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

 \frac{{{a^2} +  {b^2}}}{{{c^2} + {d^2}}} = \frac{{{b^2}}}{{{a^2}}}

11.  If ax = by =  cz then

 \frac{{{a^2} + {b^2} +  {c^2}}}{{{x^2}{y^2} + {y^2}{z^2} + {z^2}{x^2}}} = \frac{{ab + bc + ca}}{{xyz(x  + y + z)}}

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

 \frac{{{a^2} + {b^2}}}{{{a^2} - {b^2}}} = \frac{{ac  + bd}}{{ac - bd}}

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

 \frac{{a - b}}{a}  = \frac{{c - d}}{c}

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

 \frac{{pa +  qb}}{{ra + sb}} = \frac{{pc + qd}}{{rc + sd}}

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

 m = \frac{{pa + qc + re + \cdots }}{{pb + qd + rf + \cdots }} = \frac{{a + c + e + \cdots }}{{b + d + f + \cdots }}

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