Ratios, percentages and averages

Build a model, justify why it applies and check the result.

Identify the whole that a fraction or percentage refers to, especially after the whole changes.

Represent quantities in a ratio $a:b$ as $ak$ and $bk$ with one common unit $k$.

Apply percentage changes as multiplying factors, including successive changes.

Find a combined mean by weighting each group mean by its group size.