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Properties of basic operations

Rules Rules and laws are a part of our society and they help to maintain order and peace. There are laws of nature, such as gravity, and laws of science, and even laws of mathematics. Over the next few days you will learn about properties of the basic operations of mathematics (Properties by which numbers abide by).

Schedule: Monday- Zero Property and Identity property. Tuesday- Commutative property. Wednesday- Associative property. Thursday- Distributive property. Friday- All of them together.

Page 110 Zero was a number that took a long time to come on the scene as numbers were developed but it is considered one of the five most important numbers of all. The other four numbers are 1, ∏, e, and i. The number 1 was probably the first number ever learned by students. The number ∏ will be studied later in this school year. The numbers e and i will not be studied until high school.

Zero Zero has the unique property that when it is multiplied by any number, the answer is zero. Based on that concept, if two numbers are multiplied together and the result is zero, then at least one of those numbers is zero. This information is very important for you to know for future work in algebra. Examples: 3 x 0 = 0, 3.7 x 0 = 0, 0x0=0, ½ x 0=0

Identity Properties of Addition Adding zero to a number is quite different from multiplying by zero. Zero is called the additive identity because adding zero to any number does not affect the value of the number. Given an amount of money, adding nothing or no money to a specified amount of money does not change the amount of money. Examples: = = /5 + 0 = 4/5

If zero is subtracted from any number, the value is still that number. Just like adding zero, subtracting nothing from a specified amount of money does not affect the amount of money. Examples: 5 – 0 = – 0 = /5 – 0 = 4/5

Identity Properties of Multiplication The number one functions in multiplication like zero functions in addition. One is called the multiplicative identity because multiplying or dividing by one does not change the value of the number. Examples: 5 x 1 = x 1 = 1.4 3/5 x 1 = 3/5 5 ÷ 1 = ÷ 1 = 1.4

Work and label each problem as an example of the zero property of multiplication, the identity property of addition/subtraction, or the identity property of multiplication/division _____ = 53 ___________________________________ 45 x _____ = 0 ___________________________________ x _____= ______________________________ ¾ x ______= 0 ____________________________________ 855- _______= 855 ________________________________ ______= 1.56 _______________________________ _____ + 0 = 457 __________________________________ 85 ÷_____= 85 ___________________________

Homework Compare and contrast Multiplication Property of Zero and the Identity Property of Addition or Multiplication.

Closure: You have studied two properties today— identity and zero. Remember, identity you get the same number and zero you get zero as answers.