Question

Daca a/b=7/3, valoarea raportului a-b/2a este

Answer 1

$\it \dfrac{a}{b}=\dfrac{7}{3}\Rightarrow \dfrac{a}{7}=\dfrac{b}{3} =\dfrac{a-b}{7-3}=\dfrac{a-b}{4}\Rightarrow \dfrac{a-b}{4}=\dfrac{a}{7} \Rightarrow \dfrac{a-b}{a}=\dfrac{4}{7}|_{\cdot\frac{1}{2}} \Rightarrow \\ \\ \\ \Rightarrow \dfrac{a-b}{2a}=\dfrac{4}{14}$

Sau:

$\it \dfrac{a}{b}= \dfrac{7}{3} \Rightarrow \dfrac{b}{a}= \dfrac{3}{7}\\ \\ \\\dfrac{a-b}{2a}= \dfrac{a}{2a}- \dfrac{b}{2a}= \dfrac{1}{2}- \dfrac{1}{2}\cdot \dfrac{b}{a} = \dfrac{1}{2}-\ \dfrac{1}{2}\cdot \dfrac{3}{7}= \dfrac{^{7)}1}{\ 2}-\ \dfrac{3}{14} = \dfrac{7-3}{14} =\dfrac{4}{14}$