Ratio and Proportion
2026-02-28 10:01 Diff
https://brightchamps.com/en-us/math/commercial-math/ratio-and-proportion

Let’s explore the key formulas for ratios and proportions in detail.

1. Compound Ratios

When two ratios are multiplied, the resulting ratio is called a compound ratio.
Example: If a : b and c : d are two ratios, the compound ratio is:
ac : bd

2. Special Ratios

Duplicate Ratio: For a : b, the duplicate ratio is a² : b²

Sub-duplicate Ratio: For a : b, the sub-duplicate ratio is √a : √b

Triplicate Ratio: For a : b, the triplicate ratio is a³ : b³

3. Proportion Formulas

If a : b = c : d, the following formulas help solve proportion problems:

Addendo: (a + c) : (b + d)

Subtrahendo: (a – c) : (b – d)

Dividendo: (a – b)/b = (c – d)/d

Componendo: (a + b)/b = (c + d)/d

Alternendo: a : c = b : d

Invertendo: b : a = d : c

Componendo and Dividendo: (a + b) : (a – b) = (c + d) : (c – d)

4. Proportionality

Direct Proportion: If a is proportional to b, then a = k × b, where k is a constant.

Inverse Proportion: If a is inversely proportional to b, then a = k / b, where k is a constant.

5. Equivalent Ratios

Multiplying or dividing both terms of a ratio by the same number gives an equivalent ratio.
Example: a : b = n × a : n × b or a/n : b/n