Integers & Order of Operations
Understand positive and negative integers on a number line, and master the order of operations using BODMAS.
The Integer Number Line
Integers are whole numbers that can be positive, negative, or zero. They do not include fractions or decimals. The number line extends infinitely in both directions.
Visual: The Number Line
Negative Numbers
Numbers less than zero. Found to the left of zero on the number line. Example: -3 means "3 below zero".
Positive Numbers
Numbers greater than zero. Found to the right of zero on the number line. Example: +5 or just 5.
Order of Operations: BODMAS
When a calculation has more than one operation, we must follow a specific order. The acronym BODMAS tells us which operations to do first.
BODMAS Flow (Do in this order)
Division & Multiplication are done left-to-right (same priority). Addition & Subtraction are done left-to-right (same priority).
Key Vocabulary
Integer
A whole number that can be positive, negative, or zero. Examples: -3, 0, 7.
BODMAS
The rule for the order of operations: Brackets, Orders, Division, Multiplication, Addition, Subtraction.
Absolute Value
The distance of a number from zero, always positive. |−5| = 5.
Operations
Mathematical processes: addition (+), subtraction (−), multiplication (×), division (÷).
Worked Examples
Calculate: 3 + 4 × 2
Step 1: Identify operations: addition (+) and multiplication (×).
Step 2: BODMAS says multiplication comes before addition.
Step 3: Do multiplication first: 4 × 2 = 8
Step 4: Then add: 3 + 8 = 11
Answer: 11 (not 14 — a common mistake is to add first!)
Calculate: (6 + 3) × 2 − 4
Step 1: Brackets first: 6 + 3 = 9
Step 2: Multiplication next: 9 × 2 = 18
Step 3: Subtraction last: 18 − 4 = 14
Answer: 14
Calculate: −3 + 7 − (−2)
Step 1: Brackets first: −(−2) means "subtract negative 2", which is the same as +2.
Step 2: Rewrite: −3 + 7 + 2
Step 3: Work left-to-right: −3 + 7 = 4
Step 4: Then: 4 + 2 = 6
Answer: 6 (Remember: subtracting a negative is the same as adding!)
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
Calculate: 5 + 3 × 4
Question 2
Calculate: (8 − 3) × 2 + 1
Question 3
Which integer is smaller: −7 or −2?
Question 4
Calculate: −4 + 9
Question 5
Calculate: 12 ÷ (2 + 4) × 3
Key Concepts Summary
- ● Integers include all positive whole numbers, negative whole numbers, and zero.
- ● On the number line, numbers increase to the right and decrease to the left.
- ● BODMAS gives the order: Brackets, Orders, Division/Multiplication (left-to-right), Addition/Subtraction (left-to-right).
- ● Subtracting a negative number is the same as adding a positive: a − (−b) = a + b.
- ● Always work through BODMAS step by step to avoid errors.