You can place opposites of whole numbers. Fractions and decimals have opposites too, and they fill in the spaces between the negative integers.
Key idea
To place a negative fraction or decimal, find its opposite on the positive side, then reflect across 0. $-2.5$ is halfway between $-3$ and $-2$, because $2.5$ is halfway between 2 and 3.
Why it works
$-2.5$ means "2.5 units to the left of 0". Walking left from 0, you pass $-1$, then $-2$, and then you still have half a unit to go. So $-2.5$ is past $-2$, halfway to $-3$. Going left, the numbers get smaller, so the farther left a number is, the more negative it is.
Worked example: A negative fraction
Where is $-\frac{3}{4}$?
- $\frac{3}{4}$ is between 0 and 1, three quarters of the way to 1.
- Reflect: $-\frac{3}{4}$ is between $-1$ and 0, three quarter-steps left of 0.
Answer: Between $-1$ and 0, closer to $-1$.
Worked example: Read a point
A number line from $-2$ to 0 is cut into fourths. Point P is 3 small steps left of $-1$. What number is P?
- Each small step is $\frac{1}{4}$.
- Three quarter-steps left of $-1$ means $\frac{3}{4}$ farther from 0 than $-1$: that is $-1\frac{3}{4}$.
Answer: $-1\frac{3}{4}$, or $-1.75$.
Common mistake
Putting $-2.5$ between $-2$ and $-1$, as if you read the negative side from left to right like the positive side. Quick check: $-2.5$ is farther from 0 than $-2$ is (2.5 units against 2), so it must sit to the left of $-2$.