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Study Notes 007:
By William E. Steinman:
Algebra 2:
Symbols and
Operators:
Equal sign (=)
Indicates logical
or mathematical equality.
Left caret (<)
The symbol is
used to indicate Ais less than.@
Right caret
(>)
The symbol is
used to indicate Ais greater than.@
Percent (%).
Indicates
percentage.
Plus sign (+)
Indicates
addition or a positive quantity.
Minus sign (‑)
Indicates
subtraction or a negative quantity.
Slash (/)
Indicates
division.
Times sign (x) or
(.) a raised dot
Vertical bars
(|10|)
Indicates the
absolute value of a given number.
An equality is a statement that two
expressions have the same value.
That means, the
expressions are equal to each other.
5x = 10 is an
equality.
We defined an
equation as an equality wherein the unknown quantity or quantities may have only
one value or values.
We define an
identity to be an equality in which a letter or letters may have any value.
The statement 4y
+ 5y = 9y is an identity since y may have any value.
An equation is a
conditional equality because only one value of the unknown will satisfy it.
An identity is an
unconditional equality because the unknown may have any value.
We defined the
root of an equation as the number which when substituted for the unknown,
will make the equation equal.
So the root is
just the solution to the equation.
In the statement
5z + 4 = 19 the root is 3.
2x + 78 = 22, is
an equation.
5z - 4 = 21, is
an equation
2a + 3a = 5a, is
an identity.
Inverse operations are two operations such
that if one is involved with the unknown in an equation, the other is used to solve
the equation.
Addition and subtraction are inverse
operations.
If addition is
involved in the unknown of an equation, we can use subtraction to solve for the
unknown.
Multiplication and division are inverse
operations.
We can use
multiplication to check division and vice versa.
We do not change
the equality of an equation when we perform the same operation on both sides
using the same number except in division by zero.
The Addition Rule of Equality is if equal
numbers are added to both sides of an equation the equality does not change.
The Subtraction Rule of Equality is if equal
numbers are added to both sides of an equation the equality does not change.
The Multiplication Rule of Equality is if both
sides of an equation are multiplied by the same number, the equality does not
change.
The Division Rule of Equality is if both sides
of an equation are divided by the same number, the value does not change.
Formally, a
formula is a statement or equation of a fact, rule, or other logical
relationship.
In other words, a
formula is just a standardized equation for a particular kind of situation.
Signed numbers
are positive or negative numbers used to opposite quantities.
For example, +90
is the opposite of -90.
If I gained 90
lbs over the holidays (+ 90 lbs), I must needs lose 90 lbs (- 90 lbs) if I want
to wear my old suit.
The absolute
value of a signed number is the number with the sign removed.
17 is the
absolute value of + 17 and of – 17.