# Theorem on Equal Ratios

If \(\dfrac{a_1}{b_1}=\dfrac{a_2}{b_2}=\dfrac{a_3}{b_3}=\dots =\dfrac{a_n}{b_n}\) then, each ratio equals \(\dfrac{m_1a_1+m_2a_2+m_3a_3+\dots + m_na_n}{m_1b_1+m_2b_2+m_3b_3+\dots + m_nb_n}\) for some constants \(m_i\) .

**Cite as:**Theorem on Equal Ratios.

*Brilliant.org*. Retrieved from https://brilliant.org/wiki/theorem-on-equal-ratios/