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.
Por qué funciona
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.
Idea clave
To place $\frac{a}{b}$: cut each whole into $b$ equal parts, start at 0, and count $a$ parts.
Ejemplo resuelto: 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.
Respuesta: the third mark after 0
Ejemplo resuelto: 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.
Respuesta: $\frac{5}{3}$
Error común
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.