Question

Evaluate the expression shown below and write your answer as a fraction or mixed number in simplest form.
start fraction, 7, divided by, 2, end fraction, divided by, minus, start fraction, 2, divided by, 3, end fraction, dot, start fraction, 3, divided by, 5, end fraction
2
7
​
÷−
3
2
​
⋅
5
3
​

Answer 1

To evaluate the expression

\[
\frac{7}{2} \div -\frac{2}{3} \cdot \frac{3}{5},
\]

first, we need to simplify the multiplication and division.

1. Rewrite the division as multiplication by the reciprocal:

\[
\frac{7}{2} \div -\frac{2}{3} = \frac{7}{2} \cdot -\frac{3}{2}.
\]

2. Now compute \(-\frac{2}{3} \cdot \frac{3}{5}\):

\[
-\frac{2}{3} \cdot \frac{3}{5} = -\frac{2 \cdot 3}{3 \cdot 5} = -\frac{6}{15}.
\]

3. Simplify \(-\frac{6}{15}\):

We can simplify \(-\frac{6}{15}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 3:

\[
-\frac{6 \div 3}{15 \div 3} = -\frac{2}{5}.
\]

4. Now, substitute back into the original expression:

\[
\frac{7}{2} \cdot -\frac{2}{5} = -\frac{7 \cdot 2}{2 \cdot 5} = -\frac{14}{10}.
\]

5. Simplify \(-\frac{14}{10}\):

The greatest common divisor of 14 and 10 is 2:

\[
-\frac{14 \div 2}{10 \div 2} = -\frac{7}{5}.
\]

Thus, the final answer is

\[
\boxed{-\frac{7}{5}}.
\]