Question

evaluate the expression.
\\(\frac{3}{4} + \frac{2}{5} div \frac{2}{3} \times \frac{1}{2}\\)
write your answer as a fraction

Explanation:

Step1: Perform division (÷) first

To divide fractions, we multiply by the reciprocal. So, $\frac{2}{5} \div \frac{2}{3} = \frac{2}{5} \times \frac{3}{2}$.
Simplify: The 2s cancel out, so we get $\frac{3}{5}$.

Step2: Perform multiplication (×) next

Now, multiply the result from Step 1 by $\frac{1}{2}$: $\frac{3}{5} \times \frac{1}{2} = \frac{3 \times 1}{5 \times 2} = \frac{3}{10}$.

Step3: Perform addition (+) last

Add $\frac{3}{4}$ and $\frac{3}{10}$. First, find a common denominator, which is 20.
Convert $\frac{3}{4}$ to tenths: $\frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}$.
Convert $\frac{3}{10}$ to twentieths: $\frac{3}{10} = \frac{3 \times 2}{10 \times 2} = \frac{6}{20}$.
Now add: $\frac{15}{20} + \frac{6}{20} = \frac{15 + 6}{20} = \frac{21}{20}$.

Answer:

$\frac{21}{20}$