Whole Numbers — Class 6 IMO

Whole Numbers & Their Properties

Whole numbers are 0, 1, 2, 3, … The smallest whole number is 0 and there is no largest. Natural numbers start from 1.

Key properties: addition and multiplication are commutative (a + b = b + a) and associative, and multiplication is distributive over addition: a × (b + c) = a × b + a × c.

Example 1: Which property does 7 + 5 = 5 + 7 show?

The commutative property of addition.

Example 2: Use the distributive property: 4 × (10 + 2).

4 × 10 + 4 × 2 = 40 + 8 = 48.

Quick recap

Whole numbers: 0, 1, 2, 3, … (smallest is 0).
Commutative: a + b = b + a; distributive: a × (b + c) = a×b + a×c.

✓ Quick check

What is the smallest whole number?

The smallest whole number is 0.

Using the distributive property, 6 × (5 + 2) = ?

6 × 5 + 6 × 2 = 30 + 12 = 42.

The Number Line & Successor/Predecessor

Whole numbers can be shown on a number line. Moving right adds and moving left subtracts. The successor of a number is one more; the predecessor is one less.

0 is the only whole number with no predecessor (in whole numbers).

Example 1: What is the successor of 99?

99 + 1 = 100.

Example 2: On a number line, where does 3 + 4 land?

Start at 3 and move 4 right to reach 7.

Quick recap

Successor = number + 1; predecessor = number − 1.
0 has no predecessor among whole numbers.

✓ Quick check

What is the predecessor of 1000?

1000 − 1 = 999.

Which whole number has no predecessor?

0 is the smallest whole number, so it has no predecessor.

Patterns, Brackets & Simplifying

When simplifying, do the work inside brackets first, then multiplication and division, then addition and subtraction (the BODMAS order).

So 2 + 3 × 4 = 2 + 12 = 14, and 12 − (3 + 4) = 12 − 7 = 5.

Example 1: Simplify 12 − (3 + 4).

Brackets first: 12 − 7 = 5.

Example 2: Simplify 2 + 3 × 4.

Multiply first: 2 + 12 = 14.

Quick recap

Do brackets first, then × and ÷, then + and −.
This order is called BODMAS.

✓ Quick check

Simplify: 20 − (5 × 2) = ?

5 × 2 = 10, so 20 − 10 = 10.

Simplify: (8 + 2) × 3 = ?

Brackets first: 10 × 3 = 30.