Compensation Method for Addition

Mental Math · Axiom Academy

LESSON Compensation for Addition Nudge one addend to a round number, add the easy way, then undo the nudge. Take 47 + 29 . The 29 is what makes you hesitate — but it is only one step from 30 , a round, friendly number. So nudge it up: add 1 to make 30, do the easy sum 47 + 30 = 77 , then give that borrowed 1 straight back. 77 − 1 = 76 . The single unit you add to round is the exact unit you take off the total. Add 1 to round the addend, subtract 1 from the answer You do not always round up. When a number sits just above a round one — like 93 , a hair over 90 — round it down instead. For 93 + 68 , drop 93 to 90 (that is 3 fewer), add the easy way to get 90 + 68 = 158 , then put the 3 back: 158 + 3 = 161 . Rounding down leaves the sum short, so this time you add to make up the difference. Both nudges undo cleanly, and both give 97: Here is the slip almost everyone makes at first. You rounded 29 up to 30, so 47 + 30 = 77 is one too big. The borrowed 1 is already sitting inside that 77 — so you must take it back out. Subtract: 77 − 1 = 76 . Adding the 1 again would count it twice and give 78 , which is wrong. Round up, you subtract. Round down, you add. Match the give-back to the nudge and you are always right. You can now turn an awkward sum into an easy one and undo the nudge without thinking about it. Scroll up to revisit any step.

This is the written version of the interactive lesson above. See the full Mental Math course.