properties of real numbers. opposites two real numbers that are the same distance from the origin of...
TRANSCRIPT
![Page 1: Properties of REAL Numbers. Opposites Two real numbers that are the same distance from the origin of the real number line are opposites of each other.EXAMPLES](https://reader035.vdocument.in/reader035/viewer/2022081516/56649e245503460f94b12432/html5/thumbnails/1.jpg)
Properties of REAL Properties of REAL NumbersNumbers
![Page 2: Properties of REAL Numbers. Opposites Two real numbers that are the same distance from the origin of the real number line are opposites of each other.EXAMPLES](https://reader035.vdocument.in/reader035/viewer/2022081516/56649e245503460f94b12432/html5/thumbnails/2.jpg)
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
![Page 3: Properties of REAL Numbers. Opposites Two real numbers that are the same distance from the origin of the real number line are opposites of each other.EXAMPLES](https://reader035.vdocument.in/reader035/viewer/2022081516/56649e245503460f94b12432/html5/thumbnails/3.jpg)
ReciprocalsReciprocals
04/21/23 www.numberbender.com 3
![Page 4: Properties of REAL Numbers. Opposites Two real numbers that are the same distance from the origin of the real number line are opposites of each other.EXAMPLES](https://reader035.vdocument.in/reader035/viewer/2022081516/56649e245503460f94b12432/html5/thumbnails/4.jpg)
Absolute ValueAbsolute Value
04/21/23 www.numberbender.com 4
![Page 5: Properties of REAL Numbers. Opposites Two real numbers that are the same distance from the origin of the real number line are opposites of each other.EXAMPLES](https://reader035.vdocument.in/reader035/viewer/2022081516/56649e245503460f94b12432/html5/thumbnails/5.jpg)
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
![Page 6: Properties of REAL Numbers. Opposites Two real numbers that are the same distance from the origin of the real number line are opposites of each other.EXAMPLES](https://reader035.vdocument.in/reader035/viewer/2022081516/56649e245503460f94b12432/html5/thumbnails/6.jpg)
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
![Page 7: Properties of REAL Numbers. Opposites Two real numbers that are the same distance from the origin of the real number line are opposites of each other.EXAMPLES](https://reader035.vdocument.in/reader035/viewer/2022081516/56649e245503460f94b12432/html5/thumbnails/7.jpg)
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
![Page 8: Properties of REAL Numbers. Opposites Two real numbers that are the same distance from the origin of the real number line are opposites of each other.EXAMPLES](https://reader035.vdocument.in/reader035/viewer/2022081516/56649e245503460f94b12432/html5/thumbnails/8.jpg)
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
![Page 9: Properties of REAL Numbers. Opposites Two real numbers that are the same distance from the origin of the real number line are opposites of each other.EXAMPLES](https://reader035.vdocument.in/reader035/viewer/2022081516/56649e245503460f94b12432/html5/thumbnails/9.jpg)
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
![Page 10: Properties of REAL Numbers. Opposites Two real numbers that are the same distance from the origin of the real number line are opposites of each other.EXAMPLES](https://reader035.vdocument.in/reader035/viewer/2022081516/56649e245503460f94b12432/html5/thumbnails/10.jpg)
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
![Page 11: Properties of REAL Numbers. Opposites Two real numbers that are the same distance from the origin of the real number line are opposites of each other.EXAMPLES](https://reader035.vdocument.in/reader035/viewer/2022081516/56649e245503460f94b12432/html5/thumbnails/11.jpg)
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
![Page 12: Properties of REAL Numbers. Opposites Two real numbers that are the same distance from the origin of the real number line are opposites of each other.EXAMPLES](https://reader035.vdocument.in/reader035/viewer/2022081516/56649e245503460f94b12432/html5/thumbnails/12.jpg)
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
![Page 13: Properties of REAL Numbers. Opposites Two real numbers that are the same distance from the origin of the real number line are opposites of each other.EXAMPLES](https://reader035.vdocument.in/reader035/viewer/2022081516/56649e245503460f94b12432/html5/thumbnails/13.jpg)
Multiplicative Inverse PropertyMultiplicative Inverse Property
04/21/23 www.numberbender.com 13
![Page 14: Properties of REAL Numbers. Opposites Two real numbers that are the same distance from the origin of the real number line are opposites of each other.EXAMPLES](https://reader035.vdocument.in/reader035/viewer/2022081516/56649e245503460f94b12432/html5/thumbnails/14.jpg)
PRACTICE EXERCISESPRACTICE EXERCISES
04/21/23 www.numberbender.com 14
![Page 15: Properties of REAL Numbers. Opposites Two real numbers that are the same distance from the origin of the real number line are opposites of each other.EXAMPLES](https://reader035.vdocument.in/reader035/viewer/2022081516/56649e245503460f94b12432/html5/thumbnails/15.jpg)
Identify which property justifies each of the following:
4 × (8 × 2) = (4 × 8) × 2
04/21/23 www.numberbender.com 15
![Page 16: Properties of REAL Numbers. Opposites Two real numbers that are the same distance from the origin of the real number line are opposites of each other.EXAMPLES](https://reader035.vdocument.in/reader035/viewer/2022081516/56649e245503460f94b12432/html5/thumbnails/16.jpg)
Identify which property justifies each of the following:
6 + 8 = 8 + 6
04/21/23 www.numberbender.com 16
![Page 17: Properties of REAL Numbers. Opposites Two real numbers that are the same distance from the origin of the real number line are opposites of each other.EXAMPLES](https://reader035.vdocument.in/reader035/viewer/2022081516/56649e245503460f94b12432/html5/thumbnails/17.jpg)
Identify which property justifies each of the following:
12 + 0 = 12
04/21/23 www.numberbender.com 17
![Page 18: Properties of REAL Numbers. Opposites Two real numbers that are the same distance from the origin of the real number line are opposites of each other.EXAMPLES](https://reader035.vdocument.in/reader035/viewer/2022081516/56649e245503460f94b12432/html5/thumbnails/18.jpg)
Identify which property justifies each of the following:
5(2 + 9) = (5 × 2) + (5 × 9)
04/21/23 www.numberbender.com 18
![Page 19: Properties of REAL Numbers. Opposites Two real numbers that are the same distance from the origin of the real number line are opposites of each other.EXAMPLES](https://reader035.vdocument.in/reader035/viewer/2022081516/56649e245503460f94b12432/html5/thumbnails/19.jpg)
04/21/23 www.numberbender.com 19
![Page 20: Properties of REAL Numbers. Opposites Two real numbers that are the same distance from the origin of the real number line are opposites of each other.EXAMPLES](https://reader035.vdocument.in/reader035/viewer/2022081516/56649e245503460f94b12432/html5/thumbnails/20.jpg)
Identify which property justifies each of the following:
5 × 24 = 24 × 5
04/21/23 www.numberbender.com 20
![Page 21: Properties of REAL Numbers. Opposites Two real numbers that are the same distance from the origin of the real number line are opposites of each other.EXAMPLES](https://reader035.vdocument.in/reader035/viewer/2022081516/56649e245503460f94b12432/html5/thumbnails/21.jpg)
Identify which property justifies each of the following:
18 + (-18) = 0
04/21/23 www.numberbender.com 21
![Page 22: Properties of REAL Numbers. Opposites Two real numbers that are the same distance from the origin of the real number line are opposites of each other.EXAMPLES](https://reader035.vdocument.in/reader035/viewer/2022081516/56649e245503460f94b12432/html5/thumbnails/22.jpg)
Identify which property justifies each of the following:
-34 × 1 = -34
04/21/23 www.numberbender.com 22