Question

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1. evaluate.

\\(\frac{1}{2} + \left(\frac{4}{5} \div \frac{2}{3}\
ight)\\)

Explanation:

Step1: Solve the division inside the parentheses

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. So, $\frac{4}{5} \div \frac{2}{3} = \frac{4}{5} \times \frac{3}{2}$.
Simplifying the multiplication: $\frac{4\times3}{5\times2} = \frac{12}{10} = \frac{6}{5}$.

Step2: Add the result to $\frac{1}{2}$

Now we need to add $\frac{1}{2}$ and $\frac{6}{5}$. First, find a common denominator, which is 10.
Convert $\frac{1}{2}$ to tenths: $\frac{1}{2} = \frac{5}{10}$.
Convert $\frac{6}{5}$ to tenths: $\frac{6}{5} = \frac{12}{10}$.
Now add them: $\frac{5}{10} + \frac{12}{10} = \frac{17}{10}$.

Answer:

$\frac{17}{10}$ (or $1\frac{7}{10}$)