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Componendo and Dividendo

If a: b = 5 :...

Question

If a: b = 5 : 3, find : $\frac{5 a - 3 b}{5 a + 3 b}$

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Solution

$i f space a colon b equals 5 colon 3 s o a over b equals 5 over 3 t h e n fraction numerator 5 a minus 3 b over denominator 5 a plus 3 b end fraction equals fraction numerator begin display style fraction numerator 5 a minus 3 b over denominator b end fraction end style over denominator begin display style fraction numerator 5 a plus 3 b over denominator b end fraction end style end fraction equals fraction numerator 5 begin display style a over b end style minus 3 over denominator 5 a over b plus 3 end fraction equals fraction numerator 5 cross times begin display style 5 over 3 end style minus 3 over denominator 5 cross times 5 over 3 plus 3 end fraction equals fraction numerator begin display style 25 over 3 end style minus 3 over denominator begin display style 25 over 3 end style plus 3 end fraction equals fraction numerator 25 minus 9 over denominator 25 plus 9 end fraction equals 16 over 34 equals 8 over 17$

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Similar questions

a : b = 5 : 3

\frac{5 a - 3 b}{5 a + 3 b}

\frac{a}{b} = \frac{7}{3}

, then find the value of

\frac{5 a + 3 b}{5 a - 3 b}

.

a : b = 3 : 5

(10 a + 3 b) : (5 a + 2 b)

3

5

(10 a + 3 b) : (5 a + 2 b)

a ∶ b = 5 : 3

, that will be the value of

\frac{5 a - 3 b}{5 a + 3 b}

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