Question

plzzz answers guys plz

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Answer 1

Question:

If $\displaystyle{\sf\:\dfrac{a}{b}\:=\:\dfrac{2}{3}}$, then find the value of the following:

$\displaystyle{\sf\:\dfrac{4a\:+\:3b}{3b}}$

Answer:

$\displaystyle{\boxed{\red{\sf\:\dfrac{4a\:+\:3b}{3b}\:=\:\dfrac{17}{9}}}}$

Step-by-step-explanation:

We have given that, $\displaystyle{\sf\:\dfrac{a}{b}\:=\:\dfrac{2}{3}}$

We have to find the value of, $\displaystyle{\sf\:\dfrac{4a\:+\:3b}{3b}}$.

Now,

$\displaystyle{\sf\:\dfrac{a}{b}\:=\:\dfrac{2}{3}}$

$\displaystyle{\implies\sf\:\dfrac{a\:\times\:4}{b\:\times\:3}\:=\:\dfrac{2\:\times\:4}{3\:\times\:3}\:\:\:-\:-\:-\:\left[\:Multiplying\:both\:sides\:by\:\dfrac{4}{3}\:\right]}$

$\displaystyle{\implies\sf\:\dfrac{4a}{3b}\:=\:\dfrac{8}{9}}$

$\displaystyle{\implies\sf\:\dfrac{4a\:+\:3b}{3b}\:=\:\dfrac{8\:+\:9}{9}\:\:\:-\:-\:-\:[\:By\:Componendo\:]}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:\dfrac{4a\:+\:3b}{3b}\:=\:\dfrac{17}{9}}}}}$