Question

simplify the expression.
\\(\frac{5}{9}\left(\frac{18}{15}y + \frac{36}{45}z - \frac{72}{35}\
ight)\\)
\\(\frac{5}{9}\left(\frac{18}{15}y + \frac{36}{45}z - \frac{72}{35}\
ight) = \square\\)

Explanation:

Step1: Distribute the outer fraction

Multiply each term inside the parentheses by $\frac{5}{9}$.
$$\frac{5}{9} \times \frac{18}{15}y + \frac{5}{9} \times \frac{36}{45}z - \frac{5}{9} \times \frac{72}{35}$$

Step2: Simplify each term

Calculate the product of fractions for each variable/constant.

• For the $y$-term: $\frac{5 \times 18}{9 \times 15}y = \frac{90}{135}y = \frac{2}{3}y$
• For the $z$-term: $\frac{5 \times 36}{9 \times 45}z = \frac{180}{405}z = \frac{4}{9}z$
• For the constant term: $\frac{5 \times 72}{9 \times 35} = \frac{360}{315} = \frac{8}{7}$, so the term is $-\frac{8}{7}$

Answer:

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