You can place unit fractions on the number line, and you know $\frac{3}{4}$ is 3 pieces of size $\frac{1}{4}$. Put those together: $\frac{3}{4}$ is 3 lengths of $\frac{1}{4}$, measured from 0.
Why it works
A point on the number line shows a distance from 0. For $\frac{3}{4}$, the distance is three pieces of length $\frac{1}{4}$, laid end to end starting at 0. That is why fractions are numbers: each one is a single point, and fractions bigger than 1, like $\frac{5}{4}$, simply keep going past 1.
Key idea
To place $\frac{a}{b}$: cut each whole into $b$ equal parts, start at 0, and count $a$ parts.
Worked example: Less than 1
Where is $\frac{3}{4}$?
- Cut 0 to 1 into 4 equal parts.
- Start at 0 and count 3 parts: one, two, three.
Answer: the third mark after 0
Worked example: More than 1
A line is cut into thirds. Point B is 2 marks past 1. What fraction is at B?
- From 0 to 1 there are 3 thirds.
- 2 more thirds makes 5 thirds in all.
Answer: $\frac{5}{3}$
Common mistake
Starting to count at the first tick after 0. If you count the first mark as "one" you are already one part from 0, and the count comes out one too many. $\frac{1}{4}$ is the first mark because it is one jump from 0. Count jumps, starting at 0.