Skill: Use partial differences

To use partial differences, break each number into hundreds, tens, and ones. Then subtract each place-value part and combine the answers.

Example:

$$463-278$$

First decompose the numbers:

$$463=400+60+3$$ $$278=200+70+8$$

The ones part, $3$, is too small to subtract $8$. Regroup one ten as $10$ ones:

$$400+60+3=400+50+13$$

Now the tens part, $50$, is too small to subtract $70$. Regroup one hundred as $100$ tens:

$$400+50+13=300+150+13$$

The amount is still $463$; it is just written in a different way.

Now find the partial differences:

• Hundreds: $300-200=100$
• Tens: $150-70=80$
• Ones: $13-8=5$

Combine the partial differences:

$$100+80+5=185$$

Therefore,

$$463-278=\boxed{185}$$