Question

Evaluate the expression. Use estimation to check your answer. $$ -13.87-(-13.87)+5.8 $$

Short answer

The solution to the equation is 5.8.

Step-by-step solution

Recognize the Double Negative

In the expression, -13.87 is subtracted by -13.87. Since subtraction is the addition of the negative value, this can also be interpreted as -13.87 plus 13.87.

Simplify the Expression

Now, start by simplifying -13.87 + 13.87. These cancel each other out since they are the same number but of opposing signs. Therefore, -13.87 + 13.87 equals 0. Next, we add this result to the remaining number 5.8. So, 0 + 5.8 equals 5.8.

Estimate to check the answer

An estimation of the equation can be achieved by rounding up the decimals to whole numbers: -14 - (-14) + 6. Simplifying this, -14 + 14 equals 0 and adding 6 gives 6. This estimated result is close to the calculated result which is 5.8. Thus, the answer is likely correct.