Math 6A ( Periods 2 & 5)

Algebraic Expressions 3.1 

An algebraic expression is an expression that may contain numbers, operations and one or more symbols (called variables) A variable is a symbol used to represent one or more numbers. The numbers are called the values of the variable.


Parts of an algebraic expression are called TERMS
5p + 4


When we write a product that involves a variable, we usually omit the multiplication symbol (whether that be written as x or as ∙ or even with parentheses). Thus, 3 x n is written as 3n
and 2 x a x b is written as 2ab

In numerical expressions for products a multiplication symbol must be used to avoid confusion.

9 x 7 may be written as 9 ∙ 7 or even 9(7)

5p + 4
Let's look at the term 5p
The number that modifies the variable is called a coefficient  Our book defines it as the numerical factor of a term that contains a variable
now let's look at the term +4 It is a term without a variable and it is called a constant.
We will
a)identify terms,
b)name the coefficients ,
c) name the constants

5x + 13                     a)5x , +13                b) 5              c) 13
2x²  + y + 3              a) 2x²  ,y ,  3            b) 2, 1           c) 3
4x²  -3y + z - 5      a) 4x²  ,-3y, z,  - 5     b) 4, -3, 1        c) -5


Using Exponents
d∙d∙d∙d = d⁴ 
1.5h∙h∙h = 1.5h³

h∙h∙h∙o∙o∙o= h³o³ = (ho)³ = hohoho!

When a mathematical sentence uses an equal sign, it is called an equation. An equation tells us that two expressions name the same number. The expression to the left of the equals sign is called the left side of the equation and the expression to the right of the equals sign is called the right side.
expression = expression

When a number is substituted for a variable in the variable expression and the indicated operation is carried out, we say that the variable expression has been evaluated. For example, if n has the value 6 in the variable expression 3n, then 3n has the value 3 (6), or 18
Example: Evaluate the expression 6a when the variable has the following values:
6a; 2, 4, 6, 8
You would substitute in each value for the variable a
6(2) = 12
6(4) = 24
6(6) = 36
6(8) = 48

148 ÷ 4 =
148/4
37


if m = 3 and n = 18
n ÷ m
substitute in
n/m or (18)/(3) = 6


If y = 18 and x = 8
4y ÷ 3x immediately set this up as
4y/3x

Now substitute in your values
4(18) / 3(8)
72/24 = 3

Evaluate k + 10 when k = 25
(25) + 10 = 35
When k = -25
(-25) + 10 = -15
Evaluate 4n when n = -12
4(-12) = -48
Now  a÷b   when a= 16 and b = 2/3
Yikes... think
16 ÷ 2/3  WOW-- instead of dividing we think multiply by its reciprocal.
The reciprocal of 2/3 is 3/2
so 16 ( 3/2) = 24
What happens with
3x-14 if x = 5
3(5) - 14 = 1
You must use the ORDER OF OPERATIONS
z² + 8.5 when z = 2
(2)² + 8.5
4 + 8.5
12.5
What about 30 - 24÷  y  when y = 6
THINK:  Order of Operations
30 - 24 ÷ 6
30 - 4 = 26
Saving for a Skateboard
It's on sale for $125. You have $45.00 and you are saving $3.00 each week.
How could we write an expression for how much you could save after w weeks?
We made a chart for weeks 1-4
and then realized we could write
45 + 3w
Why did we put the 3 in front of the w?
The three represents the $3 we save each week-- and you always put the coefficient first
How much did you save after
4 weeks? Substitute 4 for w--> 45 + 3(4) = 57  $57
10 weeks? 45 + 3(10) = 75  $75
20 weeks? 45 + 3(20) = 105  $ 105
What would be the expression if you could save $5 a week?
45 + 5w