Basic Arithmetic

Arithmetic is the basic manipulation of numbers. Four fundamental operations are the building blocks of all mathematics.

The Four Operations

➕ Addition

Adding combines quantities.

3 + 4 = 7 “Three plus four equals seven”

Addition is commutative: 3 + 4 = 4 + 3

➖ Subtraction

Subtracting removes a quantity from another.

10 - 3 = 7 “Ten minus three equals seven”

Subtraction is NOT commutative: 10 - 3 ≠ 3 - 10

✖️ Multiplication

Multiplying is repeated addition. 4 × 3 means “four, three times.”

4 × 3 = 12 “Four times three equals twelve”

Key insight: 7 × 0 = 0 (anything times zero is zero) 7 × 1 = 7 (anything times one is itself)

➗ Division

Dividing splits a quantity into equal parts.

12 ÷ 4 = 3 “Twelve divided by four equals three”

This means: if you split 12 into 4 equal groups, each group has 3.

Never divide by zero — this is mathematically undefined.

Order of Operations

When multiple operations appear together, humans follow a specific order (remembered by the acronym PEMDAS or BODMAS):

Parentheses / Brackets — do what’s inside first
Exponents / Orders — powers (2³ = 8)
Multiplication and Division — left to right
Addition and Subtraction — left to right

Example: 2 + 3 × 4 = 2 + 12 = 14 (not 5 × 4 = 20)

Practical Examples

Splitting a bill: 4 friends eat dinner. The total is $48. How much does each person owe? $48 ÷ 4 = $12 each

Tipping at a restaurant: Bill is $50. You want to leave a 20% tip. $50 × 0.20 = $10 tip

How long until something: It’s 2pm. You have a meeting at 6pm. How many hours? 6 - 2 = 4 hours

Calories: You ate 3 cookies. Each has 120 calories. How many calories total? 3 × 120 = 360 calories

Estimation

You don’t always need an exact answer. Estimation — getting close enough — is a vital real-world skill.

If something costs $47.92, you can estimate it as “about $48” for quick mental math. If you need 4 bags of flour at 3.2kg each, that’s “about 12–13 kg.”

Calculators

Humans invented devices called calculators — physical tools or software on phones and computers — that perform arithmetic instantly. These are widely available and acceptable to use. You are not expected to do complex arithmetic in your head.