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Create and Evaluate Algebraic Expressions

You will be able to write and evaluate simple algebraic expressions by the end of this lesson.

Vocabulary:

Order of Operations

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The rules of which calculation comes first in an expression

They are:
. do everything inside parentheses first: ()
. then do exponents, like x2
. then do multiplies and divides from left to right
. lastly do the adds and subtracts from left to right

Example: 5 × (3 + 4) - 2 × 8 = 5 × 7 - 2 × 8 = 35 - 16 = 19

Value

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Money: how much something is worth.
Example: the value of this coin is one dollar.
Mathematics: the result of a calculation.
Example: 3 × 4 gives the value of 12.

Equation

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An equation says that two things are the same, using mathematical symbols.

An equal sign (=) is used

Example: 7+2 = 10-1

Substitute:

In Algebra "Substitution" means putting numbers where the letters are:
Example: If x=5, then what is x + 10/x ?
Put "5" where "x" is: 5 + 10/5 = 7

Evaluate:

To calculate the value of.

Example: Evaluate the cost of each pie if 3 pies cost $6. Answer: $2 each.
solve

Expression

Numbers, symbols and operators (such as + and ×) grouped together that show the value of something.

Example 2×3 is an expression

Constant

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A fixed value. 

In Algebra, a constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number. 

Example: in "x + 5 = 9", 5 and 9 are constants

If it is not a constant it is called a variable.

Operation

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A mathematical process. 

The most common are add, subtract, multiply and divide (+, -, ×, ÷ ).

But there are many more, such as squaring, square root, etc.

If it isn't a number it is probably an operation.

Example: In 25 + 6 = 9, the operation is add

Variables:

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A symbol for a number we don't know yet. It is usually a letter like x or y.

Example: in x + 2 = 6, x is the variable

If it is not a variable it is called a Constant

Classify Algebraic Expressions

An Algebraic Expression consists of arithmetic numbers (numeral coefficients) and literal numbers (letters or variables) combined by addition, subtraction, multiplication or division. Each part of an expression and the sign before it is called a term. Terms are separated by positive/addition and negative/subtraction signs.

Binomial

A polynomial with two terms such as 4x - 7

Trinomial

A polynomial with three terms such as 3x^2 - 4x + 2

Degree of a Polynomial

The same as that of the term of greatest degree.

Polynomial

Many terms

Poly - Many

-nomial may derive from Greek nomos, "law", influenced by Latin nomen, "name"

Monomials

The following expressions are monomials:

-2     y     5w     0     -7x^2      



The following expressions are not monomials:

5x + y     2 + x + z        6x^3 - 9


The non-variable factor of a monomial is called the numerical coefficient.

A monomial like -3 or 25 has no variable factor and is called a constant.


The degree of a monomial in a variable is the number of times the variable is a factor in the monomial. 

Name the operation indicated by the expression

1. 19x
2. 5 - b
3. 14 / m
4. 8 + 24
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Picture
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Do the following expressions
when y = 4:

y + 8

10 - y

y - y

Do the following expressions
when g = 6

g x 3

18/g

g/3
Do the following expressions 
when a = 2

a + 7 + a


a - 5

5a

Do the following expressions
when x = 5

10/x

10x

3x - 1
The cost for a movie ticket is $8.
Marlo wants to buy t tickets.
Create and evaluate an expression for the following:

Write an expression for the cost of tickets.

Evaluate your expression to evaluate the cost of 4 tickets (t = 4).

Evaluate your expression to evaluate the cost of 8 tickets (t = 8).

Evaluate your expression to evaluate the cost of 10 tickets (t = 10).

The total profit (p) from a bake sale is going to be shared between 5 workers.
Create and evaluate expressions for the information given.

Write an expression for the amount of profit that each worker gets.

Evaluate your expression to find the amount of what each worker gets if the total profit was $50 (p = 50).

Evaluate your expression to find the amount of what each worker gets if the total profit was $100 (p = 100).

Evaluate your expression to find the amount of what each worker gets if the total profit was $200 (p = 200).
Create four different expressions that equal 50. 
Use the four primary operations (+ addition , - subtraction, x multiplication, and /division).

Explain in your own words what it means to evaluate an expression.

Using only division, can you create an expression that evaluates to 2.5?

There are many ways to create an expression that equals 2.5 using division. One example is 10/4. Can you come up with another?

Evaluate the following expressions:

2 + 12 + 6

-8 + 8

4 - 7

18 - 10 - 2

9 x 11

2 x 4 x 6

40/10

36/4
Evaluate each of the expressions when x = 3

5 + x

x + 10 + x

12 - x

x - 2

4x

5x

24/x

18/x
Anna is paid $12 per hour. Write an expression to represent Anna's pay if she works h hours.

Evaluate your expression to find Ana's pay for 2 hours (h=2).

Evaluate your expression to find Ana's pay for 5 hours (h=5).

Evaluate your expression to find Ana's pay for 10 hours (h=10).
Jackson was given the expression 2x + 4 and was told to evaluate it when x = 5. Jackson did not know what to do. Explain in your own words what Jackson needs to do. Please use at least three sentences. 



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