Question

find the value of the expression.
\\(\frac{4}{5} \cdot \frac{2}{3} + \frac{3}{4} \cdot \frac{1}{3}\\)

\\(\frac{4}{5} \cdot \frac{2}{3} + \frac{3}{4} \cdot \frac{1}{3} = \square\\)
(type a fraction and use lowest terms.)

Explanation:

Perform multiplications first

$$ \frac{4}{5} \cdot \frac{2}{3} = \frac{4 \cdot 2}{5 \cdot 3} = \frac{8}{15} $$

$$ \frac{3}{4} \cdot \frac{1}{3} = \frac{3 \cdot 1}{4 \cdot 3} = \frac{3}{12} = \frac{1}{4} $$

Find a common denominator and add

$$ \text{LCD}(15, 4) = 60 $$

$$ \frac{8}{15} + \frac{1}{4} = \frac{8 \cdot 4}{60} + \frac{1 \cdot 15}{60} = \frac{32}{60} + \frac{15}{60} = \frac{47}{60} $$

Verify simplification

$$ \gcd(47, 60) = 1 $$

$$ \frac{47}{60} $$

Answer:

\(\frac{4}{5} \cdot \frac{2}{3} + \frac{3}{4} \cdot \frac{1}{3} =\) <blank>\(\frac{47}{60}\)</blank>