Simplify 100 − 15 × 2 + (−204) ÷ 3.

Step-by-step solution

1. 1

   Identify the operations and rank them. The expression mixes subtraction, multiplication, addition and division. Multiplication and division outrank addition and subtraction, so those two must be evaluated before anything is combined — working strictly left to right would give the wrong answer here.

2. 2

   Do the multiplication.

   $15\times 2=30$

3. 3

   Do the division, keeping the sign. A negative divided by a positive is negative:

   $(-204)\div 3=-68$

   Check: $3\times 68=204$, so the magnitude is right.

4. 4

   Rewrite with only additions and subtractions.

   $100-30+(-68)$

   Adding a negative is the same as subtracting, so this is $100-30-68$.

5. 5

   Work left to right.

   $100-30=70,\qquad 70-68=2$

   $\boxed{2}$

6. 6

   Check by regrouping. The expression equals $100-(30+68)=100-98=2$ ✓. A common wrong answer is $100-30+68=138$, which comes from dropping the minus sign on the quotient.