Proportion Formula
A proportion states that two ratios are equal.
Cross-multiplication
a/b = c/d ⇔ a × d = b × c
d = b × c ÷ a
Direct and inverse proportion
direct: y = kx (y ÷ x stays constant)
inverse: y = k ÷ x (x × y stays constant)
More hours worked means more pay (direct). More painters means fewer days to finish a job (inverse).
Examples
Direct: 5 kg cost 12; what do 8 kg cost?
- 5/12 = 8/d
- d = 12 × 8 ÷ 5
19.20
Inverse: 4 painters take 6 days; how long for 3?
- 4 × 6 = 3 × d
- d = 24 ÷ 3
8 days