Skill: Subtract across zeros

When subtracting across zeros, regroup from the first nonzero place to the left. Each regrouping changes 1 unit into 10 units of the next smaller place.

Example:

$$5{,}000-2{,}347$$

1. Start in the ones place. There are $0$ ones, so we cannot subtract $7$ ones. The tens and hundreds places are also $0$, so regroup from the thousands place.
2. Take $1$ thousand from $5$ thousands. This leaves $4$ thousands and makes $(10)$ hundreds.
3. Regroup $1$ hundred into $(10)$ tens. Now there are $9$ hundreds and $(10)$ tens.
4. Regroup $1$ ten into $(10)$ ones. Now there are $9$ tens and $(10)$ ones.

The number is now ready to subtract by place value:

$$\begin{array}{rrrr} 4 & 9 & 9 & 10\\ 2 & 3 & 4 & 7\\ \hline \end{array}$$

Subtract from right to left:

• Ones: $(10-7=3)$
• Tens: $(9-4=5)$
• Hundreds: $(9-3=6)$
• Thousands: $(4-2=2)$

Therefore,

$$5{,}000-2{,}347=\boxed{2{,}653}$$

The zeros were placeholders, so they did not provide any units to subtract until we regrouped from a larger place.