Download Distributive Property

Bell Ringer
• Solve the matrices:
Distributive Property
Mr. Haupt
CC.2.1.8.E.1
Distributive Property
• The easiest definition is the multiplication of
everything inside a set of parentheses by what is
on the outside.
Some Important Words
• Term – a term is a number, variable, or a combination of a
number and a variable.
• For example: 3, b, 4x, -9y2
• Constant – a constant is a number with no variable attached.
• Coefficient – a coefficient is a number attached to a variable
and is what you multiply the variable by.
• For example: in 7g the coefficient is the 7
• Like Terms – like terms have the exact same variable factors.
• 7x and 3x are like terms, but 7x and 3x2 are not
Like Terms
• Combine the like terms:
12 x + 7y – 3x
-6x2 + 4x + 13x2
4w + 6j – 5w2
14b + 14c – 8a2 + 7a – 5b + 2c – a2
Time to Distribute
• Simplify and combine like terms:
7(a + 4)
12b + 3(5 – b)
-5q – q(4 + q)
16 + 3(7a + 2) – 8(10 – 3a)
Additional Properties of Numbers
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Commutative Property of Addition
Commutative Property of Multiplication
Associative Property of Addition
Associative Property of Multiplication
Identity Property of Addition
Identity Property of Multiplication
Inverse Property of Addition
Inverse Property of Multiplication
Symmetric Property
Commutative Property of
Addition
• a+b=b+a
• Example: 7 + 3 = 3 + 7
Commutative Property of
Multiplication
• a*b=b*a
• Example: 3 * 7 = 7 * 3
Associative Property of
Addition
• (a + b) + c = a + (b + c)
• Example: (6 + 4) + 5 = 6 + (4 + 5)
Associative Property of
Multiplication
• (a * b) * c = a * (b * c)
• Example: (6 * 4) * 5 = 6 * (4 * 5)
Identity Property of Addition
• a+0=a
• Example: 8 + 0 = 8
Identity Property of
Multiplication
• a*1=a
• Example: 8 * 1 = 8
Inverse Property of Addition
• For every a there is an additive inverse –a so that a + (-a) = 0
• Example: 4 + (-4) = 0
Inverse Property of
Multiplication
• For every a that is not zero there is a multiplicative inverse,
1/a so that a(1/a) = 1
• Example: 5 * 1/5 = 1
Symmetric Property
• If a = b then b = a
• Example: 2 * 3 = 6, so 6 = 2 * 3