Ratio and Proportion Formulas

1. If $\frac{a}{b} = \frac{c}{d}$ then $ad = bc$

2. If $\frac{a}{b} = \frac{c}{d}$ then $\frac{a}{c} = \frac{b}{d}$

3. If $\frac{a}{b} = \frac{c}{d}$ then $\frac{b}{a} = \frac{d}{c}$

4. If $\frac{a}{b} = \frac{c}{d}$ then $\frac{{a + b}}{b} = \frac{{c + d}}{d}$

5. If $\frac{a}{b} = \frac{c}{d}$ then $\frac{{a - b}}{b} = \frac{{c - d}}{d}$

6. If $\frac{a}{b} = \frac{c}{d}$ then $\frac{{a + b}}{{a - b}} = \frac{{c + d}}{{c - d}}$ called Componendo-Dividendo Rule.

7. If $\frac{a}{b} = \frac{b}{c}$ then $\frac{a}{c} = \frac{{{a^2}}}{{{b^2}}}$

8. If $\frac{a}{b} = \frac{c}{d}$ and $a = c$ then $b = d$

9. If $\frac{a}{{b + c}} = \frac{b}{{c + a}} = \frac{c}{{a + b}}$and $a + b + c \ne 0$ then $a = b = c$

10.  If $\frac{a}{b} = \frac{c}{d}$ then

11.  If $ax = by = cz$ then

12.  If  $\frac{a}{b} = \frac{c}{d}$ then

13.  If $\frac{a}{b} = \frac{c}{d} = \frac{e}{f} = \frac{{la + mc + ne}}{{lb + md + nf}}$

14.  If $\frac{a}{b} = \frac{c}{d}$ then

15.  If $\frac{a}{b} = \frac{c}{d}$ then

16.  If $\frac{a}{b} = \frac{c}{d} = \frac{e}{f} = \cdots = m$ then