Complements to 100

Mental Math · Axiom Academy

Find any number's partner to 100 in your head: pair the tens to nine, the ones to ten. A complement to 100 is just the partner a number needs to reach 100. Picture a hundred-square of 100 little cells. Colour in 37 of them, and the cells left over — 63 — are the complement. Together they fill the square exactly. A number and its complement fill the hundred-square exactly 2. Pair the Tens to 9, the Ones to 10 Here is the fast rule the square just showed us. Take the tens digit and pair it to 9 ; take the ones digit and pair it to 10 . For 37 : the 3 pairs with 6 (because 3 + 6 = 9) and the 7 pairs with 3 (because 7 + 3 = 10). Read the two partners together — 63 . It works every time — tens to nine, ones to ten: 3. Round Numbers and Making Change Numbers ending in zero are the easiest of all. There are no ones to pair, so the tens do all the work — and they pair to 10 , not 9. For 30 , the tens 3 pair with 7 (3 + 7 = 10) and there are no ones: the complement is 70 . That is exactly making change — spend 30 cents of a dollar and you get 70 cents back. These still use the Step 2 rule — just mind the zeros. A one-digit number like 7 has a 0 in the tens place (think of it as 07), so it pairs to 93 . A number in the nineties like 96 pairs its tens 9 to 9, giving 0 tens — so 04 , which we just write as 4. You can now find any number's partner to 100 in about two seconds — right in your head. Scroll up to revisit any step.

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