The Same Change Method

Mental Math · Axiom Academy

Slide both numbers by the same amount and the difference never budges — so slide until the number you are subtracting turns friendly. 1. Slide Both, and the Difference Never Moves A subtraction is really a gap — the distance from the smaller number up to the larger one. Picture both numbers as markers on a number line, then push them the same distance in the same direction . The pair moves; the gap between them is simply carried along, because whatever you added to the far end you also added to the near end. Take 72 − 38 and slide both up by 2: the markers land on 40 and 74, and the gap is still 34 . Shift both by the same amount and that amount cancels — for any shift at all Two different-looking problems, one difference 2. Slide Until the Subtrahend Turns Friendly Once you know the gap survives the slide, you get to choose where to slide it. Aim at the second number — the subtrahend , the one being taken away — and steer it onto a multiple of ten, because subtracting a round number is easy. For 83 − 47 , the 47 is 3 short of 50. Add that same 3 to both numbers and the problem becomes 86 − 50 = 36 . 47 is the number being taken away, and it is the awkward one. It is also sitting close to 50. 50 − 47 = 3. That 3 is the distance you are about to slide the whole pair. 83 + 3 = 86 and 47 + 3 = 50. This is the step people skip, and it is the only one that matters. 86 − 50 = 36. No borrowing, no carrying, and no correction at the end. The same slide, bigger numbers

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