# Math > Year 3

## Adding and subtracting 3-digit numbers mentally

3-digit numbers
3-digit numbers are made up of hundreds, tens and ones.
For example, 865, 201 etc.

Mentally
‘Mentally’ means working out questions in your head without writing them down.

There are different methods of adding and subtracting numbers mentally.

Partitioning numbers

214 + 356

To add these two numbers, we can partition the numbers according to the value of the digits and then add.

214 + 356 = 570

Compensation method

In the compensation method, we add or subtract an easier closer number and then adjust the answer at the end. For example, adding 10 instead of 9 and taking away 1.

Example 1: 423 + 9

Step 1: Add 10 to 423
423 + 10 = 433

Step 2: Take away 1 from 433
433 – 1 = 432

Hence, 423 + 9 = 432

Example 2: 756 – 195

Step 1: Subtract 200 as 200 is an easier closer number to 195

756 – 200 = 556

Step 2: Add 5 to the answer to adjust the subtraction of the extra 5 in step 1.

556 + 5 = 561

Hence, 756 – 195 = 561

Let's try a question.

At the start, there were 409 people at the party. Nine people arrived after a few hours. In total, how many people attended the party?

Number of people at the start of the party = 409

Number of people who arrived after a few hours = 9

Total number of people who attended the party = 409 + 9

We can firstly add 10 to 409 and then take away 1.

409 + 10 = 419

419 - 1 = 418

Total number of people who attended the party = 418

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