Comparing Ratios

Once you understand what a ratio is, a natural next question is: given two ratios, which one represents a “bigger” comparison? The most reliable method is cross-multiplication – multiply diagonally across the two ratios and compare the results, avoiding the need to convert to decimals or find a common denominator by hand.

Cross-Multiplication Method

To compare a:b and c:d, calculate a × d and c × b. Whichever product is larger tells you which ratio is larger.

Which ratio is larger: 3:5 or 5:8?

Cross-multiply: 3 × 8 = 24, and 5 × 5 = 25. Since 25 > 24, 5:8 is the larger ratio.

Checking for Equivalent Ratios

Two ratios are equivalent if they represent the exact same comparison, just scaled up or down – like 2:3 and 4:6. Cross-multiplication confirms this: if a × d = c × b exactly, the ratios are equivalent.

Are 4:6 and 6:9 equivalent?

Cross-multiply: 4 × 9 = 36, and 6 × 6 = 36. These are equal, so yes, the ratios are equivalent.

Real-Life Application

Recipe scaling: checking if a doubled recipe keeps the same taste balance.
Sports statistics: comparing win ratios between two seasons.
Shopping: comparing ratios of active ingredient to total volume in two products.

Key Takeaways

Cross-multiplication compares two ratios without needing a common denominator.
For a:b vs c:d, compare a×d to c×b – the larger product marks the larger ratio.
Equal cross-products mean the two ratios are equivalent.

Practice: Comparing Ratios

Compare Two Ratios