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An introduction to common 'grammatical' errors in algebra

Mathematics is a language, and like any language, it is possible to have bad grammar. One might be able to intelligibly communicate something in nonstandard English, but it still might be bad grammar, and you might still get a bad grade on an English paper for not using correct grammar. The same is true in a mathematics class. The mathematics teacher might know what you intended to communicate, but might still mark the answer you've provided wrong because you did not use proper mathematical grammar. It might seem irritating to have to learn this grammar for the student of mathematics, but, for lack of a better way of saying it, it's the rules. So let's get down to learning some basic mathematical grammar.

First, let's talk about unnecessary coefficients. 1x means the same thing as x. But technically, 1x is bad grammar. So instead of writing 1x, you just write x. This goes for more than just a simple variable with an unnecessary coefficient. If we have an equation such as 6 + ab, for example, we write it that way instead of writing the unnecessary and cumbersome (and grammatically incorrect (6 + ab)^1. Likewise, you would write x^2 + y rather than 1(x^2 + y).

Keep in mind that the minus sign is not equivalent to the negative sign. The variable x encapsulates the negative sign when it represents a negative number. Therefore, if x equals -17, -x does not equal -17. It equals -(-17).

When you have a fraction whose denominator is zero, such as 5/0, you write "5/0 is undefined." That's it. Don't try to write anything else. It will be incorrect grammar (and possibly a straightforwardly incorrect expression) and you will get yourself into trouble. Keep in mind that 5/0 does not equal 0. It is simply "undefined." It is a poorly formed expression that makes no sense.