Negative numbers are numbers less than zero. They are written with a minus sign in front: −3, −10, −0.5. The further left (or down) a number is on a scale, the smaller it is.
Example 1 — Reading a thermometer
Step 1
The thermometer reads −6°C. This means 6 degrees below zero.
Step 2
Is −6°C warmer or colder than −2°C? Colder — it is further below zero.
Step 3
On the thermometer, −6 is lower down than −2, confirming it is colder.
Example 2 — Bank balance
Step 1
A bank balance of −£50 means the account is £50 overdrawn (in debt).
Step 2
A balance of −£20 is better than −£50, because −20 is closer to zero (less debt).
Key point: Negative numbers get smaller as you move away from zero. −10 is less than −1, even though 10 > 1.
✓ Quick Check 1 — Understanding Negative Numbers
Question 1 of 10
Comparing and Ordering Negative Numbers
A number line is the best tool for comparing negatives. Numbers increase from left to right. So any number to the right of another is greater, even if both are negative.
Example 3 — Order these from smallest to largest: 3, −5, 0, −2, 1
Step 1
Draw or imagine a number line. Negatives are on the left of zero.
Step 2
Order from left to right (smallest to largest): \(\mathbf{-5, -2, 0, 1, 3}\)
Example 4 — Which is greater: −7 or −3?
Step 1
On the number line, −3 is to the right of −7.
Step 2
Numbers to the right are greater, so \(-3 > -7\).
Step 3
Think of it as temperature: −3°C is warmer (less cold) than −7°C.
Common mistake: Thinking −7 is greater than −3 because 7 > 3. The negative sign reverses the size relationship: −7 < −3.
That "7" you compared above (ignoring the minus sign) has its own name: the absolute value — the distance a number is from zero, written with two vertical bars: \(|{-7}|\). Distance can't be negative, so the absolute value is always positive (or zero).
Example 4b — Find \(|-7|\), \(|5|\), and \(|0|\)
Step 1
\(|-7|\) means "how far is −7 from zero?" — that's 7 steps, so \(|-7| = 7\).
Step 2
\(|5|\) is already positive, still 5 steps from zero: \(|5| = 5\).
Step 3
\(|0| = 0\) — zero is zero steps from itself.
Don't confuse absolute value with size comparison: \(|-7| = 7\) is bigger than \(|-3| = 3\), but as actual numbers \(-7 < -3\) (from the Common Mistake above). Absolute value strips the sign; comparing the numbers themselves does not.
✓ Quick Check 2 — Comparing and Ordering Negatives
Question 1 of 10
Finding the Difference Between Values Including Negatives
The difference between two numbers is how far apart they are on the number line. To find the difference, count from the smaller value to the larger value, or subtract: difference = larger − smaller.
Doing this by subtraction sometimes means subtracting a negative — e.g. \(5 - (-3)\). Quick preview of why that adds: on the number line, subtracting normally means "move left." Subtracting a negative reverses direction — so you move right instead, which is the same as adding. (The next lesson, Adding and Subtracting Negatives, covers this rule properly with more examples — here it's just enough to find a difference.)
Example 5 — Temperature changes from −3°C to 5°C. Find the rise.
Step 1
Difference = higher temperature − lower temperature = \(5 - (-3)\)
Step 2
Count: from −3 to 0 is 3 steps; from 0 to 5 is 5 more steps. Total: \(\mathbf{8°C}\) rise.
Example 6 — A bank balance changes from −£40 to £120. Find the change.
Step 1
Change = \(120 - (-40) = 120 + 40 = £160\).
Step 2
The balance increased by \(\mathbf{£160}\).
✓ Quick Check 3 — Difference Between Values
Question 1 of 10
Practice: Negative Number Problems
Answer each question, then click Check All.
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Question
Answer
Result
1
Order smallest first: −4, 2, −8, 0, 3
2
Temperature falls from 4°C to −5°C. By how much did it fall?
3
A lift goes from floor −2 to floor 7. How many floors does it travel?
4
−7 + 12 = ?
5
6 − 10 = ?
6
−3 × 4 = ?
7
−20 ÷ 5 = ?
8
Order smallest first: 5, −1, −6, 3
9
Temperature is −3°C and rises by 8°C. What is the new temperature?
10
−8 − (−3) = ?
⚠ Things to Watch Out For
Confusing negative and "minus": −3 means the NUMBER negative three. "Minus" is an operation. 5 − 3 uses minus as subtraction; −3 is a position on the number line. They look the same but mean different things.
Ordering negatives: −7 is LESS than −3. Further left on the number line = smaller value. Never assume a bigger digit means a bigger negative number.
Difference between negative numbers: The difference between −3 and −7 is 4, not −4. Difference is always positive.
Temperature contexts: If it's −5°C and drops by 3°C, it becomes −8°C (colder, more negative). If it warms by 3°C it becomes −2°C. Always move in the correct direction on the number line.
Absolute value confusion: |−7| = 7. The size (absolute value) of −7 is 7. Don't confuse the size of a negative number with the number itself.