Download 1-7 Simplifying Expressions

1-7 Simplifying Expressions
Warm Up
Add.
1. 427 + 35
2. 1.06 + 0.74
3.
Multiply.
4. 25(8)
6.
5. 1.3(22)
1-7 Simplifying Expressions
LEARNING GOALS
1. Students will differentiate between
commutative and associative properties
2-3. Students will use the commutative,
associative, and distributive properties to
simplify expressions and justify using algebraic
properties.
1-7 Simplifying Expressions
The Commutative and Associative Properties
of Addition and Multiplication allow you to
rearrange an expression to simplify it.
1-7 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.
1-7 Simplifying Expressions
Example 1A: Using the Commutative and Associative
Properties
Simplify.
A.
C.
E. 1 • 7 • 8
2
B. 45 + 16 + 55 + 4
D. 410 + 58 + 90 + 2
1-7 Simplifying Expressions
Example 1a: Using the Commutative and Associative
Properties
Simplify.
a.
c.
b.
1
1
16 + 2 + 4 + 1
2
2
e. 2 • 2 • 9
3
d. 27 + 98 + 73
1-7 Simplifying Expressions
The terms of an expression are the parts to be
added or subtracted. 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
1-7 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
1-7 Simplifying Expressions
Example 3A: Combining Like Terms
Simplify the expression by combining like terms.
A. 72p – 25p
B.
C. 0.5m + 2.5n
D. 16p + 84p
E. –20t – 8.5t2
F. 3m2 + m3
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1-7 Simplifying Expressions
Example 3a: Combining Like Terms
Simplify the expression by combining like terms.
A. 27r – 18r
b. 32x 2 y 4 + 8x 2 y 4
c. 3g + 5g
e.
−15st 2 + 15s2 t
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d.
f.
19z + 14z
x2 + x3
1-7 Simplifying Expressions
Example 4: Simplifying Algebraic Expressions
Simplify 14x + 4(2 + x). Justify each step.
Procedure
1.
2.
14x + 4(2 + x)
14x + 4(2) + 4(x)
3.
14x + 8 + 4x
4.
14x + 4x + 8
5.
(14x + 4x) + 8
6.
18x + 8
Justification
Given
1-7 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
Given
1-7 Simplifying Expressions
Simplify −12x – 5x + 3a + x. Justify each step.
Procedure
1.
–12x – 5x + 3a + x
2.
–12x – 5x + x + 3a
3.
–16x + 3a
Justification
Given
1-7 Simplifying Expressions
Example 4: Simplifying Algebraic Expressions
Simplify 2(x + 6) + 3x. Justify each step.
Procedure
1.
2(x + 6) + 3x
2.
2(x) + 2(6) + 3x
3.
2x + 12 + 3x
4.
12 + 2x +3x
5.
12 + (2x + 3x)
6.
12 + 5x
Justification
Given
1-7 Simplifying Expressions
Example 4: Simplifying Algebraic Expressions
Simplify 6x – x – 3x2 + 2x. Justify each step.
Procedure
1.
6x – x – 3x2 + 2x
2.
6x – x + 2x – 3x2
3.
7x – 3x2
Justification
Given
1-7 Simplifying Expressions
Lesson Quiz: Part I
Simplify each expression.
1. 165 +27 + 3 + 5
2.
3. Simplify 4a – 2(1 - a). Justify each step.
Procedure
1.
4a – 2(1 - a)
2.
3.
4.
5.
4a – 2(1) - 2(-a)
4a – 2 + 2a
4a + 2a - 2
6a - 2
Justification
Given
1-7 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
7. 301x – x
8. 24a + b2 + 3a + 2b2