Question

Explain why the sum of −8 and 2 is negative, but the sum of 8 and −2 is positive.

Short answer

The sign depends on the greater number sign.

Step-by-step solution

Step 1. Explain the first result -8+2=-6.

Consider the given information.

• Since the value of the sum of a positive number and a negative number is the difference of the number.
• The sign of the sum is the sign of the bigger number.

As 8 is greater than 2. So, in the sum of -8 and 2, the sign will be negative.

$\begin{array}{rcl}\left(-8\right)+2& =& -8+2\\ & =& -6\end{array}$

Step 2. Explain the second result.

Refer to the concept explained in step 1.

As 8 is greater than 2. So, sign in the sum of 8 and 2, the sign will be postive.

$\begin{array}{rcl}8+\left(-2\right)& =& 8-2\\ & =& 6\end{array}$