Whole Numbers and Basic Mathematical Operations

What are Whole Numbers?

Whole numbers are the set of numbers {0, 1, 2, 3, 4, ...} — that is, all positive counting numbers together with zero. They do not include fractions, decimals, or negative numbers.

Place Value

Every digit in a whole number has a place value depending on its position, e.g. in the number 4,532, the digit 4 represents 4 thousands, 5 represents 5 hundreds, 3 represents 3 tens, and 2 represents 2 units.

Basic Operations on Whole Numbers

• Addition (+): combining two or more numbers to find their total, e.g. 245 + 138 = 383.
• Subtraction (−): finding the difference between numbers, e.g. 500 − 275 = 225.
• Multiplication (×): repeated addition of a number, e.g. 6 × 4 = 24 (adding 6 four times).
• Division (÷): sharing a number into equal parts, e.g. 48 ÷ 6 = 8.

Order of Operations (BODMAS)

When a calculation involves more than one operation, follow BODMAS: Brackets, Of, Division, Multiplication, Addition, Subtraction — performing operations in that order to get the correct answer.

Properties of Whole Number Operations

• Commutative property: the order of addition/multiplication does not change the result, e.g. 3 + 5 = 5 + 3.
• Associative property: the grouping of numbers does not change the result, e.g. (2+3)+4 = 2+(3+4).
• Identity property: adding 0 or multiplying by 1 leaves a number unchanged.

Importance

Whole numbers and the four basic operations form the foundation of all further mathematics — from fractions and algebra to statistics — and are used daily in counting, shopping, measuring and everyday problem-solving.