lesson 1 algebraic properties of equality and identity ncscos obj.: 1.01, 1.02 objective tlw...
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Lesson 1 Algebraic Properties of Equality and Identity
NCSCOS Obj.: 1.01, 1.02
ObjectiveTLW recognize and use the properties of identity and
equality.
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Identity Properties
1) Additive Identity
What do you add to get the same?
a + 0 = a
2) Multiplicative Identity
What do you mult. to get the same?
a • 1 = a
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Inverse Properties
1) Additive Inverse (Opposite)
a + (-a) = 0
2) Multiplicative Inverse (Reciprocal)
a 1
a 1
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Multiplicative Property of Zero
a • 0 = 0
(If you multiply by 0, the answer is 0.)
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Properties of Equality1) Reflexive: a = a
5 = 5
2) Symmetric: If a = b then b = a.
If 4 = 2 + 2 then 2 + 2 = 4.
3) Transitive:If a = b and b = c, then a = c.
If 4 = 2 + 2 and 2 + 2 = 3 + 1 then 4 = 3 + 1.
4) Substitution: If a = b, then a can be replaced by b.
(5 + 2)x = 7x
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Name the Property1. 0 12 = 0
Multiplicative Prop. Of Zero2. (10 + 2) 3 = 12 3
Substitution3. 2 + 3 = 5 then 5 = 2 + 3
Symmetric
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4. If 5 2 = 10 & 10 = 5 + 5 then 5 2 = 5 + 5
Transitive
5. 6 + (-6) = 0
Additive Inverse
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6. 1 m = mMultiplicative Identity
7. k + 7 = k + 7 Reflexive
8. x + 0 = x Additive Identity
9.
111
11 1
Multiplicative Inverse
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Name the property.0 + 4 = 4
1. Additive Identity
2. Additive Inverse
3. Additive Property of Zero
4. Substitution
Answer NowAnswer Now
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Name the property.8 – (6 + 2) = 8 - 8
1. Additive Identity
2. Additive Inverse
3. Associative
4. Substitution
Answer NowAnswer Now
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Name the property.2 + (x – 3)1 = 2 + (x – 3)
1. Reflexive
2. Multiplicative Inverse
3. Multiplicative Identity
4. Symmetric
Answer NowAnswer Now
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Commutative PropertyCommutative means that the order
does not make any difference.a + b = b + a a • b = b • a
Examples
4 + 5 = 5 + 4
2 • 3 = 3 • 2
The commutative property does not work for subtraction or division.
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Associative PropertyAssociative means that the grouping
does not make any difference.(a + b) + c = a + (b + c) (ab) c = a (bc)
Examples
(1 + 2) + 3 = 1 + (2 + 3)
(2 • 3) • 4 = 2 • (3 • 4)
The associative property does not work for subtraction or division.
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Name the property
1) 5a + (6 + 2a) = 5a + (2a + 6)
commutative (switching order)
2) 5a + (2a + 6) = (5a + 2a) + 6
associative (switching groups)
3) 2(3 + a) = 6 + 2a
distributive
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Which property would justify rewriting the following expression without parentheses?
3(2x + 5y)1. Associative property of
multiplication2. Distributive property3. Addition property of
zero4. Commutative property
of multiplication
Answer Now
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Which property would justify the following statement?
8x + 4 = 4 + 8x1. Associative property of
addition
2. Distributive property
3. Addition property of zero
4. Commutative property of addition
Answer Now
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Which property would justify the following statement?
8 + (2 + 6) = (8 + 2) + 6 1. Associative property of
addition
2. Distributive property
3. Addition property of zero
4. Commutative property of addition
Answer Now
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The Distributive PropertyThe process of distributing the number
on the outside of the parentheses to each term on the inside.a(b + c) = ab + ac and (b + c) a = ba + ca
a(b - c) = ab - ac and (b - c) a = ba - ca
Example #1
5(x + 7)
5 • x + 5 • 7
5x + 35
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Example #2
3(m - 4)3 • m - 3 • 4
3m - 12
Example #3
-2(y + 3)-2 • y + (-2) • 3
-2y + (-6)-2y - 6
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Which statement demonstrates the distributive property incorrectly?
1. 3(x + y + z) = 3x + 3y + 3z
2. (a + b) c = ac + bc
3. 5(2 + 3x) = 10 + 3x
4. 6(3k - 4) = 18k - 24
Answer Now
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A term is a1) number,
2) variable, or
3) a product / quotient of numbers and variables.
Example
5
m
2x2
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The coefficient isthe numerical part of the term.
Examples1) 4a
4
2) y2
1
3) 5x2
7 5
7
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Like Terms are terms with the same variable AND exponent.
To simplify expressions with like terms, simply combine the like terms.
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Are these like terms?
1) 13k, 22k
Yes, the variables are the same.
2) 5ab, 4ba
Yes, the order of the variables doesn’t matter.
3) x3y, xy3
No, the exponents are on different variables.
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Which of the following is the simplified form of
-4x + 7x ?1. -4
2. 3x
3. -3x
4. 4
Answer Now
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8x 2 2x2 5a a
The above expression simplifies to:
10x2 6a
8x 2 2x2
5a and a are like terms
and are like terms
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12a
2) 6.1y - 3.2y
2.9y
3) 4x2y + x2y
5x2y
4) 3m2n + 10mn2 + 7m2n - 4mn2
10m2n + 6mn2
Simplify1) 5a + 7a
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21a + 6b
6) 4d + 6a2 - d + 12a2
18a2 + 3d3y
4
y
47)
3y
4
1y
4
4y
41y
y
5) 13a + 8a + 6b
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Which of the following is the simplified form of
5x - 4 - 7x + 14 ?
Answer Now
1. -12x + 10
2. -2x + 10
3. 2x - 18
4. 12x – 18
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If a triangle has sides 3x - 2, 5 - x and 2x - 5, what is the perimeter of the triangle?
Answer Now
1. 4x - 2
2. 4x + 2
3. 5x - 2
4. 5x - 7
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Which figure below models the simplification of - 4x - 5 + 7x + 7 using these tiles?
Answer Now
1.
2.
3.
4.
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Bonus! Which of the following is the simplified form of a + 3a - 4(9 - a) ?
Answer Now
1. -36
2. 3a - 36
3. 8a - 36
4. 8a + 36