Calculer sous forme de fraction 3÷4+3÷4×64÷-9

Bonjour Shezine9999

[tex]\dfrac{3}{4}+\dfrac{3}{4}\times\dfrac{64}{-9}\\\\=\dfrac{3}{4}\times1+\dfrac{3}{4}\times\dfrac{64}{-9}\\\\=\dfrac{3}{4}\times(1-\dfrac{64}{9})\\\\=\dfrac{3}{4}\times(\dfrac{9}{9}-\dfrac{64}{9})\\\\=\dfrac{3}{4}\times(-\dfrac{55}{9}))\\\\=\dfrac{\not{3}\ 1}{4}\times(-\dfrac{55}{\not{9}\ 3})[/tex]

[tex]\\\\=-\dfrac{55}{12}\\\\\boxed{\dfrac{3}{4}+\dfrac{3}{4}\times(\dfrac{64}{-9})=-\dfrac{55}{12}}[/tex]

ou encore 

[tex]\dfrac{3}{4}+\dfrac{3}{4}\times(\dfrac{64}{-9})\\\\=\dfrac{3}{4}-\dfrac{3}{4}\times\dfrac{64}{9}\\\\= \dfrac{3}{4}-\dfrac{\not{3}}{\not{4}}\times\dfrac{\not{4}\times16}{\not{3}\times 3}\\\\= \dfrac{3}{4}-\dfrac{16}{3}\\\\= \dfrac{9}{12}-\dfrac{64}{12}\\\\= -\dfrac{55}{12}[/tex]

[tex]\\\\\boxed{\dfrac{3}{4}+\dfrac{3}{4}\times(\dfrac{64}{-9})=-\dfrac{55}{12}}[/tex]