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G.1 Subtract using compensation - up to three digits

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What is subtraction with compensation?

Subtraction with compensation is a strategy where we adjust one or both numbers to make the subtraction easier. By doing this, we avoid regrouping and work with friendlier numbers, but the difference (answer) stays the same.

Example:
  • Problem: 503 – 298
  • Think: 298 is close to 300.
  • Add 2 to both numbers → 505 – 300
  • Now subtract → 505 – 300 = 205
Note

We can add or subtract the same amount from both numbers without changing the result. This makes the subtraction easier.

How do you use compensation in subtraction?

We use compensation by changing the second number (the number being subtracted) into a friendly number, like a multiple of 10 or 100. To keep the subtraction fair, we adjust the first number the same way.

Steps:
  • Start with the problem: 642 – 298
  • Notice that 298 is close to 300 (a friendly number).
  • Add 2 to both numbers → 644 – 300
  • Subtract: 644 – 300 = 344
  • Check: 298 + 344 = 642 ✔
Note

Compensation works because we adjust both numbers equally, keeping the difference the same while making subtraction faster and simpler.

Worked-out examples

Here are subtraction problems solved step by step using compensation:

Examples:
  • 431 – 299
    299 is close to 300. Add 1 to both numbers → 432 – 300 = 132
  • 725 – 498
    498 is close to 500. Add 2 to both numbers → 727 – 500 = 227
  • 806 – 297
    297 is close to 300. Add 3 to both numbers → 809 – 300 = 509
Note

When the second number is just below a multiple of 10 or 100, compensation makes subtraction much easier.

Why use compensation?

We use compensation to simplify subtraction. Instead of regrouping or subtracting tricky numbers, we adjust them to friendlier ones.

Example:
  • Problem: 812 – 397
  • 397 is close to 400. Add 3 to both numbers.
  • New problem: 815 – 400
  • Solve: 815 – 400 = 415
  • Check: 397 + 415 = 812 ✔
Note

Compensation is most useful when the number you subtract is close to a friendly number like 10, 100, or 1,000.