Evaluate {2.7 − (0.7 − 3)} ÷ (−1/5).

Step-by-step solution

1. 1

   Work the innermost bracket first. Nested grouping symbols are always resolved from the inside out:

   $0.7-3=-2.3$

2. 2

   Substitute and handle the double negative. Subtracting a negative number is the same as adding its positive:

   $2.7-(-2.3)=2.7+2.3=5$

   This sign flip is the step most often skipped.

3. 3

   Rewrite the whole expression.

   $5\div\left(-\frac15\right)$

4. 4

   Divide by the fraction. Dividing by $-\tfrac15$ means multiplying by its reciprocal $-5$:

   $5\times(-5)=-25$

   $\boxed{-25}$

5. 5

   Check the sign and magnitude. A positive divided by a negative is negative ✓, and dividing by a number of size $\tfrac15$ multiplies the magnitude by $5$, so $5\to 25$ ✓. A useful reality check: dividing by a number smaller than 1 always makes the result larger in magnitude, which rules out common wrong answers such as $-1$.