Fractions on a number line, step by step

A number line shows a fraction as a distance, not a piece of pie — the idea that unlocks comparing and adding later.

The question

2/3 on a number line

gaps:3marks:4
each gap:
each gap:
gaps counted:2
  1. Count the GAPS between the marks, not the marks. A line cut into 3 has 4 marks on it — counting those gives 4, and the answer comes out wrong in a way that still looks like a fraction.
  2. 3 gaps between 0 and 1, so each one is a third — that is the bottom number.
  3. Then count gaps from 0 to the mark: 2. So it is 2/3.

How it works.

  1. 01

    Count the GAPS between the marks, not the marks. A line cut into 3 has 4 marks on it — counting those gives 4, and the answer comes out wrong in a way that still looks like a fraction.

  2. 02

    3 gaps between 0 and 1, so each one is a third — that is the bottom number.

  3. 03

    Then count gaps from 0 to the mark: 2. So it is 2/3.