Download 1-18 PPT

5 Minute Check
Complete in your notes. Factor each expression.
1. 4x + 8
2. 10x + 35
3. 18x + 81
4. 42 + 18x
5 Minute Check
Complete in your notes. Factor each expression.
1. 4x + 8
2. 10x + 35
3. 18x + 81
4. 42 + 18x
5 Minute Check
Complete in your notes. Factor each expression.
1. 4x + 8
5 Minute Check
Complete in your notes. Factor each expression.
1. 4x + 8
4(x + 2)
5 Minute Check
Complete in your notes. Factor each expression.
2. 10x + 35
5 Minute Check
Complete in your notes. Factor each expression.
2. 10x + 35
5(2x + 7)
5 Minute Check
Complete in your notes. Factor each expression.
3. 18x + 81
5 Minute Check
Complete in your notes. Factor each expression.
3. 18x + 81
9(2x + 9)
5 Minute Check
Complete in your notes. Factor each expression.
4. 42 + 18x
5 Minute Check
Complete in your notes. Factor each expression.
4. 42 + 18x
6(7 + 3x)
OST Test Prep
A company manufactures small, solid, plastic cubes.
They use the expression sᶾ, where s is the length of a
side, to find the volume of plastic needed to make a
cube. Luis claims that the volume of plastic needed to
make a cube with a side length 8 millimeters is 24
cubic millimeters. Is he correct? Explain why.
OST Test Prep
A company manufactures small, solid, plastic cubes.
They use the expression sᶾ, where s is the length of a
side, to find the volume of plastic needed to make a
cube. Luis claims that the volume of plastic needed to
make a cube with a side length 8 millimeters is 24
cubic millimeters. Is he correct? Explain why.
sᶾ, where s = 8
8∙8∙8
64 ∙ 8
512
He is not correct.
What fraction is LeBron of Paul?
What fraction is LeBron of Paul?
What fraction is the average guy of Paul?
What fraction is LeBron of Paul?
Questions to be answered:
What do we know?
What is a prediction that is too low?
What is a prediction that is too high?
Can we make an accurate prediction or is there
additional information that is needed to make
What
fraction
is
the
average
guy
of
Paul?
a prediction?
What fraction is LeBron of Paul?
Questions to be answered:
What do we know?
What is a prediction that is too low?
What is a prediction that is too high?
Can we make an accurate prediction or is there
additional information that is needed to make
a prediction?
Inquiry Lab
Work with a partner and complete page 294
Inquiry Lab
Work with a partner and complete page 294
Inquiry Lab
Work with a partner and complete page 294
Wednesday, Jan 18
Lesson 6.7
Equivalent Expressions
Equivalent Expressions
Objective: To understand how to use
properties to simplify expressions.
Equivalent Expressions
A term can be a single number or variable or
numbers and variables multiplied together
and separated by addition or subtraction.
e.g.
4x + 4
This expression has 2 terms.
Equivalent Expressions
A coefficient is the numerical factor of a term
that contains a variable.
e.g.
4x + 4
In this expression there is only one term that
has a variable and the coefficient is 4.
Equivalent Expressions
A term without a variable is called a constant.
e.g.
4x + 4
Constant.
Equivalent Expressions
Like terms are terms that contain the same
variable. Only like terms and constants can
be added or subtracted.
e.g.
4x + 6 + 5x
Like terms
Equivalent Expressions
Complete on the back of your homework.
Simplify.
4. 10 – ( 4 + 2²) + 3³
10 – ( 4 + 4) + 3³
10 – 8 + 3³
10 - 8+ 27
2 + 27
29
Equivalent Expressions
To simplify an algebraic expression, use
properties to write an equivalent expression
that has no like terms and no parentheses.
Numbers
3 + 3 = 2(3) or 6
Variables
x + x = 2x
Equivalent Expressions
Simplify the expression.
3(4x)
Equivalent Expressions
Simplify the expression.
3(4x)
According to the Associative Property if an
expression has all multiplication or all
addition, we can remove the parenthesis.
3·4·x
Can we perform any operation?
Equivalent Expressions
Simplify the expression.
3(4x)
Equivalent Expressions
Simplify the expression.
3(4x)
If we had 3 times this, how many x’s would
we have?
Equivalent Expressions
Simplify the expression.
3(4x)
Equivalent Expressions
Simplify the expression.
3(4x)
12x
Unlike terms can be multiplied and divided.
Apply the operation to the coefficients and
/or numbers.
Equivalent Expressions
Simplify the expression.
11 · 3x
Do this on your own.
Equivalent Expressions
Simplify the expression.
11 · 3x
33x
Equivalent Expressions
Simplify the expression
5x + 3x + 6x
Equivalent Expressions
Simplify the expression.
5x + 3x + 6x
+
+
Equivalent Expressions
Simplify the expression
5x + 3x + 6x
8x + 6x
14x
Like terms can be added and subtracted.
When adding or subtracting like terms, add
or subtract the coefficients.
Equivalent Expressions
Simplify the expression.
64s – 7s
Equivalent Expressions
Simplify the expression.
64s – 7s
57s
Equivalent Expressions
Simplify the expression
4(2x + y)
Equivalent Expressions
Simplify the expression
4(2x + y)
8x + 4y
Remember – you must distribute the factor
outside the parenthesis to both terms inside .
Equivalent Expressions
Simplify the expression.
6(f + 7)
Equivalent Expressions
Simplify the expression.
6(f + 7)
6f + 42
Equivalent Expressions
Properties can be used to simplify or factor
expressions with two variables.
Compare the effects of operations on
numbers to the effects of operations on
variables.
Numbers
Variables
3+3+4
x+x+y
6+4
2x + y
10
Equivalent Expressions
Simplify the expression.
3x + 5y + 2x
Equivalent Expressions
Simplify the expression.
3x + 5y + 2x
+
How many x tiles are there?
+
Equivalent Expressions
Simplify the expression.
3x + 5y + 2x
+
5x
+
Equivalent Expressions
Simplify the expression.
3x + 5y + 2x
+
How many y tiles are there?
5x
+
Equivalent Expressions
Simplify the expression.
3x + 5y + 2x
+
5x + 5y
+
Equivalent Expressions
Simplify the expression.
8b + 5 – 5b
Equivalent Expressions
Simplify the expression.
8b + 5 – 5b
3b + 5
Equivalent Expressions
Simplify the expression.
(6x + 21c) + 14x
Equivalent Expressions
Simplify the expression.
(6x + 21c) + 14x
20x + 21c
Equivalent Expressions
Simplify the expression.
6(7g+ 4h)
Equivalent Expressions
Simplify the expression.
6(7g+ 4h)
42g + 24h
Unlike terms can not be added.
Equivalent Expressions
Simplify the expression.
3(5b + h) + 6h
Equivalent Expressions
Simplify the expression.
3(5b + h) + 6h
15b + 3h + 6h
15b + 9h
Equivalent Expressions
Simplify the expression
9(3x + 2y)
Equivalent Expressions
Simplify the expression
9(3x + 2y)
27x + 18y
Equivalent Expressions
Factor the expression.
27x + 18y
Remember – find the GCF of the coefficients.
Equivalent Expressions
Factor the expression.
27x + 18y
9(3x + 2y)
Equivalent Expressions
Factor the expression.
18a + 24b
Equivalent Expressions
Factor the expression.
18a + 24b
6(3a + 4b)
Equivalent Expressions
Mikayla bought five skirts at $x each. Three
of the five skirts came with a matching top for
an additional $9 each. Write and simplify an
expression that represents the total cost of
her purchase.
Equivalent Expressions
Mikayla bought five skirts at $x each. Three
of the five skirts came with a matching top for
an additional $9 each. Write and simplify an
expression that represents the total cost of
her purchase.
What is the expression that represent the a
skirt that came with a top?
Equivalent Expressions
Mikayla bought five skirts at $x each. Three
of the five skirts came with a matching top for
an additional $9 each. Write and simplify an
expression that represents the total cost of
her purchase.
x+9
How many of those are there and how do we
notate that?
Equivalent Expressions
Mikayla bought five skirts at $x each. Three
of the five skirts came with a matching top for
an additional $9 each. Write and simplify an
expression that represents the total cost of
her purchase.
3(x + 9)
What is the expression that represent the
skirts that came without tops?
Equivalent Expressions
Mikayla bought five skirts at $x each. Three
of the five skirts came with a matching top for
an additional $9 each. Write and simplify an
expression that represents the total cost of
her purchase.
3(x + 9) + 2x
Can we simplify this?
Equivalent Expressions
Mikayla bought five skirts at $x each. Three
of the five skirts came with a matching top for
an additional $9 each. Write and simplify an
expression that represents the total cost of
her purchase.
3(x + 9) + 2x
3x + 27 + 2x
5x + 27
Equivalent Expressions
Translate the verbal expression into an
Simplify.
7x + 5(x + 3) + 4x – x - 2
Equivalent Expressions
Translate the verbal expression into an
Simplify.
7x + 5(x + 3) + 4x – x – 2
7x + 5x + 15 + 4x – x – 2
15x + 13
Equivalent Expressions
Complete on the back of your homework.
Simplify.
4. 10 – ( 4 + 2²) + 3³
10 – ( 4 + 4) + 3³
10 – 8 + 3³
10 - 8+ 27
2 + 27
29
Equivalent Expressions
Agenda Notes
Skills Practice 6.7
Due Thursday, Jan 19
Help session
Thursday, Jan 19 – 2:10-2:40
Chapter 6 Test
Friday, Jan 20