4/7 × -14/20 - -1 /3/2

1. Compute the product:

\frac{4}{7} \times -\frac{14}{20} = \frac{4 \times -14}{7 \times 20} = \frac{-56}{140} = -\frac{2}{5}

2. Simplify the division in the second term:

3 \div 2 = \frac{3}{2}

So,

-\frac{1}{\frac{3}{2}} = -\frac{1 \times 2}{3} = -\frac{2}{3}

3. Now substitute the simplified terms into the original expression:

-\frac{2}{5} - -\frac{2}{3} = -\frac{2}{5} + \frac{2}{3}

4. Find a common denominator for the fractions:

The least common multiple of 5 and 3 is 15.

Rewrite the fractions:

-\frac{2}{5} = -\frac{2 \times 3}{5 \times 3} = -\frac{6}{15}
\frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15}

5. Combine the fractions:

-\frac{6}{15} + \frac{10}{15} = \frac{-6 + 10}{15} = \frac{4}{15}

6. Therefore, the final simplified answer is:

\frac{4}{15}