.

Example: Find $(1{,}487 \div 27)$ .

First, estimate:

1{,}500 \div 30 \approx 50

So the answer should be close to $(50)$ .

Step 1: Divide the first group

$(27)$ does not fit into $1$ or $(14)$ , so use $(148)$ .

Ask: How many groups of $(27)$ fit into $(148)$ ?

27 \times 5=135

So write $5$ in the tens place of the quotient.

Subtract:

148-135=13

Step 2: Bring down the next digit

Bring down the $7$ to make $(137)$ .

Ask: How many groups of $(27)$ fit into $(137)$ ?

27 \times 5=135

Write another $5$ in the ones place of the quotient.

Subtract:

137-135=2

There are no more digits to bring down, so $2$ is the remainder.

\boxed{1{,}487\div27=55\text{ R }2}

Check the answer:

27\times55+2=1{,}485+2=1{,}487

The remainder $2$ is less than the divisor $(27)$ , so the answer is correct.

Learn by doing: Divide multi-digit numbers by 2-digit divisors

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Long Division - No Remainder 4 x 2

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