Simplify (−1000) ÷ 25 × (−2).

Step-by-step solution

1. 1

   Recognise the trap: these two operations have equal rank. Division and multiplication sit at the same level of precedence, so the acronym letters (BODMAS/PEMDAS) do not mean "divide before multiply". They are evaluated strictly left to right. Doing the multiplication first would give $25\times(-2)=-50$ and then $-1000\div(-50)=20$ — a different, wrong answer.

2. 2

   Perform the division first, because it is leftmost.

   $(-1000)\div 25=-40$

   A negative divided by a positive is negative, and $25\times 40=1000$.

3. 3

   Now multiply by −2.

   $-40\times(-2)=80$

   A negative times a negative is positive.

4. 4

   State the result.

   $\boxed{80}$

5. 5

   Verify by writing it as one fraction. $(-1000)\div 25\times(-2)=\dfrac{-1000\times(-2)}{25}=\dfrac{2000}{25}=80$ ✓. Writing division as a fraction and collecting all multipliers in the numerator is a reliable way to avoid the left-to-right slip.