Compensation for Subtraction

Mental Math · Axiom Academy

LESSON Compensation for Subtraction Round the number you are taking away, subtract the easy amount, then undo the nudge. 1. Take Away Too Much, Then Give It Back Take 73 − 29 . The 29 is what slows you down, and it sits one step below a friendly 30 . So take away 30 instead: 73 − 30 = 43 , no thinking required. But you were only asked to take away 29 — you removed one too many . That extra 1 has to come back: 43 + 1 = 44 . Round the subtrahend up by 1, add 1 back to the answer Match the give-back to the nudge Round 39 up by 1, add 1 back. Round 48 up by 2 , add 2 back — adding only 1 there is the classic careless version. Round 78 up by 2, add 2. Round 99 up by 1, add 1: 2. When You Take Away Too Little Not every awkward number sits just below a round one. In 84 − 21 the 21 sits just above 20, so round it down . Take away 20: 84 − 20 = 64 . This time you did not take away enough — one of the 21 is still sitting there. So take that one away as well: 64 − 1 = 63 . Toward whichever multiple of ten is closer, because that keeps the give-back small enough to hold in your head. 29 is one below 30, so round up. 21 is one above 20, so round down. Either way the nudge is 1, and either way you undo exactly that 1 — the only thing that changes is the direction. 3. The Opposite of the Addition Rule

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