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Word Gems 

exploring self-realization, sacred personhood, and full humanity

Editor’s collection of notes:

Algebra

What is an expression? 

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mathematical "phrase" that stands for a single number: 3x + 1; never true or false but just has a numerical value
 

a representation of a number, denoted but not evaluated

say "the sum of" or "the product of"; x + 3 is "the sum of an unknown number and 3"

expressions cannot be cleared of fractions, while equations can

not a sentence; does not have a verb: 2x - 8

formed by combining numbers and variables using various operations such as addition, subtraction, etc.

never true or false but just has a numerical value; an incomplete algebraic thought

consists of at least one operand and can have one or more operators

combines numbers, operators, grouping symbols and/or free variables and bound variables

Why does a + b/c = a/c + b/c? When an expression is divided by a number, ea term in that expression is divided by that number. This makes sense because "a + b" is a symbol of a number, of a quantity, meaning that "a and b" do not stand alone but represent a quantity, and therefore must be acted upon as a unit. 

can be modeled with blocks: 2x + 6/2 = 2 groups of x (large block) + 3 (small blocks)

can also be rep as a mult problem: 1/2 (2x + 6)

rational expression: a/b where a or b is a polynomial

We use algebra to solve for an unknown, that is, when we have incomplete information and we're trying to find out the missing parts; therefore, in order to address, to speak about, the problem, we arrange what we know and don't know as single-item "words" (terms) and "phrases" (expressions) and "sentences" (statements) with which we might structure the issue, or begin to formulate the data into a complete thought of problem solving.