Algebra Basics

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Algebra Basics
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Variables and Expressions

• Variable a symbol used to represent a quantity
  that can change.
• Coefficient the number that is multiplied by
  the variable in an algebraic expression.
• Numerical expression an expression that
  contains only numbers and operations.
• Algebraic expression an expression that
  contains numbers, operations and at least one
  variable.
• Constant a value that does not change.
• Evaluate To find the value of a numerical or
  algebraic expression.
• Simplify perform all possible operations
  including combining like terms.
• Order of operations a rule for evaluating
  expressions from left to right.

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Order of OperationsWhen a numerical expression
involves 2 or more operations, there is a
specific order in which these operations must be
performed.In earlier grades you learned to solve
numerical expressions using order of operations
or as most of us say PEMDAS which stands
forParenthesis, Exponents, (Multiplication/Divisi
on) then (Add/Subtract)PEMDASPlease Excuse
(My Dear) (Aunt Sally)
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Please Excuse (My Dear)(Aunt Sally)

• The reason (multiplication division) and (add
  subtract) are grouped is when those operations
  are next to each other you do the math from left
  to right. You do not necessarily do addition
  first if it is written next to subtraction.

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equation is a mathematical statement that two
expressions are equal ().formula is an
equation that shows a mathematical relationship
between 2 or more quantities.reflexive property
of equality for all real numbers a, a
a.symmetric property of equality for all real
numbers a and b, if a b, then b a.transitive
property of equality for all real numbers a, b,
and c, if a b and b c, then a c
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Numerical expression

• 8 6 2
• Subtraction is first
• Remember when those operations, (multiplication
  division) and (add subtract) are grouped next
  to each other you do the math from left to right.

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When there are 2 or more operations, and we use
grouping symbols such as parenthesis or brackets,
you perform the inner most grouping symbol first.

• 2 35 (4-1)²
• 2 35 (3)²
• 2 35 9
• 2 314
• 2 42
• 44

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Summary of Basic Steps

• Copy the problem.
• Simplify any grouping symbols (such as
  parenthesis) first, starting with the inner most
  group.
• Simplify any powers (exponents).
• Perform the multiplication division in order
  from left to right.
• Do the addition subtraction last, from left to
  right.
• Remember, if operations are written next to each
  other, work from left to right.

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It is very important to understand that it does
make a difference if the order is not performed
correctly!!!!!!!!!
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Order of Operations is not an isolated skill.

• This skill applies to almost every topic in Math.
  Remember that Aunt Sally is used with
  evaluating formulas, solving equations,
  evaluating algebraic expressions, simplifying
  monomials polynomials, etc

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Order of OperationsGet your pencil and
calculator ready and try these problems.

• 20 3(5 1)
• 3 2²(1 8)
• (5 4)²
• 4) 2(3 5) 9
• 5) 213 (1 6)

• 48 / 3 5
• 7) 3(6 4)(5 3)
• 8) 100 4(7 4)³
• 9) 1² 2³ 3³
• 10) (24 6)/2

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Here is an example of an algebraic expression. 4
is the coefficient.X is the variable.7 is the
constant.
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Evaluating Algebraic Expressions

• To evaluate an algebraic expression, substitute a
  given number for the variable, and find the value
  of the resulting numerical expression.
• X 5 for x 12
• (12) 5 7
• 2y 1 for y 4
• 2(4) 1 9
• 6(n 2) 4 for n 5, 6, 7
• 38, 44, 50

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Evaluate each expression fort 0, x 1.5, y
6, z 23

• 1) y 5
• 2) 3z 3y
• 3) z 2x
• 4) xy
• 5) 4(y x)

• 6) 3(4 y)
• 7) 3(6 t) 1
• 8) 2(y 6) 3
• 9) y(4 t) - 5
• 10) x y z

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Properties of Real Numbers