Chris says that $6-(-4)=2$ since 6 minus 4 is 2. Is he correct? Explain.
Chris is incorrect. His reasoning that subtracting a negative number is the same as simply subtracting the positive version of that number is flawed. In arithmetic, subtracting a negative number is equivalent to adding its positive counterpart. The mathematical rule is expressed as \[a - (-b) = a + b.\] Applying this to Chris's expression, \(6 - (-4)\), we replace the subtraction of \(-4\) with the addition of \(4\): \[6 - (-4) = 6 + 4.\] Calculating this sum, we find \(6 + 4 = 10\). Therefore, the correct evaluation of the expression is \(10\), not \(2\).
Think of subtracting a negative number like removing a debt. If you owe someone money (a negative balance) and that debt is taken away (subtracted), your overall financial position improves just as if you had received an equivalent amount of cash. If you start with 6 dollars and 4 dollars of debt are taken away, you are left with \(6 - (-4) = 6 + 4 = 10\) dollars. This concept of double negatives appears frequently in accounting, physics, and even language, helping us understand how opposing actions can result in positive gains.