Evaluate [(2/3 − 1/2) ÷ 1/30] × (−2 × 1/10).

Step-by-step solution

1. 1

   Deal with the innermost bracket first. The denominators $3$ and $2$ have LCM $6$:

   $\frac23-\frac12=\frac46-\frac36=\frac16$

2. 2

   Divide by 1/30. Dividing by a fraction means multiplying by its reciprocal, and dividing by $\tfrac{1}{30}$ therefore multiplies by 30:

   $\frac16\div\frac{1}{30}=\frac16\times 30=5$

   So the whole square bracket equals $5$.

3. 3

   Evaluate the second bracket.

   $-2\times\frac{1}{10}=-\frac{2}{10}=-\frac15$

4. 4

   Multiply the two results.

   $5\times\left(-\frac15\right)=-1$

   $\boxed{-1}$

5. 5

   Check the sign and the structure. Exactly one negative factor appears, so the answer is negative ✓. Note the neat design: the first bracket produces $5$ and the second produces $\tfrac15$ with a minus, so they are exact reciprocals up to sign — recognising that would have given the answer $-1$ in one line.