Question

simplify the expression
\\(\frac{3}{5}\left(\frac{10}{9}y + \frac{20}{27}z - \frac{40}{21}\
ight)\\)
\\(\frac{3}{5}\left(\frac{10}{9}y + \frac{20}{27}z - \frac{40}{21}\
ight) = \square\\)

Explanation:

Step1: Distribute the fraction

Multiply each term inside the parentheses by $\frac{3}{5}$.
$\frac{3}{5} \times \frac{10}{9}y + \frac{3}{5} \times \frac{20}{27}z - \frac{3}{5} \times \frac{40}{21}$

Step2: Simplify each term

Calculate the product for each term by canceling common factors.
$\frac{3 \times 10}{5 \times 9}y = \frac{30}{45}y = \frac{2}{3}y$
$\frac{3 \times 20}{5 \times 27}z = \frac{60}{135}z = \frac{4}{9}z$
$\frac{3 \times 40}{5 \times 21} = \frac{120}{105} = \frac{8}{7}$

Answer:

$\frac{2}{3}y + \frac{4}{9}z - \frac{8}{7}$