Question

4. Utilizând proprietatea fundamentală a proporţiilor, verificați dacă următoarele egalita
de rapoarte sunt proportii:
2
3
6.
2
4
+
33
1
4 1 2
+
32 3
21
5 15
2 6
4 8
c)

Answer 1

Răspuns: Ai demonstratia mai jos

Explicație pas cu pas:

Salutare!

$\bf \dfrac{\dfrac{4}{2}\cdot\dfrac{1}{2}+\dfrac{2}{3}\cdot2}{\dfrac{2}{3}\cdot\dfrac{1}{2}}= \dfrac{\dfrac{2}{3}+\dfrac{4}{3} }{\dfrac{1}{3}}$

$\bf \dfrac{\dfrac{\not4}{2}\cdot\dfrac{1}{\not2}+\dfrac{2}{3}\cdot2}{\dfrac{\not2}{3}\cdot\dfrac{1}{\not2}}= \dfrac{\dfrac{2+4}{3}}{\dfrac{1}{3}}$

$\bf \dfrac{\dfrac{2}{3}+\dfrac{4}{3}}{\dfrac{1}{3}}= \dfrac{\dfrac{6}{3}}{\dfrac{1}{3}}$

$\bf \dfrac{\dfrac{2+4}{3}}{\dfrac{1}{3}}= \dfrac{\dfrac{\not6}{\not3}}{\dfrac{1}{3}}$

$\bf \dfrac{6}{3}:\dfrac{1}{3} = 2:\dfrac{1}{3}$

$\bf \dfrac{6}{3}\cdot\dfrac{3}{1} = 2\cdot\dfrac{3}{1}$

$\bf \dfrac{6}{\not3}\cdot\dfrac{\not3}{1} = \dfrac{2\cdot3}{1}$

$\bf \dfrac{6}{1} = \dfrac{6}{1}$

$\bf 6 = 6 \implies adevarat$

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