To represent $\frac{1}{2}$ on a number line, we look at the denominator (the bottom number). This tells us how many equal parts to divide one “whole” into.
The Process: Start at $0$ and end at $1$. Divide that space into 2 equal parts.
The Result: Each jump represents $\frac{1}{2}$. The first mark after zero is $\frac{1}{2}$, and the second mark is $\frac{2}{2}$ (which equals $1$).
If we need to represent a fraction like $\frac{3}{4}$, we need more divisions.
The Process: Divide the space between $0$ and $1$ into 4 equal parts.
The Labels: * The first mark is $\frac{1}{4}$
The second is $\frac{2}{4}$ (or $\frac{1}{2}$)
The third is $\frac{3}{4}$
The fourth is $\frac{4}{4}$ (which equals $1$)
Rational numbers aren’t just between $0$ and $1$; they can be greater than $1$ or even less than $0$ (negative).
When you have a common denominator (in this case, $4$), you can use a single number line to show multiple values.
| Value | Direction from Zero | Location |
| $-\frac{3}{4}$ | Move Left | Count 3 marks to the left of zero. |
| $\frac{7}{4}$ | Move Right | Count 7 marks to the right of zero. This will be past the number $1$ (since $\frac{7}{4} = 1 \frac{3}{4}$). |
Pro Tip: Always remember that the denominator tells you the “size” of the jump, while the numerator tells you “how many” jumps to take from zero!
| To represent… | Divide 1 unit into… | Each part equals… |
| Halves | 2 equal parts | $\frac{1}{2}$ |
| Fourths | 4 equal parts | $\frac{1}{4}$ |
| Eighths | 8 equal parts | $\frac{1}{8}$ |