Multiplying by 25, 250, 2500

Mental Math · Axiom Academy

LESSON Multiplying by 25, 250, 2500 25 is a quarter of a hundred — so scale by a hundred, and take a quarter. 1. 25 Is a Quarter of a Hundred Take a hundred and cut it four ways — one cut across, one cut down. You get four equal pieces, and every one of them is 25 . That is the whole lesson in one picture: 25 is not a number you have to wrestle with, it is a quarter of a hundred . The coin is even named after it — 25 cents is a quarter because 25 is a quarter of 100. Four 25s make one hundred — so 25 is a hundred, quartered Why a quarter, and not a fifth or a third Because 25 lands on 100 exactly when you count it four times, and no other count works: 25, 50, 75, 100 . Three 25s fall short at 75 and five overshoot at 125. That exactness is what lets you trade a multiplication by 25 for a division by 4 without losing anything. 2. Quarter First, or Scale First Now put it to work on 48 × 25 . You have to scale by 100 and take a quarter, but nothing says which one goes first. Quarter first and you get 48 ÷ 4 = 12 , then 12 × 100 = 1,200 . Scale first and you get 48 × 100 = 4,800 , then 4,800 ÷ 4 = 1,200 . Same answer, and it always will be — the two moves never interfere with each other. Quarter first — the numbers stay small Scale first — the number grows, but only by zeros So the choice is not about being right — it is about which route keeps you holding a number you can actually hold. That is decided by one question: does 4 divide the number?

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