Minus vs. Negative
Why is it that sometimes we hear the symbol (-) referred to as “minus” and other times as “negative”? For example:
Is read “Five Minus Three Equals Two” but
Reads, “Three Minus Five Equals Negative Two”
In the second equation we use the word “Minus” when referring to the first symbol but “negative” when referring to the second.
Why?
As it turns out, negative symbols can be viewed as either verbs or adjectives depending on context.
When we first learn subtraction, the sign is treated as a verb that instructs us as to what operation or ‘action’ we need to perform.
However, when talking about negative and positive numbers, we use the subtraction symbol as an adjective to describe the number that proceeds it. Like this:
Even your TI-83 graphing calculator needs a little help differentiating between the two. Take a look:
See it? Bottom right. Right next to ENTER. There’s an actual button for when we need to use to subtraction signs as adjectives instead of verbs. Suppose you want to calculate the following:
Using a regular subtraction sign (the blue button) will cause an error because the calculator doesn’t know what to subtract the 7 from. It’s not reading “negative seven” it’s reading “subtract seven.” You can work around this by giving it something to subtract from.
Now the calculator knows that the seven is to be subtracted from zero and then it needs to add 11. The only way around this is to use the (-) button provided so that the calculator knows the leading sign is being used to describe the nature of the seven. (i.e. it is a ‘negative’ seven).
Doing too much indeed. Why can’t the calculator just infer based on context like we do? Some calculators can, but that doesn’t mean we can ignore these properties. In fact, being able to work with negative signs as both verbs and adjectives is critical for understanding Coordinate Geometry. For example, negative and positive signs are used as adjectives to describe the location of points on a number line. We also subtraction as a verb when we’re calculating a change in distance. We can even put these concepts together to explain the elusive “two negatives make a positive” rule. You can read more about it in my next article “Why Do Two Negatives Make A Positive”
