Negative Inputs

Substituting a negative number works the same way, and here the parentheses earn their place. Evaluate 6 - 3n when n is -2. Write -2 in place of n, inside parentheses: v = 6 - 3 × (-2). Without them the line would read 6 - 3 · -2, with two signs crashed together and no telling which belongs to the number.

Then use the sign rules from Section 1. A positive times a negative is negative, so 3 times -2 is -6. The line becomes 6 - (-6), and taking away a negative is adding: v = 6 + 6, so v = 12.

The usual slip is to drop the minus sign of the input and work out 6 - 3 · 2, which gives 0. Keeping the substituted number in parentheses, sign and all, is what stops that from happening.