Breaking Apart Numbers

Mental Math · Axiom Academy

The one move behind almost all mental math: split a number into easy pieces, work the pieces, then put them back together. 1. Split, Add the Pieces, Recombine The most natural way to break a number apart is by place value : 47 is just 40 and 7. Do that to both numbers in a sum, add the tens to the tens and the ones to the ones, then snap the two subtotals back together. Split each number into its tens and its ones Add the tens, add the ones, then recombine 2. Borrow to a Friendly Number, Then Pay It Back Some numbers are almost round. 48 is a hair under 50, and 50 is a friendly number — effortless to add. So split 48 into 50 minus 2, add the easy 50, and give the 2 back at the very end. Round 48 up to the friendly 50, holding the 2 aside Add the easy 50, then pay the 2 back 3. Split a Factor, Multiply Each Piece Decomposition works for multiplication too. To do 6 × 47, break the 47 into 40 + 7, hand the 6 to each piece separately, and add the two easy products. This is the distributive property doing your mental math for you. Multiply the 6 by each piece, then add the products you are adding or subtracting. Combine tens with tens and ones with ones. a value sits just below (or above) a round one like 10, 50, or 100 — round it, then adjust. Every strategy here is the same single move — break a number into easy pieces, work the pieces, and recombine. Choose the split that makes the arithmetic effortless. Scroll up to revisit any step.

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