Question

Respondam para mim por favor!!! Quero com cálculos!!! Vejam a imagem para não responderem errado!
a)- (5/4 - 1/3)² : 2/7
b)- (1 - 1/3)² : (1- 2/5)²

Answer 1

a) $\left(\dfrac{5}{4}-\dfrac{1}{3} \right )^{\!2}:\dfrac{2}{7}$

Para fazer a subtração nos parênteses, reduza as frações ao mesmo denominador, mmc(4, 3) = 12:

$=\left(\dfrac{15}{12}-\dfrac{4}{12} \right )^{\!2}:\dfrac{2}{7}\\\\\\ =\left(\dfrac{15-4}{12} \right )^{\!2}:\dfrac{2}{7}\\\\\\ =\left(\dfrac{11}{12} \right )^{\!2}:\dfrac{2}{7}\\\\\\ =\dfrac{11^2}{12^2}:\dfrac{2}{7}\\\\\\ =\dfrac{121}{144}:\dfrac{2}{7}\\\\\\ =\dfrac{121}{144}\times \dfrac{7}{2}\\\\\\ =\dfrac{121\times 7}{144\times 2}\\\\\\ =\boxed{\begin{array}{c}\dfrac{847}{288} \end{array}}$

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b) $\left(1-\dfrac{1}{3} \right )^{\!\!2}:\left(1-\dfrac{2}{5}\right)^{\!\!2}$

$=\left(\dfrac{3}{3}-\dfrac{1}{3} \right )^{\!\!2}:\left(\dfrac{5}{5}-\dfrac{2}{5}\right)^{\!\!2}\\\\\\ =\left(\dfrac{3-1}{3} \right )^{\!\!2}:\left(\dfrac{5-2}{5}\right)^{\!\!2}\\\\\\ =\left(\dfrac{2}{3} \right )^{\!\!2}:\left(\dfrac{3}{5}\right)^{\!\!2}\\\\\\ =\dfrac{2^2}{3^2}:\dfrac{3^2}{5^2}$

$=\dfrac{4}{9}:\dfrac{9}{25}\\\\\\ =\dfrac{4}{9}\times \dfrac{25}{9}\\\\\\ =\dfrac{4\times 25}{9\times 9}\\\\\\ =\boxed{\begin{array}{c}\dfrac{100}{81} \end{array}}$


Bons estudos! :-)

Answer 2

Oi Carol

5/4 - 1/3 = 15/12 - 4/12 = 11/12

(11/12)²/(2/7) = (121/144)*(7/2) = 847/288
1 - 1/3 = 2/3
1 - 2/5 = 3/5

(2/3)²/(3/5)² = (4/9)/(9/25) = (4/9)*(25/9) = 100/81 

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