Whole Numbers & Integers
Explore negative numbers on a number line, learn to order integers, and add or subtract with negatives using real-world contexts.
What Are Integers?
Integers are whole numbers that can be positive, negative, or zero. They do not include fractions or decimals.
Examples: ..., -3, -2, -1, 0, 1, 2, 3, ...
The Number Line
Numbers get smaller as you move left and larger as you move right.
Ordering Integers
When ordering integers, remember: a number further right on the number line is always greater. This means -1 is greater than -5, even though 1 is less than 5.
Example: Order from smallest to largest
Numbers: 3, -7, 0, -2, 5
Answer: -7, -2, 0, 3, 5
Adding & Subtracting with Negative Numbers
Adding a positive number
Move right on the number line.
-3 + 5 = 2
Subtracting a positive number
Move left on the number line.
2 - 5 = -3
Adding a negative number
Same as subtracting: move left.
4 + (-3) = 4 - 3 = 1
Subtracting a negative number
Same as adding: move right.
-2 - (-5) = -2 + 5 = 3
Visual: -3 + 5 on a Number Line
Start at -3, move 5 places right, land on 2.
Real-World Contexts
Temperature
"It was -3°C in the morning and rose by 8°C. What is the temperature now?"
-3 + 8 = 5°C
Money / Debt
"You owe $4 and then owe another $3. How much do you owe?"
-4 + (-3) = -7, so you owe $7
Sea Level / Altitude
"A submarine is at -200 m and rises 150 m."
-200 + 150 = -50 m (still below sea level)
Floors in a Building
"You are on floor -2 (basement) and go up 5 floors."
-2 + 5 = floor 3
Key Vocabulary
Integer
A whole number that can be positive, negative, or zero.
Negative Number
A number less than zero, written with a minus sign (e.g. -3).
Positive Number
A number greater than zero (e.g. 5).
Number Line
A line showing numbers in order, with negative numbers on the left and positive on the right.
Worked Examples
Calculate: 4 - 7
Step 1: Start at 4 on the number line.
Step 2: Move 7 places to the left.
Answer: 4 - 7 = -3
Calculate: -6 + 10
Step 1: Start at -6 on the number line.
Step 2: Move 10 places to the right.
Answer: -6 + 10 = 4
Order these from smallest to largest: 2, -8, 5, -1, 0
Step 1: Place on a number line. The further left, the smaller.
Step 2: -8 is furthest left, then -1, then 0, then 2, then 5.
Answer: -8, -1, 0, 2, 5
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
What is -4 + 7?
Question 2
What is 3 - 8?
Question 3
Which is the smallest number? -2, 4, -6, 0, 1
Question 4
The temperature was -5°C and it rose by 12°C. What is the temperature now?
Question 5
What is -3 - (-5)?
Key Concepts Summary
- ●Integers are whole numbers: ..., -3, -2, -1, 0, 1, 2, 3, ...
- ●Numbers get smaller to the left on the number line and bigger to the right.
- ●Adding a positive: move right. Subtracting a positive: move left.
- ●Subtracting a negative is the same as adding.
- ●Negative numbers appear in real life: temperature, debt, depth below sea level.