Fractions & Ratios · Difficulty 3/10 · ~35 min
Ratios & Proportional Reasoning
- Translate between ratios and fractions of a whole
- Scale ratios through shared quantities
- Solve mixture and rate problems by ratio
Ratios are the first place school arithmetic becomes contest mathematics. The numbers stop being amounts and start being *relationships* — and relationships can be scaled, chained, and combined in ways raw numbers cannot.