Transcript numerical expression

1.2- Algebraic Expressions
and Models
It is time to start remembering 
Numerical Expressions
• A numerical expression consists of numbers,
operations, and grouping symbols.
• For example, an exponent is a numerical
expression that represents repeated factors in
multiplication
2  22222
5
Base
Exponent
Power
Algebraic Expressions
• A variable is a letter that represents one or more numbers.
• When a number replaces a variable it is called the value of
the variable.
• An expression with variables is called a
____________________________.
• When variables are replaced by numbers, you are
evaluating the expression and finding the value.
Write the expression 
Substitute values of variables 
S________
Order of Operations
(What we use when evaluating the expressions)
•
•
•
•
•
•
P
E
M
D
A
S
*Multiply/Divide
and Add/Subtract
from left to right!
Please excuse my dear Aunt Sally?
Simplifying
Algebraic Expressions
3x  5x  4 x  10
2
Terms
Coefficient
Like Terms
Constant Terms
2
Models
• An expression that represents a real-life
situation is a mathematical model.
• When you create the expression, you are
modeling the real-life situation.
Examples
• Evaluate the expression using exponents.
3
4
( 3)
4
(7a  7a )  (5z  5z)
Examples
• Evaluate the expression.
( 2)
5
1  (3  2)
2
14  (7  5)  1
Examples
• Evaluate the expression for the given value of x.
3x  0.5( x  1); x  3
Examples
• Evaluate the expression for the given value of x.
(25x  3)  x; x  3
Examples
• Evaluate the expressions for the given values of x and y.
(2 y)  5x; x  2, y  1
3
Examples
• Write an expression for the area of the right
triangle, then evaluate it for x=6.
x
4x  1
Examples
• You want to buy either a CD or a cassette as a gift for
each or 10 people. CD’s cost $13 each and cassettes
cost $8 each. Write an expression for the total amount
you must spend. Then evaluate the expression when 4
people get CDs.
Homework
• Worksheet 1.2B (Left Column 1-28)
Answers