Breaking Apart the Subtrahend

Mental Math · Axiom Academy

LESSON Breaking Apart the Subtrahend Split what you are taking away into easy bites and remove them one at a time — choosing a bite that drops you onto a friendly round number. Take 84 − 37 . Leave the 84 sitting there as your pile and split the 37 — the number being taken away — into friendlier pieces: 30 + 7 . Remove the big piece first: 84 − 30 is 54. Then remove the small one: 54 − 7 is 47. The pieces leave the pile one at a time, and the pile counts down as they go. The subtrahend leaves in bites; the pile counts down 37 becomes 30 + 7. The tens bite is a round number, so 84 − 30 = 54 comes instantly. Removing the tens keeps you on round-ish numbers longer. For 76 − 23, drop the 20 to reach 56, then the 3 gives 53. 60 + 7 = 67, so 90 − 60 − 7 really is 90 − 67 = 23. If the pieces do not add back exactly, the answer will not be right either. You never take away too much and hand some back — that is a different technique. Here each bite is removed once and it is gone. For 85 − 47 , split the 47 as 40 + 7 : 85 − 40 is 45, and 45 − 7 is 38. 2. Land on a Friendly Number First Here is the powerful move. Same 84 − 37 , but split the 37 as 4 + 33 instead. The 84 is only 4 above a round 80 , so bite off exactly that 4 first: 84 − 4 is 80. Now you are standing on a friendly number, and the rest is easy — 80 − 33 is 47. The first bite was chosen for one reason only: to land you on the ten. The first bite is sized to land the pile on 80

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