Download Number Properties

Warm up
Determine if the set finite or infinite:
1. {Even numbers greater than 4, but less
than 100}
2. {odd numbers}
3.{Fractions less than 1}
4. -3 is a member of what group(s)?
5. 2 Is a member of what group(s)?
Warm up Answers
1. Finite
2. Infinite
3. Infinite
4. integers, rational, real
5. irrational, real
Lesson 1.2
Properties of Real Numbers
Obj: SWBAT
Justify manipulations of expressions using the
properties of real numbers.
Associative Property
The grouping of the numbers does not
change the sum or the product.
Addition:
a + (b + c) = (a + b) + c
Multiplication:
(a·b)·c = a·(b·c)
Hint: The different GROUPS of numbers can all
associate with each other….they are all
friends!
Commutative Property
The order of the numbers does not
change the sum or the product.
Addition:
a+b=b+a
Multiplication:
a·b = b·a
No matter how you flip
them…the answer is always
the same!
Distributive Property
The term outside the parentheses can
be multiplied by all the terms on the
inside of the parentheses.
a(b + c) = (a·b) + (a·c)
a(b – c) = (a·b) – (a·c)
You distribute so that everyone gets
an equal turn…get it?!
Identity Property of Addition
The sum of a number and zero is the
number.
a+0=a
+
Identity Property of
Multiplication
The product of a number and one is
the number.
a·1=a
Inverse Property of Addition
The sum of a number and its opposite
is zero.
-a + a =0
Inverse Property of
Multiplication
The product of a number and its
reciprocal is one.
1
a 1
a
a0
When might you use this property in solving equations?
Zero Product Property
The product of a number and zero is
zero.
a·0=0
Closure Property
The sum or product of any two real
numbers is a unique real number.
(If you add or multiply any two real
numbers, the sum or product is one
and only one real number.)
a + b = real number
a * b = real number
Summary
Write down two properties and tell
how you will remember them.
Classwork: BD Book 1 pg 17 in class
Homework: WS 1.3