Transcript 1-8

1-8 Simplifying Expressions
Warm Up
Lesson Presentation
Lesson Quiz
1-8 Simplifying Expressions
Warm Up
Add.
1. 427 + 35 462
3.
2. 1.06 + 0.74 1.80
10
Multiply.
4. 25(8) 200
6.
5. 1.3(22) 28.6
1-8 Simplifying Expressions
Sunshine State Standards
MA.912.A.3.2 Identify and apply the
distributive, associative, and commutative
properties of real numbers….
1-8 Simplifying Expressions
Objectives
Use the Commutative, Associative, and
Distributive Properties to simplify expressions.
Combine like terms.
1-8 Simplifying Expressions
Vocabulary
term
like terms
coefficient
1-8 Simplifying Expressions
The Commutative and Associative Properties
of Addition and Multiplication allow you to
rearrange an expression to simplify it.
1-8 Simplifying Expressions
1-8 Simplifying Expressions
Additional Example 1A: Using the Commutative and
Associative Properties
Simplify.
Use the Commutative Property.
Use the Associative Property
to make groups of compatible
numbers.
11(5)
55
1-8 Simplifying Expressions
Additional Example 1B: Using the Commutative and
Associative Properties
Simplify.
45 + 16 + 55 + 4
45 + 55 + 16 + 4
(45 + 55) + (16 + 4)
(100) + (20)
120
Use the Commutative Property.
Use the Associative Property
to make groups of compatible
numbers.
1-8 Simplifying Expressions
Helpful Hint
Compatible numbers help you do math mentally.
Try to make multiples of 5 or 10. They are simpler
to use when multiplying.
1-8 Simplifying Expressions
Check It Out! Example 1a
Simplify.
Use the Commutative Property.
Use the Associative Property
to make groups of compatible
numbers.
21
1-8 Simplifying Expressions
Check It Out! Example 1b
Simplify.
410 + 58 + 90 + 2
410 + 90 + 58 + 2
Use the Commutative Property.
Use the Associative Property
(410 + 90) + (58 + 2) to make groups of compatible
numbers.
(500) + (60)
560
1-8 Simplifying Expressions
Check It Out! Example 1c
Simplify.
1 •
7•8
2
1
2
1
(2
•
8
•
•
7
8) 7
4•7
28
Use the Commutative Property.
Use the Associative Property
to make groups of compatible
numbers.
1-8 Simplifying Expressions
The Distributive Property is used with Addition to
simplify expressions.
The Distributive Property also works with
subtraction because subtraction is the same as
adding the opposite.
1-8 Simplifying Expressions
Additional Example 2A: Using the Distributive
Property with Mental Math
Write the product using the Distributive
Property. Then simplify.
5(59)
5(50 + 9)
5(50) + 5(9)
250 + 45
295
Rewrite 59 as 50 + 9.
Use the Distributive Property.
Multiply.
Add.
1-8 Simplifying Expressions
Additional Example 2B: Using the Distributive
Property with Mental Math
Write the product using the Distributive
Property. Then simplify.
8(33)
8(30 + 3)
8(30) + 8(3)
240 + 24
264
Rewrite 33 as 30 + 3.
Use the Distributive Property.
Multiply.
Add.
1-8 Simplifying Expressions
Check It Out! Example 2a
Write the product using the Distributive
Property. Then simplify.
9(52)
9(50 + 2)
9(50) + 9(2)
450 + 18
468
Rewrite 52 as 50 + 2.
Use the Distributive Property.
Multiply.
Add.
1-8 Simplifying Expressions
Check It Out! Example 2b
Write the product using the Distributive
Property. Then simplify.
12(98)
12(100 – 2)
12(100) – 12(2)
Rewrite 98 as 100 – 2.
Use the Distributive Property.
1200 – 24
Multiply.
1176
Subtract.
1-8 Simplifying Expressions
Check It Out! Example 2c
Write the product using the Distributive
Property. Then simplify.
7(34)
7(30 + 4)
7(30) + 7(4)
210 + 28
238
Rewrite 34 as 30 + 4.
Use the Distributive Property.
Multiply.
Add.
1-8 Simplifying Expressions
The terms of an expression are the parts that
are added together. Like terms are terms that
contain the same variables raised to the same
powers. Constants are also like terms.
Like terms
Constant
4x – 3x + 2
1-8 Simplifying Expressions
A coefficient is a number multiplied by a
variable. Like terms can have different
coefficients. A variable written without a
coefficient has a coefficient of 1.
Coefficients
1x2 + 3x
1-8 Simplifying Expressions
Using the Distributive Property can help you
combine like terms. You can factor out the
common factor to simplify the expression.
7x2 + 4x2 = (7 + 4)x2
= (11)x2
Factor out x2 from both terms.
Perform operations in
parentheses.
= 11x2
Notice that you can combine like terms by
adding the coefficients and keeping the
variables and exponents the same.
1-8 Simplifying Expressions
Caution!
Add only the coefficients.
6.8y2 + (-y2) ≠ 6.8
1-8 Simplifying Expressions
Additional Example 3A: Combining Like Terms
Simplify the expression by combining like
terms.
72p – 25p
72p – 25p
47p
72p and 25p are like terms.
Subtract the coefficients.
1-8 Simplifying Expressions
Additional Example 3B: Combining Like Terms
Simplify the expression by combining like
terms.
A variable without a coefficient
has a coefficient of 1.
and
are like terms.
Write 1 as .
Add the coefficients.
1-8 Simplifying Expressions
Additional Example 3C: Combining Like Terms
Simplify the expression by combining like
terms.
0.5m + 2.5n
0.5m + 2.5n
0.5m and 2.5n are not like terms.
0.5m + 2.5n
Do not combine the terms.
1-8 Simplifying Expressions
Check It Out! Example 3
Simplify by combining like terms.
3a. 16p + 84p
16p + 84p
100p
3b. –20t – 8.5t
–20t – 8.5t
–28.5t
16p + 84p are like terms.
Add the coefficients.
20t and 8.5t are like terms.
Add the coefficients.
3c. 3m2 + m3
3m2 + m3
3m2 + m3
3m2 and m3 are not like terms.
Do not combine the terms.
1-8 Simplifying Expressions
Additional Example 4: Simplifying Algebraic
Expressions
Simplify 14x + 4(2 + x). Justify each step.
Procedure
1.
2.
Justification
14x + 4(2 + x)
14x + 4(2) + 4(x)
Distributive Property
3.
14x + 8 + 4x
Multiply.
4.
14x + 4x + 8
Commutative Property
5.
(14x + 4x) + 8
6.
18x + 8
Associative Property
Combine like terms.
1-8 Simplifying Expressions
Check It Out! Example 4a
Simplify 6(x – 4) + 9. Justify each step.
Procedure
1.
6(x – 4) + 9
2.
6(x) – 6(4) + 9
3.
6x – 24 + 9
4.
6x – 15
Justification
Distributive Property
Multiply.
Combine like terms.
1-8 Simplifying Expressions
Check It Out! Example 4b
Simplify −12x – 5x + 3a + x. Justify each step.
Procedure
1.
–12x – 5x + 3a + x
2.
–12x – 5x + x + 3a
3.
–16x + 3a
Justification
Commutative Property
Combine like terms.
1-8 Simplifying Expressions
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
1-8 Simplifying Expressions
Lesson Quiz: Part I
Simplify each expression.
1. 165 +27 + 3 + 5 200
2.
8
Write each product using the Distributive
Property. Then simplify.
3. 5($1.99)
4. 6(13)
5($2) – 5($0.01) = $9.95
6(10) + 6(3) = 78
1-8 Simplifying Expressions
Lesson Quiz: Part II
Simplify each expression by combining like
terms. Justify each step with an operation or
property.
5.
6. 14c2 – 9c
14c2 – 9c
7. 301x – x
300x
8. 24a + b2 + 3a + 2b2
27a + 3b2
1-8 Simplifying Expressions
Lesson Quiz for Student Response Systems
1. Which property states that you can add or
multiply in any order?
A. Associative
B. Commutative
C. Multiplicative
D. Grouping
1-8 Simplifying Expressions
Lesson Quiz for Student Response Systems
2. Simplify
A. 5
B. 6
C. 10
D. –5
1-8 Simplifying Expressions
Lesson Quiz for Student Response Systems
3. Which of the following are like terms?
A. 3x and 2y
B. 3x and 2x
C. 3x and x2
D. 3x and 2x
1-8 Simplifying Expressions
Lesson Quiz for Student Response Systems
4. Simplify by combining like terms.
2x2 + x2
A. 2x4
B. 3x4
C. 3x2
D. 4x2