Upload
barbra-porter
View
215
Download
0
Tags:
Embed Size (px)
Citation preview
Properties of REAL Properties of REAL NumbersNumbers
OppositesOpposites
Two real numbers that are the same distance from the origin of the real number line are
opposites of each other.
EXAMPLESEXAMPLES-100 AND 100
2 AND -2
04/21/23 www.numberbender.com 2
ReciprocalsReciprocals
04/21/23 www.numberbender.com 3
Absolute ValueAbsolute Value
04/21/23 www.numberbender.com 4
Commutative Property of AdditionCommutative Property of Addition
a + b = b + aa + b = b + aWhen adding two numbers, the order of the
numbers does not matter.
EXAMPLESEXAMPLES2 + 3 = 3 + 2
(-5) + 4 = 4 + (-5)
04/21/23 www.numberbender.com 5
Commutative Property of MultiplicationCommutative Property of Multiplication
a × b = b × aa × b = b × aWhen multiplying two numbers, the order of the
numbers does not matter.
EXAMPLESEXAMPLES2 × 3 = 3 × 2
(-3) × 24 = 24 × (-3)
04/21/23 www.numberbender.com 6
Associative Property of AdditionAssociative Property of Addition
a + (b + c) = (a + b) + ca + (b + c) = (a + b) + cWhen three numbers are added, it makes no
difference which two numbers are added first.
EXAMPLESEXAMPLES2 + (3 + 5) = (2 + 3) + 5(4 + 2) + 6 = 4 + (2 + 6)
04/21/23 www.numberbender.com 7
Associative Property of MultiplicationAssociative Property of Multiplication
a(bc) = (ab)ca(bc) = (ab)cWhen three numbers are multiplied, it makes no
difference which two numbers are multiplied first.
EXAMPLESEXAMPLES2 × (3 × 5) = (2 × 3) × 5(4 × 2) × 6 = 4 × (2 × 6)
04/21/23 www.numberbender.com 8
Distributive PropertyDistributive Property
a(b + c) = ab + aca(b + c) = ab + acMultiplication distributes over addition.
EXAMPLESEXAMPLES2 (3 + 5) = (2 × 3) + (2 × 5)
(4 + 2) × 6 = (4 × 6) + (2 × 6)
04/21/23 www.numberbender.com 9
Additive Identity PropertyAdditive Identity Property
The additive identity property states that if 0 is added to a number, the result is that number.
EXAMPLEEXAMPLE3 + 0 = 0 + 3 = 3
04/21/23 www.numberbender.com 10
Multiplicative Identity PropertyMultiplicative Identity Property
The multiplicative identity property states that if a number is multiplied by 1, the result is that
number.
EXAMPLEEXAMPLE5 1 = 1 5 = 5
04/21/23 www.numberbender.com 11
Additive Inverse PropertyAdditive Inverse Property
The additive inverse property states that opposites add to zero.
EXAMPLEEXAMPLE7 + (-7) = 0 and -4 + 4 = 0
04/21/23 www.numberbender.com 12
Multiplicative Inverse PropertyMultiplicative Inverse Property
04/21/23 www.numberbender.com 13
PRACTICE EXERCISESPRACTICE EXERCISES
04/21/23 www.numberbender.com 14
Identify which property justifies each of the following:
4 × (8 × 2) = (4 × 8) × 2
04/21/23 www.numberbender.com 15
Identify which property justifies each of the following:
6 + 8 = 8 + 6
04/21/23 www.numberbender.com 16
Identify which property justifies each of the following:
12 + 0 = 12
04/21/23 www.numberbender.com 17
Identify which property justifies each of the following:
5(2 + 9) = (5 × 2) + (5 × 9)
04/21/23 www.numberbender.com 18
04/21/23 www.numberbender.com 19
Identify which property justifies each of the following:
5 × 24 = 24 × 5
04/21/23 www.numberbender.com 20
Identify which property justifies each of the following:
18 + (-18) = 0
04/21/23 www.numberbender.com 21
Identify which property justifies each of the following:
-34 × 1 = -34
04/21/23 www.numberbender.com 22