$$ \left(\frac{5}{6}-\frac{2}{5}\right) \cdot \frac{3}{8} $$ Write your answer in simplest form.

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UpStudy AI · Accepted Answer

1. Compute the difference inside the parentheses:
   $$
   \frac{5}{6} - \frac{2}{5}
   $$
   To subtract these fractions, find a common denominator. The least common denominator of 6 and 5 is 30.
   
   Rewrite each fraction with denominator 30:
   $$
   \frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30}, \quad \frac{2}{5} = \frac{2 \times 6}{5 \times 6} = \frac{12}{30}
   $$
   
   Now, subtract:
   $$
   \frac{25}{30} - \frac{12}{30} = \frac{25 - 12}{30} = \frac{13}{30}
   $$

2. Multiply the result by $$ \frac{3}{8} $$:
   $$
   \frac{13}{30} \times \frac{3}{8} = \frac{13 \times 3}{30 \times 8} = \frac{39}{240}
   $$

3. Simplify the fraction $$ \frac{39}{240} $$:
   Divide the numerator and the denominator by their greatest common divisor, which is 3:
   $$
   \frac{39 \div 3}{240 \div 3} = \frac{13}{80}
   $$

The answer in simplest form is:
$$
\boxed{\frac{13}{80}}
$$
The answer in simplest form is $$ \frac{13}{80} $$.

Write your answer in simplest form.

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