Negative numbers & integers on a number line
Theory
Integers are the whole numbers, the negative whole numbers and zero, set out in order on a number line. The further left a number is, the smaller it is; the further right, the larger.
The integers are the positive whole numbers, the negative whole numbers and zero. A number like \(-2.5\) is not an integer because it is not whole.
On a number line, zero sits in the middle, positive integers to its right and negative integers to its left.
The further left a number is, the smaller it is. Moving right adds and moving left subtracts, so counting back past zero gives a negative integer.
Compare integers by their position: further left is smaller.
| Pair | Positions | Result |
|---|---|---|
| \(-7,\ -2\) | \(-7\) further left | \(-7 < -2\) |
| \(-1,\ -6\) | \(-1\) closer to zero | \(-1 > -6\) |
| \(0,\ -3\) | \(0\) right of \(-3\) | \(0 > -3\) |
How to compare integers
- Place each integer on the number line.
- Read left to right: numbers further left are smaller.
- Order them from left to right for ascending order.
\(-7\) is further left than \(-2\).
| \(-7\) | \(=\) | \(-2 \text{ (larger)}\) |
Read left to right along the number line.
| \(\text{order}\) | \(=\) | \(-5,\ -3,\ 0,\ 2\) |
Start at \(3\) and count back \(8\).
| \(3 - 8\) | \(=\) | \(-5\) |
Below sea level is negative; rising adds.
| \(-6 + 4\) | \(=\) | \(-2\text{ m}\) |
Common pitfalls
Frequently asked questions
What is an integer?
An integer is a whole number that can be positive, negative or zero. Examples are \(-4\), \(0\) and \(7\). A decimal or fraction is not an integer.
Which is smaller, -7 or -2?
\(-7\), because it is further to the left on the number line. For negatives, the further from zero, the smaller the number.
How do you show a temperature below zero?
Use a negative integer. A temperature of five degrees below zero is written \(-5\).
What does moving left on the number line do?
Moving left subtracts. Starting at \(3\) and counting back \(8\) reaches \(-5\).