Finding Difference Shortcuts

Mental Math · Axiom Academy

EXAMPLE Difference Shortcuts: 10 , 000 - 8 , 347 Walk the gap in friendly hops instead of borrowing across a row of zeros — then pick the shortcut that fits each problem. Find 10 , 000 - 8 , 347 mentally. Taking it away digit by digit means borrowing through every zero in 10 , 000 ; counting up never borrows at all — stand on 8 , 347 , walk up to 10 , 000 in friendly hops, and add the hops. Six differences, four shortcuts, and not one borrow. The habit worth building is the glance you take before you subtract: Zeros on top? Count up. Stand on the smaller number and hop to the next round ten, then hundred, then thousand, then the benchmark. The hops add to the difference: 3 + 50 + 600 + 1 , 000 = 1 , 653 . The benchmark can be any round number: 1 , 000 , 500 and 10 , 000 all work the same way — the stops just have to be easy to land on and easy to leave. Just below a friendly number? Round and adjust. 597 is 3 short of 600 , so take away 600 and hand the 3 back. Round the subtrahend up and you took away too much, so the excess comes back — that direction is the whole trick. Or slide both numbers instead. Same change turns 803 - 597 into 806 - 600 = 206 with nothing to undo afterwards. Two shortcuts, one answer. Taking something from 100 is a complement: pair the tens digit to 9 and the ones digit to 10 , so 67 pairs to 33 . A number ending in zero has no ones to pair, so its tens pair to 10 instead — 30 pairs to 70 .

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