1. Tools for Algebra and Geometry
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2. Order of Operations
 When 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
for:
 Parenthesis, Exponents, (Multiplication/Division)
then (Add/Subtract)
PEMDAS
 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.

3. 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.

4. 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.
 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 + 3[5 +(4-1)²]
2 +3[5 + (3)²]
2 + 3[5 + 9]
2 + 3[14]
2 + 42
44

5. Summary of Basic Steps
 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.
It is very important to understand that it does make a
difference if the order is not performed correctly!!!!!!!!!
70 – 2(5 + 3)
70 – 2(8)
68(8)
544 incorrect
(subtraction was done before multiplication)
70 – 2(5 + 3)
70 – 2(8)
70 – 16
54 correct

6. Order of Operations is not an isolated skill.
 This skill applies to almost every topic in Math.
 Remember that “PEMDAS” is used with evaluating formulas, solving
equations, evaluating algebraic expressions, simplifying monomials &
polynomials, etc…
Get your pencil and calculator ready and try these problems.
1) 20 + 3(5 – 1) =
2) 3 + 2²(1 + 8) =
3) (5 · 4)² =
4) 2(3 + 5) – 9 =
5) 2[13 – (1 + 6)] =
6) 48 / 3 + 5 =
7) 3(6 + 4)(5 – 3) =
8) 100 – 4(7 – 4)³ =
9) 1² + 2³ + 3³ =
10) (24 – 6)/2 =

7. Here is an example of an algebraic expression.
4 is the coefficient.
X is the variable.
7 is the constant.
Algebraic Expression
4x + 7
4 = coefficient
x = variable
7 = constant

8. 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

9. Evaluate each expression for
t = 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

10. The End
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