Concept 7 of 7
Integers: Numbers Below Zero
Today's big idea
Negative numbers sit to the left of zero, and further left always means smaller.
A bigger digit after the − sign makes a smaller number, not a larger one.
How it works
👀 What's going on?
A thermometer reading below zero, a lift going to a basement, an overdrawn account. Numbers below zero describe ordinary things, and they order themselves in a way that feels backwards at first.
💡 Here's the trick
Look at the line above. Zero sits in the middle, positives run right and negatives run left. The rule is that whatever sits further left is smaller, which means the negative numbers get smaller as their digits get bigger.
🪄 How to do it
- 1.Place the numbers on the line above, with negatives to the left of zero.
- 2.Read them off from left to right.
- 3.That reading order is smallest to largest.
✍️ Try it
Which is greater, −8 or −3? Then put −6, 2, −9 and 0 in ascending order.
−3 sits to the right of −8, so −3 is greater. In order from smallest: −9, −6, 0, 2.
⚠️ Watch out
You might be thinking a bigger digit after the − sign means a bigger number. It means the opposite. −9 sits further left than −6, so it is the smaller of the two, despite 9 being more than 6.
🌟 Why this matters
Temperatures, floors below ground and money owed all live below zero, and getting the order wrong flips the meaning entirely.
Exam tip: Sketch the line and mark zero first; comparisons stop being guesswork once the numbers have positions.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“The temperature was 4°C and dropped by 9°C. What is the new temperature?”
- 1
Start on the integer line
Begin at +4. 🌡️
- 2
Move left by 9 steps
Subtracting means stepping LEFT. 4 − 9 crosses zero into the negatives.
- 3
Land at the answer
4 − 9 = −5
- 4
Answer ✓
New temperature = −5°C
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
CHALLENGE 1 OF 4
Drag to −4 on the number line
Drag the marker along the line. Negatives are LEFT of zero.
Quick check
✅ VERIFICATION
The temperature was −4 degrees and rose by 7 degrees. What is it now?
⚡ Finish the activity above first to answer.
Keep going!