Questions: Evaluate the expression. [ left(3 frac34+-2 frac34 times 2right) div-5 ] Write your answer as a fraction

Solution Steps

To solve the given expression, follow these steps:

1. Convert the mixed numbers to improper fractions.
2. Perform the multiplication operation.
3. Perform the addition operation.
4. Perform the division operation.
5. Simplify the resulting fraction if possible.

Convert \(3 \frac{3}{4}\) and \(-2 \frac{3}{4}\) to improper fractions: \[ 3 \frac{3}{4} = \frac{3 \times 4 + 3}{4} = \frac{15}{4} \] \[ -2 \frac{3}{4} = \frac{-2 \times 4 - 3}{4} = \frac{-11}{4} \]

Multiply \(\frac{-11}{4}\) by \(2\): \[ \frac{-11}{4} \times 2 = \frac{-11 \times 2}{4} = \frac{-22}{4} = \frac{-11}{2} \]

Add \(\frac{15}{4}\) and \(\frac{-11}{2}\): \[ \frac{15}{4} + \frac{-11}{2} = \frac{15}{4} + \frac{-22}{4} = \frac{15 - 22}{4} = \frac{-7}{4} \]

Divide \(\frac{-7}{4}\) by \(-5\): \[ \frac{-7}{4} \div -5 = \frac{-7}{4} \times \frac{1}{-5} = \frac{-7 \times 1}{4 \times -5} = \frac{7}{20} \]

Final Answer