Two-Digit by Two-Digit Examples

Mental Math · Axiom Academy

EXAMPLE Multiplying by Cutting One Factor Both factors sit three from a ten — cut the one that leaves the smaller correction, then take the overshoot back. Work out in your head. Both factors sit 3 away from a ten, so either one can be cut — the real question is which cut leaves less to carry. Pick it, do one easy multiplication, and make one small correction. Nicely done — one product, four different places to cut it, and the same answer every time. Worth holding on to: One cut, two pieces, one correction: . That is the entire method. The correction is the distance times the other factor: both 47 and 23 sit 3 from a ten, yet cutting 47 costs while cutting 23 costs . Equal distances, unequal prices — which is what makes the choice worth making. Which side the ten is on sets the sign, not the method: a ten below the factor leaves a piece to add ( 940 + 141 ); a ten above leaves an overshoot to take back ( 1150 - 69 ). One identity, , with a - T carrying its own sign. Cutting both factors is legal too: (40 + 7)(20 + 3) gives 800 + 140 + 120 + 21 = 1081 — four pieces to hold instead of two, each kept in its own place. The digit products behind them are 8 , 14 , 12 and 21 , and stripping the place values off them is what turns a correct method into a wrong answer.

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