Skill: 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.