Module 0, Assignment 4
Commutative Properties:
Addition:
a+b=b+a
Multiplication: ab = ba
*These properties state that the order in which any two numbers are added or multiplied does
not change their sum or product.
Associative Properties:
Addition:
(a + b) + c = a + (b + c)
Multiplication: (ab)c = a(bc)
*These properties state that the way in which three numbers are grouped does not change their
sum or product.
Distributive Property of Multiplication over Addition or Subtraction
a(b + c) = ab + ac
or
a(b – c) = ab – ac
Examples:
Use the distributive property to write each expression without parentheses, then
simplify if possible.
1)
2(x + y)
2)
-5(-3 + 2z)
3)
5(x + 3y – 2z)
4)
-1(2 – y)
5)
-(3 + x – w)
6)
𝟏
(𝟔𝒙 +
𝟐
7)
Use the distributive property to write the sum as a product.
−7 ∙ 𝑥 + (−7) ∙ 𝑦
Use the order of operations to simplify.
8)
−𝟗𝟐 +𝟒𝟕
𝟕−𝟗
10)
|𝟕−𝟖|+ |𝟏𝟓−𝟏𝟕|
|𝟖(−𝟑)|
9)
𝟕−𝟓(−𝟒)
𝟔−𝟑(−𝟓)
𝟏𝟒) + 𝟏𝟎