You have put whole numbers on a number line. Fractions live there too, between the whole numbers. First, the unit fractions: the space from 0 to 1 is the whole, and we cut it into equal parts.
Why it works
On a number line, a number tells how far it is from 0. The whole is the length from 0 to 1. Cut it into 4 equal lengths, and each length is $\frac{1}{4}$. The point that is one of those lengths from 0 is at $\frac{1}{4}$. So $\frac{1}{4}$ is a number, a distance from 0, just like 1 or 2.
Key idea
To place $\frac{1}{b}$, cut the space from 0 to 1 into $b$ equal parts. $\frac{1}{b}$ is at the end of the first part, one part away from 0.
Worked example: Read the point
The space from 0 to 1 is cut into 3 equal parts. Point A is at the first mark after 0. Where is A?
- Each part is $\frac{1}{3}$ long.
- A is one part from 0.
Answer: $\frac{1}{3}$
Worked example: Count spaces
A line from 0 to 1 has 7 marks, counting the marks at 0 and at 1. How many equal parts is it cut into?
- Count the spaces between the marks, not the marks.
- 7 marks make 6 spaces.
Answer: $6$ parts, so each is $\frac{1}{6}$
Common mistake
Counting tick marks instead of spaces. The line below has 5 marks (numbered under it), but only 4 spaces, so it shows fourths, not fifths. The marks at 0 and at 1 are ends, not parts. Count the jumps from 0 to 1.