Use place-value models for division

Place-value models show division of whole numbers by decomposing a dividend into thousands, hundreds, tens, and ones, then sharing or grouping each unit and regrouping when a place-value unit cannot be divided evenly. They connect the model to an equation, quotient, and possible remainder, making clear that a remainder is less than the divisor and that place-value units may be exchanged rather than dividing digits independently; multi-digit divisors and decimal division are not included.

Detailed Explanation: Use place-value models for division

A place-value model helps you divide by sharing whole-number units. You may exchange a larger unit for smaller units when needed:

$1$ thousand = $10$ hundreds
$1$ hundred = $10$ tens
$1$ ten = $10$ ones

Let’s find:

1{,}327 \div 6

1. Build the dividend

Represent $1{,}327$ as:

$1$ thousand
$3$ hundreds
$2$ tens
$7$ ones

We will share these units equally among $6$ groups.

2. Regroup the thousand

One thousand cannot be shared into $6$ whole thousands, so exchange it for $10$ hundreds:

1\text{ thousand}=10\text{ hundreds}

Now there are $13$ hundreds. Share them among $6$ groups:

Each group gets $2$ hundreds.
$1$ hundred is left over.

Exchange that leftover hundred for $10$ tens. With the original $2$ tens, there are:

10+2=12\text{ tens}

3. Share the tens

Share $12$ tens among $6$ groups:

Each group gets $2$ tens.
No tens are left over.

4. Share the ones

There are $7$ ones. Share them among $6$ groups:

Each group gets $1$ one.
$1$ one is left over.

Each group received:

$2$ hundreds
$2$ tens
$1$ one

So each group has $221$ , with $1$ left over.

Therefore,

1{,}327\div 6=221\text{ R}1

Check the answer:

6\times221+1=1{,}327

The remainder is $1$ , which is less than the divisor $6$ . The place-value model shows why we exchange units instead of dividing the digits independently.

Learn by doing: Use place-value models for division

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Long Division - With Remainder 1 x 1

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