P2B · Fractions & decimals · RATIO.CONCEPT

Understand ratios

Intuition

Understand first, compress later.

Fractions, decimals and percentages are different representations of the same quantity idea.

Switch representations

Ratio table2 : 3

first quantitysecond quantitysame factor

Each column is made by multiplying both numbers by the same factor — the arrow above matches the arrow below. That is why every column reduces back to 2 : 3; the ratio never changes.

Formal view

You can understand ratios when you can recognise the underlying objects, select valid rules and check each step for equivalence or logical implication.

Why does it work?

This skill sits on a prerequisite network. If a step is unstable, repair the missing prerequisite instead of merely doing more items of the same type.