The Kingdom of Infinite Numbers by Bryan Bunch

Author:Bryan Bunch
Language: eng
Format: epub
Published: 2011-06-05T16:00:00+00:00

PERSONALITY Beginning algebra students often have difficulty in dealing with problems that include -1 hidden in one way or another. It helps if they first learn to abandon the operation of subtraction completely, since it only causes confusion. Algebra, in theory at least, replaces subtraction entirely by the definition that subtraction is addition of the opposite, so an expression such as x - 2, while often read as “ex minus two,” is considered to be an abbreviation for x + (-2) and is handled by the rules of addition. Since multiplication by -1 is the same operator as taking the opposite, an apparent subtraction problem such as 3x - 5x is taken to be a shorthand way of writing 3x + (-1)5x. In such a simple example there is usually no confusion, but when a problem becomes somewhat more complicated, such as “subtract 3x - 5y from 2x - y,” rather more difficulty is encountered. This can be greatly eased if a person learns to think “subtract 3x - 5y from 2x - y; that means add (-1) (3x - 5y), or -3x + 5y, to 2x - y, so the answer is -x + 4y.” A related problem occurs when an expression with several terms appears within parentheses and preceded by the subtraction sign, for example, 7x - (2x + 3). A surprisingly high percentage of algebra students interpret this to mean 7x - 2x + 3 instead of the correct 7x - 2x - 3. They do better if they recognize that the expression 7x - (2x + 3) is shorthand for 7x + (-1)(2x + 3).

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