Algebra! The area of mathematics that generalizes the concepts and rules of arithmetic using symbols...
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Transcript of 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
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What is arithmetic?
AdditionSubtractionMultiplicationDivisionExponents
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What are some examples of symbols you see inside and outside of school?
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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
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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
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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
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Set up the problem!
2 times a number 2 multiplied by a number The product of 2 and a number
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Set up the problem!
6 divided into a number A number divided by 6 The quotient of a number and 6
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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
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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!
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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
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Write a verbal phrase for each algebraic expression
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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
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To evaluate an algebraic expression, substitute a number for the variable!
Example: Evaluate n + 7 when n = 4
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To evaluate an algebraic expression, substitute a number for the variable!
Example: Evaluate 5n + 3 when n = 6
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To evaluate an algebraic expression, substitute a number for the variable!
Example: Evaluate 6n² + 2n when n = 3
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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
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What about two variables? Example: Evaluate a + 7 - c when a = 9
b = 6
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What about two variables? Example: Evaluate 2n + 7b when n = 5
b = 2
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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
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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!
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Definitions Term: A term can be a number, a
variable, or a product of numbers and variables.
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Definitions Please list all of the terms in this
algebraic expression.
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Definitions Like terms: Terms that have the same
variable raised to the same power. Examples
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Definitions Unlike terms: Terms that do not have the
same variable raised to the same power. Examples
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Definitions Like terms: Terms that have the
same variable raised to the same power.
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Identify the like terms in the list:
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You can only combine LIKE TERMS
Example: _s_ + 10s = 5
Example: 72c + 5b =
Example: 4x² + 53x =
Example: 7x + 5x =
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Now let’s practice!
1. 3m + 4m =
2. 6t + 4 – 3t =
3. 17y + 3y – 2y²
4. 5 + 4r – 3 =
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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
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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
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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
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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!
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Lets try a few!
2 + x = 72 plus “some number” equals 7Answer = 5How did you know this?
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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
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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
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Now try on your own!
1. 16 + x = 292. X + 11 = 343. 18 + X = 864. X + 12 = 195. 27 + X = 258
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Problem #1
16 + x = 29
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Problem #2
X + 11 = 34
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Problem #3
18 + X = 86
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Problem #4
X + 12 = 19
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Problem #5
27 + X = 258
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