Divide multi-digit whole numbers by one-digit divisors

Division partitions a multi-digit whole number into equal groups of a one-digit size, relating the dividend, divisor, quotient, and any remainder through multiplication and subtraction. Place-value reasoning supports the standard algorithm, including regrouping, estimating to check reasonableness, and recording zeros when a place contributes no groups; a remainder must be smaller than the divisor and may need interpretation in context. The scope is whole-number dividends and one-digit divisors, excluding decimal divisors, fractional quotients, and more advanced forms of division.

Detailed Explanation: Divide multi-digit whole numbers by one-digit divisors

Division finds how many equal groups the divisor can make from the dividend.

Dividend: the number being divided, $4{,}207$
Divisor: the number of groups, $6$
Quotient: the answer, or number in each group
Remainder: what is left over

Example: $4{,}207 \div 6$

First, estimate:

4{,}200 \div 6 = 700

So, the quotient should be close to $700$ .

Use place value and divide from left to right:

Look at $42$ .
$6$ goes into $42$ exactly $7$ times.

7 \times 6 = 42

Subtract:

42-42=0

The $7$ belongs in the hundreds place of the quotient.

Bring down the $0$ from the tens place.
Since $6$ goes into $0$ zero times, record a $0$ in the quotient.
Bring down the $7$ from the ones place.
$6$ goes into $7$ one time.

1 \times 6 = 6

Subtract:

7-6=1

The remainder is $1$ .

Therefore,

4{,}207 \div 6 = 701\text{ R}1

Check the answer using multiplication and addition:

6 \times 701 + 1 = 4{,}206+1=4{,}207

The remainder, $1$ , is less than the divisor, $6$ , so the answer is reasonable.

Learn by doing: Divide multi-digit whole numbers by one-digit divisors

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Long Division - With Remainder 2 x 1

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