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F.1 Add using compensation - up to three digits

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What is addition using compensation?

Addition using compensation is a strategy to make numbers easier to add. You adjust one number to a nearby "friendly" number, then compensate by adjusting the other number to keep the total the same.

Example:
  • 398 + 52 → (400 + 50) = 450
Note

This strategy uses mental math by rounding numbers to make addition faster and simpler.

How do you use compensation in addition?

To use compensation, change one number to a friendlier number (like a multiple of 10 or 100), then adjust the other number so the total does not change.

Steps:
  • Take the problem: 498 + 36
  • Adjust 498 up to 500 (+2)
  • Compensate by subtracting 2 from 36 (36 - 2 = 34)
  • Now add: 500 + 34 = 534
Note

The total stays the same because you increased one number and decreased the other by the same amount.

Why use compensation?

Compensation makes addition easier by turning numbers into friendly numbers, which are simpler to work with mentally.

Example:
  • 389 + 61
  • Round 389 up to 390 (+1), then subtract 1 from 61 → 60
  • Now add: 390 + 60 = 450
Note

This method avoids regrouping and builds number sense by using place value and relationships between numbers.

Using compensation in word problems

You can also apply compensation to solve real-life problems that involve adding larger numbers.

Example:
  • Sarah read 297 pages and later read 54 more pages. How many pages did she read in total?
  • 297 + 54 → Adjust 297 up to 300 (+3), then subtract 3 from 54 → 51
  • Now add: 300 + 51 = 351
Note

Compensation is useful when one number is close to a multiple of 10 or 100.