Question

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

Explanation:

Step1: Calculate the multiplication part

First, calculate \(-\frac{1}{4} \times \frac{3}{4}\). When multiplying fractions, we multiply the numerators and the denominators: \(-\frac{1}{4} \times \frac{3}{4}=-\frac{1\times3}{4\times4}=-\frac{3}{16}\)

Step2: Calculate the division part

Next, calculate \(-\frac{1}{2} \div -\frac{1}{3}\). Dividing by a fraction is the same as multiplying by its reciprocal, so \(-\frac{1}{2} \div -\frac{1}{3}=-\frac{1}{2} \times -\frac{3}{1}=\frac{1\times3}{2\times1}=\frac{3}{2}\)

Step3: Substitute the results into the original expression

The original expression is \(-\frac{3}{16}-\frac{3}{2}\). To subtract these fractions, we need a common denominator. The common denominator of 16 and 2 is 16. So we rewrite \(\frac{3}{2}\) as \(\frac{24}{16}\) (since \(\frac{3}{2}=\frac{3\times8}{2\times8}=\frac{24}{16}\)). Now we have \(-\frac{3}{16}-\frac{24}{16}\). When subtracting, we subtract the numerators: \(-\frac{3 + 24}{16}=-\frac{27}{16}\) (which can also be written as \(-1\frac{11}{16}\))

Answer:

\(-\frac{27}{16}\) (or \(-1\frac{11}{16}\))