Distributive Property

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Transcript Distributive Property

Do Now
1. Write down any math properties you know
and give an example. (ex. Commutative)
2. Write down any similarities or differences
between expressions and equations
Objective
The student will be able to:
• Identify parts of an algebraic
expression
A term is a
1) number,
2) variable, or
3) a product / quotient of numbers
and variables.
Example
5
m
2x2
A term is a
*** Terms are separated by either an
addition sign (+) or subtraction
sign (-).
4x + 5y
(2 terms)
3r * 5p
(1 term)
The coefficient is
the numerical part of the term.
Examples
1) 4a
4
2) y2
1
2
5x
3)
7
5
7
A variable is alphabetic
character representing a number .
Examples
1) 4a
a
2) y2
y
2
5x
3)
7
x
A constant is
a fixed value.
Examples
1) 3x – 5y + 12
12
2) 12p – 4 + 13w + 9
4 and 9
Identify the number of terms, coefficients,
variables, and constants
1. 4w + 3f – 9p + 2c2 – 10
2. 7h + 9k * 3d – 11m
3. 12 - 14d ÷ 7j – 2z
4. 5a3 + 129
End of day 1
Objective
The student will be able to:
• Review parts of an algebraic
expression
• Understand and use the
distributive property
The Distributive Property
The 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
Example #2
3(m - 4)
3•m-3•4
3m - 12
Example #3
2(y + 3)
2•y+2•3
2y + 6
Which statement demonstrates the
distributive property incorrectly?
1.
2.
3.
4.
3(x + y + z) = 3x + 3y + 3z
(a + b) c = ac + bc
5(2 + 3x) = 10 + 3x
6(3k - 4) = 18k - 24
Answer Now
Like Terms are terms with the same
variable AND exponent.
To simplify expressions with like
terms, simply combine the like
terms.
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.
Which of the following is the simplified
form of
7x – 4x ?
1.
2.
3.
4.
-4
3x
-3x
4
Answer Now
2
2
8x  2x  5a  a
2
8x and 2 x
2
are like terms
are like terms
5a and a
The above expression simplifies to:
2
10x  6a
Simplify
1) 5a + 7a
12a
2) 6.1y - 3.2y
2.9y
3) 4x2y + x2y
5x2y
4) 3m2n + 10mn2 + 7m2n - 4mn2
10m2n + 6mn2
5) 13a + 8a + 6b
21a + 6b
6) 4d + 6a2 - d + 12a2
18a2 + 3d
3y
y
7)

4 4
y
3y 1y
4y


 1y
4
4
4
Which of the following is the simplified
form of
5x + 4 + 7x + 14 ?
1.
2.
3.
4.
-12x + 14
12x + 14
2x - 18
12x – 18
Answer Now
If a triangle has sides 3x - 2, 5 - x and 2x - 5,
what is the perimeter of the triangle?
1.
2.
3.
4.
4x - 2
4x + 2
5x - 2
5x - 7
Answer Now
Which figure below models the simplification
of - 4x - 5 + 7x + 7 using these tiles?
1.
2.
3.
4.
Answer Now
Bonus! Which of the following is the
simplified form of a + 3a + 4(9 + a) ?
1.
2.
3.
4.
-36
3a - 36
8a - 36
8a + 36
Answer Now