Week 1
DQ 1
An expression is a description of a mathematical object (some class or set). For example,
9 would be an expression describing 9 sets.
An equation is an assertion (whether right or wrong) that one expression refers to the
same class as another. Therefore, 2+2=4 is a claim that, if we work out what class the
expression 2+2 is, it will be the same as the class 4. This equation is true, of course.
If an equation includes variables, you can have an equation that is sometimes right or
sometimes wrong. For example, the equation x+2=5 is true if x happens to refer to the
class 3, and is false otherwise. On the other hand, the equation x+2 = x+2 is true always.
Such equations are called identities. The whole point of solving equations is to find those
values of the variable for which the equation is true.
An equation is the assertion that two expressions are equal.
Examples of expressions:
x + 1
5x + 9
Example of equation:
x + 1 = 5x + 9
An expression makes no assertion about truth, so you can't make inferences from it, so
you can't solve it.
An equation with variables CAN be solved, by finding the variables for which it is true.
Example of mathematical phrase:
Three times the height plus one
Example of a mathematical sentence:
Three times the height plus one equals five times the height plus nine.
Essentially, an expression needs to be
equated
to something else in order to form an
equation. An equation is a statement regarding the equality between two expressions,
whereas an expression is just a set.
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You cannot solve an expression, because it is not equal to anything, thereby you can only
SIMPLIFY an expression.
As for an equation, you CAN solve it, because you have set it something equal to another
expression.
Here is an expression for classmates to translate:
Three times x plus ninety
DQ 2
Yes, you must follow PEMDAS (Parenthesis, exponents, multiply and divide, add and
subtract) and do them in that order. First do anything in parenthesis, then do any
exponents, then do any multiplication/division from left to right (Multiplication doesn't
have to be before division), then add/subtract the same rule as multiply/divide.
The order must be followed rather than just solving for something left to right, because
the answer will be different if it is not followed. The order of operations was established
by the mathematical community because there needs to be a set of “rules” for the
precedence of calculations. That is why they came up with PEMDAS, so there is no
confusion between calculations. PEMDAS specifies this certain order that people do
when solving for math so that everyone comes up with the same answer. For example,
say we have:
. If we solved this from left
to right, we would get:
9 + 4 x 9 = 13 x 9 = 117. This is INCORRECT.
If we follow the order of operations, we get:
9 + 36 = 45, which is the correct answer.
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 Winter '10
 NA
 Math, Sets, Elementary algebra, Negative and nonnegative numbers, Plus and minus signs

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