Skill: Subtract using regrouping

Regrouping means rewriting a place-value unit as 10 units in the next smaller place. The number’s value does not change; only its representation changes.

Example:

$$\begin{array}{r} 5002\\ -\ 2786\\ \hline \end{array}$$

Start in the ones place. Since $2$ is less than $6$, regroup.

1. There are no tens or hundreds to borrow, so borrow $1$ thousand from the $5$ thousands.
   This leaves $4$ thousands and creates $10$ hundreds.

2. Borrow $1$ hundred from those $10$ hundreds.
   This leaves $9$ hundreds and creates $10$ tens.

3. Borrow $1$ ten from those $10$ tens.
   This leaves $9$ tens and creates $10$ ones.

Now $5002$ is represented as $4$ thousands, $9$ hundreds, $9$ tens, and $12$ ones. Its value is still $5002$.

Subtract each place:

$$\begin{array}{r} 4\ 9\ 9\ 12\\ -\ 2\ 7\ 8\ 6\\ \hline 2\ 2\ 1\ 6 \end{array}$$

• Ones: $12-6=6$
• Tens: $9-8=1$
• Hundreds: $9-7=2$
• Thousands: $4-2=2$

Therefore,

$$5002-2786=\boxed{2216}.$$