Evaluate (4.135 + 12.896) − (2 − 0.1415).

Step-by-step solution

1. 1

   Evaluate each bracket separately before combining. Brackets outrank the middle minus sign, so neither bracket may be broken open until it has been reduced to a single number. In particular the second bracket must be worked out before subtracting.

2. 2

   First bracket: add. Both numbers have $3$ decimal places, so no padding is needed:

   $4.135+12.896=17.031$

3. 3

   Second bracket: subtract. Write $2$ as $2.0000$ to match the four decimal places of $0.1415$:

   $2.0000-0.1415=1.8585$

4. 4

   Subtract the two results. Pad $17.031$ to $17.0310$:

   $17.0310-1.8585=15.1725$

   $\boxed{15.1725}$

5. 5

   Check the size and add back. Because the second bracket is a little under $2$, the answer should be a little over $17.031-2=15.031$ — and $15.1725$ is, by exactly $0.1415$. Adding back: $15.1725+1.8585=17.031$ ✓. Dropping the second bracket's minus sign would instead give $17.031-2-0.1415=14.8895$, a common wrong answer.