algebra! the area of mathematics that generalizes the concepts and rules of arithmetic using symbols...
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Algebra!
The area of mathematics that generalizes the concepts and rules of arithmetic using symbols to represent numbers
What is arithmetic?
AdditionSubtractionMultiplicationDivisionExponents
What are some examples of symbols you see inside and outside of school?
In algebra, we use different symbols that we call variables
Many times, you will use letters as your symbolX, a, b, c, etc.
Sometimes you may see some Greek alphabet lettersβ = beta
How to set a problem up!
Add three to a number A number plus 3 The sum of a number and 3 3 more than a number A number increased by 3
How to set up a problem!
Subtract 12 from a number A number minus 12 The difference of a number and 12 12 less than a number A number decreased by 12 Take away 12 from a number A number less 12
Set up the problem!
2 times a number 2 multiplied by a number The product of 2 and a number
Set up the problem!
6 divided into a number A number divided by 6 The quotient of a number and 6
What would the expression be?
Five less than a number
The product of three and a number
The sum of a number and 10
A number divided by 9
Try one on your own!
Make up an algebraic expression on your own. Write it on your whiteboard.
When your finished, pass it to a neighbor and see if they can figure it out!
Two step algebraic expressions
Three times a number decreased by two
Four more than five times a number
The sum of a number and four divided by two
The difference of a number and four added to nine
Write a verbal phrase for each algebraic expression
Write each sentence as an equation
The product of four and a number is sixteen
Three less than an number is twenty
Nine more than “n” is eleven
To evaluate an algebraic expression, substitute a number for the variable!
Example: Evaluate n + 7 when n = 4
To evaluate an algebraic expression, substitute a number for the variable!
Example: Evaluate 5n + 3 when n = 6
To evaluate an algebraic expression, substitute a number for the variable!
Example: Evaluate 6n² + 2n when n = 3
Let’s try a few on our own!
1. p ÷ 2 + p when p = 4
2. 3a – 5 when a = 5
3. 6/s + 4s when s = 2
What about two variables? Example: Evaluate a + 7 - c when a = 9
b = 6
What about two variables? Example: Evaluate 2n + 7b when n = 5
b = 2
Let’s try a few on our own!
1. p ÷ 2 + 3x when p = 6 and x = 7
2. 3a – 5t when a = 6 and t = 2
3. 12/s + y² when s = 3 and y = 5
Try one on your own!
Make up an algebraic expression and assign the variable or variables values. Write it on your whiteboard.
When your finished, pass it to a neighbor and see if they can figure it out!
Definitions Term: A term can be a number, a
variable, or a product of numbers and variables.
Definitions Please list all of the terms in this
algebraic expression.
Definitions Like terms: Terms that have the same
variable raised to the same power. Examples
Definitions Unlike terms: Terms that do not have the
same variable raised to the same power. Examples
Definitions Like terms: Terms that have the
same variable raised to the same power.
Identify the like terms in the list:
You can only combine LIKE TERMS
Example: _s_ + 10s = 5
Example: 72c + 5b =
Example: 4x² + 53x =
Example: 7x + 5x =
Now let’s practice!
1. 3m + 4m =
2. 6t + 4 – 3t =
3. 17y + 3y – 2y²
4. 5 + 4r – 3 =
What about the more difficult ones?
3b² + 5b + 11b² - 4a² =
Step 3 : solve and bring down the rest of the terms
Step 2 : circle the numbers and the sign to the left of them
Step 1 : underline like terms
What about the more difficult ones?
2(b + 2a²) + 2b
Step 3 : solve and bring down the rest of the terms
Step 2 : circle the numbers and the sign to the left of them
Step 1 : distribute and underline like terms
2b + 4a² + 2b
Let’s try some on our own!
1. a + 2b + 2a + 3b + 4c
2. 18 + 2d³ + d + 3d
3. a² + 9b + 5a² + 2b + 6c
4. 3(4x + z) – 4x
Try one on your own!
Make up an algebraic expression with several variables. Write it on your whiteboard.
When your finished, pass it to a neighbor and see if they can figure it out!
Lets try a few!
2 + x = 72 plus “some number” equals 7Answer = 5How did you know this?
2 + x = 7subtract two from both sides
-2 -20 + x = 5
Additive inverse
Step 1: Draw a line down the equal sign
Step 2: Look at the number on the same side as the variable
Step 3: Look at the sign next to the number you underlined (no sign = positive)
Step 4: Do the opposite! Add or subtract that number from both sides
X + 14 = 27subtract 14 from both sides
-14 -14X + 0 = 13
Additive inverse
Step 1: Draw a line down the equal sign
Step 2: Look at the number on the same side as the variable
Step 3: Look at the sign next to the number you underlined (no sign = positive)
Step 4: Do the opposite! Add or subtract that number from both sides
Now try on your own!
1. 16 + x = 292. X + 11 = 343. 18 + X = 864. X + 12 = 195. 27 + X = 258
Problem #1
16 + x = 29
Problem #2
X + 11 = 34
Problem #3
18 + X = 86
Problem #4
X + 12 = 19
Problem #5
27 + X = 258