Beyond Rankers Academy
Building Minds, Not Just Rankers
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Beyond Rankers Academy
Building Minds, Not Just Rankers
Main site →
0, 1, 2, 3 … the whole numbers stretch on forever. They follow rules — properties — that always hold true, no matter which whole numbers you pick.
Whole numbers start at 0 and go on forever: 0, 1, 2, 3 … There is no biggest whole number.
0 — 1 — 2 — 3 — 4 — 5 — 6 …
The successor of a number is 1 more than it. The predecessor is 1 less.
0 has no predecessor — there is no whole number before it. But every whole number, including 0, has a successor.
Four properties always work for addition and multiplication of whole numbers — but not for subtraction or division.
| Property | Meaning | Example |
|---|---|---|
| Closure | the answer is always a whole number | 4 + 5 = 9 ✓ |
| Commutative | order does not matter | 4 + 5 = 5 + 4 |
| Associative | grouping does not matter | (2+3)+4 = 2+(3+4) |
| Distributive | multiplication spreads over addition | 7×(20+3) = 7×20 + 7×3 |
Subtraction and division break all four rules. 5 − 3 ≠ 3 − 5, and 6 ÷ 3 is a whole number but 3 ÷ 6 is not — so subtraction and division are not closed, commutative or associative.
The distributive property is a genuine shortcut — it turns a hard multiplication into two easy ones.
12 IMO-style questions on the number line and its properties. 🍀