P2A · Fractions & decimals · FRAC.COMPARE.SAME_DEN

Compare fractions with same denominator

Intuition

Understand first, compress later.

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

Switch representations

Fraction bars2/3

inked partsremaining parts

The whole is cut into 3 equal parts and 2 of them are inked — that is 2/3. The denominator names how many equal parts there are, the numerator counts the inked ones.

Formal view

You can compare fractions with same denominator 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.