Integers on the Number Line
“On the number line, further right means larger.”
The hook
Below-zero temperatures, the −2 level of a parking garage — the number line was the first picture to pin down numbers smaller than 0.
In plain words
The positive integers, 0, and the negative integers laid out in order on one line. Bigger to the right, smaller to the left.
The intuition
Put 0 in the middle as the reference point, then mark +1, +2, … to the right and −1, −2, … to the left at equal spacing. Comparing two numbers is just 'which one is further right'.
How it's built
Integers come in three groups — the positives (1, 2, 3…), zero, and the negatives (−1, −2, −3…). The number line stands all three in left-to-right order so their sizes become visible.
Example
Compare −3 and 2. On the line, 2 is to the right of −3, so 2 is larger. −3 < 2.
Common mistake
For negatives, a bigger digit means a smaller number. −7 sits to the left of −2, so −7 < −2. 'Looks bigger' and 'is bigger' are not the same.
Where it's used
Temperature, altitude, profit and loss (debt vs. savings), and the x-axis of the coordinate plane — the foundation for any quantity that has direction and a reference point.
Where it came from
Negatives were long treated as 'impossible numbers', but accounting that recorded debts as negatives in India and China, together with the number-line picture, made them full-fledged numbers.
Quick check
Which number sits furthest right (is the largest) on the number line?
- −4
- −1
- 0
- 2✓
Practice
Which is larger, −5 or 3?
Answer: 3
- On the line, 3 sits to the right of −5
- → 3 is larger
Takeaway: The number on the right is always larger.
What number is 4 less than 0?
Answer: -4
- Move 4 steps left from 0
- → −4
Takeaway: 'Getting smaller' means moving left on the line.
Which is larger, −2 or −7?
Answer: -2
- −2 is to the right of −7 (closer to 0)
- → −2 is larger
Takeaway: Among negatives, closer to 0 means larger.
Put −3, 1, −1, 2 in order from smallest to largest.
Answer: undefined
- Mark them on the line and read left to right
- −3, −1, 1, 2
Takeaway: Sorting is just the left-to-right order on the line.