Transcript Learning Target:

Learning Target:
I can…
Identify like terms and simplify expressions
Terms: A number, a ____________________ or
the product of a number and a variable.
______________Terms: Have the same variable
or variable factors
_____________________: the number in front
of the variable
*When a variable does not
have a number in front of it
(like c), there is an
understood ______ in front of
the variable
Like Terms
Not Like Terms
An expression is in simplest form when it has no
like terms and no parenthesis.
To Simplify Expressions: Add or subtract
coefficients
Examples – One Variable
1) -13c + c
Like Terms_________ Simplify _____________
2) 2x + 3x – 2 + 4x + 5
Like Terms_________ Simplify _____________
3) 0.3f – f + 10 + 0.7f + 3f – 4
Like Terms_________ Simplify _____________
4) m – ⅖ – 5m + ⅙
Like Terms_________ Simplify _____________
A store is advertising a sale where everything is
20% off.
Adam and Brandi are customers discussing how
discount and tax will be calculated.
Adam says he will take 0.8p to find the new price of any
item.
Brandi says she will take p – 0.2p to find the new price
of any item.
Who is correct?
Examples – Two or More Variables
or Variable Factors
1) 0.3a – b + 0.9a + 3b
2)
8f – 2t + 3f + t
Examples: Variables Raised to
Different Exponents
1)
3x + 2x² – 2.6x + 7x² + 7
2)
3a² – a – 7 + 5a² + 5a + 4
3)
3a² + 4b – 3b² + a² - 5b + b²
Like Terms_______________
Simplify _______________________________
4)
3x² + y² - 4x + x² + 6x + 2y²
Like Terms_______________
Simplify _______________________________
OAA Examples:
1)
OAA Example
2) Which of the following is the
simplified version of:
2x² + 3x – 2x – 5 + x²
A. x² + 5x + 5
B. x² – x – 5
C. 3x² + x – 5
D. 3x² + x + 5
OAA Example
3) Adam and Shelby are shopping in a town that
has a 5% tax. Adam says the final price of any
item can be found by the expression p + 0.05p,
where p is the original price. Shelby says the
price of any item can be found by the expression
1.05p. Who is correct? Explain.
EXIT
Simplify the following expression:
3a + 2b – 4a + b
Learning Target:
I can…
Use the distributive property to simplify
expressions
An expression is in simplest form when it has no
like terms and no parenthesis.
When you do see parenthesis, you must use:
The _______________________________Property:
a(b + c) = _____________________
*Remember when two variables are next to each other it
means _____________________.
Examples
1) With real numbers:
2(3 + 4) =
Using the Distributive Property
2)
3(x + 5)
3)
-6(c + 4)
4)
12(4a – 6)
5) -3(3f – 2) =
6) -7(9 + 3a)
To Distribute and Simplify
Step 1: Get rid of parenthesis first by
distributing
Step 2: Identify like terms
Step 3: Combine to simplify
Distribute and Simplify
1) 3(b + 9) + 10
2) -4(c + 8) + 9c + 7
3) 4y – 7 + 8(y + 5)
4) 6(b – 9 + 2b)
You Try
1) x(4 + 5) + x² + 2x
2) 2(5x – 3) + 3x
3) 11b – 2(3b + 1
OAA Example:
Which of the following is the simplified version
of:
3(x + x + y)
A.
B.
C.
D.
6x + 3y
3x² + 3y
3x²y
3x + 3y
EXIT
Simplify the expression:
2(3x + 5 + x)
Learning Target:
I can…
Identify equivalent expressions
*Remember:
An expression is in _______________when it
has no ___________and no _____________.
Equivalent Expressions
If two things are equivalent, they are the
__________________.
Equivalent expressions are expressions that are
the same, even though they may look a little
_________________.
To identify equivalent expressions, put all the
expressions in ________________________.
Which expression is NOT equivalent?
A.
B.
C.
D.
y+y+y
2y + y
3y
2(y + 1)
Which expression is NOT equivalent?
A.
B.
C.
D.
2(x + 3)
3+x+2+x+1
3(x + 2)
2x + 6
Which expression is NOT
equivalent?
A.
B.
C.
D.
3(a + a + b)
6a + b
6a + 3b
a + 5a + b + b + b
To find the perimeter of figures: __________
the sides.
To find the area of triangles _____________
To find the area of rectangles ____________
Find the perimeter of the
triangle
Find the perimeter and area of the
rectangle
a+3
5
EXIT
Which expression is NOT equivalent?
A.
B.
C.
D.
2(x + 4)
2x + 8
x+2+x+6
2x + 4
Learning Target:
I can…
Write, simplify and evaluate expressions
EXIT
1) Simplify the expression:
x + 2 + x + 6 + 2(x + 5)
2) Evaluate the expression if x = 4:
Learning Target:
I can…
Show what I know on my Algebraic Expressions
Quiz
EXIT
Mr. Wesley is deciding how to price items in his
“going out of business sale.” He decides to start
the item at $200 and give $3 off the price every
day it does not sell. Write an expression for the
cost of the item after d days.
How much would the item cost after 10 days?
Multiplying Variables
1) x(x + 5) + x² + 2x
2) 2x(5x – 3) + 3x
3) 11b² – 2b(3b + 1)
Simplifying Expressions
Combine LIKE terms using algebra tiles
x2
x
and
and
–x2
-x
Numbers (1 and -1)
Draw a model to represent x² + 2x + 4
What is the expression for this model?
Adding/Subtracting
A positive and a negative make ZERO (cancel
out)
+
+
Example:
+
What does this situation represent?
What is the solution?
What is the solution?
Without using tiles…
Example 1: Simplify the expression 5m² + 9m +
2m² +8 – m – 2
Example 2: Simplify the expression 2t² + t – 17t +
6 – 2t – t²
Simplifying Expressions
• COMBINE LIKE TERMS
4x + 2x² – 5x + 7 + 8x² - 3 + x
-a + 3a² – 5a + 4 – 7a + a²
Exit
Simplify 3x + 5x² – x + 9 + 8x²
Homework page 46
Learning Target:
I can…
Use the distributive property to simplify
expressions
Part A. Simplify the following expressions:
Together:
1.
3x + 2x² – 6x + 7x² + 7
2.
2x + 4y + 2 – x + 9y + 6x - 5
3.
3(a + 7 – b)
4.
-c(4 + c – 7)
Part B
1.
-2a + 8 – 3a² + 4a + 6
2.
8b – 3c + 7b + 1 + 9c – 3
3.
-2(a + 6)
4.
b(3 + b + 9)
Part C. Simplify
1.
2x – 3 + 4x
2.
2(2.5b – 9) + 6b
3.
-6(m + 1) + 18
4.
9a – 4 + 3(a – 11)
Learning Target:
I can…
Simplify and solve equations
Review - Simplify
2(2.5b – 9) + 6b
Simplify AND Solve
4x² + 3x + 9x + 2 – 3x² – 4x – x² = 58
3x² – 4x + 4 + 2x² + 2x + x + x = 84
6(c – 2) – 4c + 8 = -10
EXIT
3a + 2(a + 5) – 2 = 88
Part A. Simplify and solve
1.
6x + 2x² – 6x + 7x² + 7 = 151
2.
2x – 9y + 2 – x + 9y + 6x - 5 = -24
3.
3(a + 7 – 2a) = 6
4.
-2(4 + c – 7) = -16
Part B. Simplify and solve:
1.2x – 3 + 4x = 39
2. 2(2.5b – 9) + 6b = -7
3.24 = -6(m + 1) + 18
4.9a – 4 + 3(a – 11) = 23
PART C: Simplify and Solve
1.
0.7w + 16 + 4w = 27.28
2.
3(3a + 3) + 6 = 81
3.
4(1.5c + 6) – 2c = -9
4.
20 = -4(f + 6) + 14
Learning Target:
I can…
Solve equations with variables on both sides
3x + 9 = 2x
5x = 9x + 8
6x + 1 = 4x + 9
Part C. Solve the equations with
variables on both sides
Together:
1.2y + 40 = 12y
2.7p + 7 = 9 – p
3.9(d – 4) = 5d + 8
4.6(f + 5) = 2f – 8
On Your Own:
1.7y = y – 42
2.2x + 10 = -4x – 2
3.14b = 16(b + 12)
4.4(x + 0) = 2x + 6
Exit
Solve for a
2a + 8 = 4a + 2