Ratio and Proportion — Formula Sheet

a:b = a/b

a:b ≠ b:a unless a = b

If both terms are multiplied or divided by the same non-zero number, the ratio remains unchanged

Reciprocal Ratio: 1/a : 1/b = b:a

Compounded Ratio: ac:bd = (a/b) × (c/d)

Duplicate Ratio: a^2:b^2

Triplicate Ratio: a^3:b^3

Sub-duplicate Ratio: √a:√b

Sub-triplicate Ratio: ∛a:∛b

a:b = c:d

a:b = c:d ⇒ a×d = b×c

a:b::c:d

a/b = b/c = c/d = d/e = e/f

If a:b = b:c, then b is the mean proportional of a and c

If a:b = b:e, then e is the third proportional to a and b