Question

evaluate the expression.
$-\frac{2}{5} \times \frac{3}{4} + \frac{3}{5} \div -\frac{1}{3}$
write your answer as a fraction or as a whole or mixed nun

Explanation:

Step1: Calculate the multiplication

First, calculate \(-\frac{2}{5} \times \frac{3}{4}\). Multiply the numerators and denominators: \((-2) \times 3 = -6\) and \(5 \times 4 = 20\), so \(-\frac{2}{5} \times \frac{3}{4} = -\frac{6}{20} = -\frac{3}{10}\).

Step2: Calculate the division

Next, calculate \(\frac{3}{5} \div -\frac{1}{3}\). Dividing by a fraction is the same as multiplying by its reciprocal, so \(\frac{3}{5} \times (-3) = -\frac{9}{5}\).

Step3: Add the two results

Now, add the results from Step1 and Step2: \(-\frac{3}{10} + (-\frac{9}{5})\). Convert \(-\frac{9}{5}\) to tenths: \(-\frac{9}{5} = -\frac{18}{10}\). Then, \(-\frac{3}{10} + (-\frac{18}{10}) = -\frac{21}{10}\).

Answer:

\(-\frac{21}{10}\)