The 9s Tricks

Mental Math · Axiom Academy

Nine of something is ten of it with one copy handed back — so every 9s answer is a subtraction you can already do, and it arrives carrying its own fingerprint. 1. Nine Groups Are Ten Groups, Minus One Multiplying is counting groups, and 7 × 9 asks for nine groups of seven. Nine is awkward. Ten is not. So build the easy pile first — ten sevens, which is just 70 , because multiplying by ten costs you nothing. Then lift one whole seven back off. What is left standing is exactly nine sevens: 70 − 7 = 63 . You never multiplied by nine at all. Nine copies = ten copies, minus one copy One hard fact becomes two easy ones 2. The Same Move Works on Any Number Nothing in that argument cared that seven was small. Nine copies of 23 are ten copies of 23 with one copy removed — and ten copies of 23 is 230 , because multiplying by ten just slides every digit one place to the left and drops a 0 into the ones column. Take one 23 back off and you are done: 230 − 23 = 207 . 23 × 10 = 230. Every digit moves one place left and a 0 fills the ones column. That is not arithmetic, it is bookkeeping. Write the original 23 underneath — ones under ones, tens under tens. That single copy is the whole of what you owe back. 230 − 23 = 207. One subtraction, and the answer is final. There is no correction step waiting for you afterwards. 2 + 0 + 7 = 9. The digits of a 9s answer add to 9, so 207 passes. More on that in the next step. Bigger numbers, identical move

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