math properties
DESCRIPTION
Some rules to live by in Pre - Algebra class and beyond…. Math Properties. The Multiplicative Property of Zero. Any number multiplied by the number zero (0) will be zero (0). - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Math Properties](https://reader036.vdocument.in/reader036/viewer/2022062814/56816783550346895ddc94dc/html5/thumbnails/1.jpg)
Math Properties
Some rules to live by in Pre - Algebra class and beyond…
![Page 2: Math Properties](https://reader036.vdocument.in/reader036/viewer/2022062814/56816783550346895ddc94dc/html5/thumbnails/2.jpg)
The Multiplicative Property of Zero
![Page 3: Math Properties](https://reader036.vdocument.in/reader036/viewer/2022062814/56816783550346895ddc94dc/html5/thumbnails/3.jpg)
The Multiplicative Property of Zero
Any number multiplied by the number zero (0) will be zero (0).
If you start with nothing, it doesn’t matter how many times you multiply it, you still don’t have anything, right? Zippo, zilch, nada, nothing!
Consider all of the examples which follow:
![Page 4: Math Properties](https://reader036.vdocument.in/reader036/viewer/2022062814/56816783550346895ddc94dc/html5/thumbnails/4.jpg)
1. 7 x 0 = _____
2. 3x (0) = _____
3. -8 x 0 = _____
4. 35 – (52 + √100) = _____
5. 14x (32 – 8 * 4) = _____
6. 19x (25 – 52) = _____
Which of the examples to the
left does not demonstrate the
MULTIPLICATIVE
PROPERTY of
ZERO?
![Page 5: Math Properties](https://reader036.vdocument.in/reader036/viewer/2022062814/56816783550346895ddc94dc/html5/thumbnails/5.jpg)
Number Four (4) WAS NOT the
Multiplicative Property of Zero at work – it was simple subtraction…..
MMMUAHAHA!
![Page 6: Math Properties](https://reader036.vdocument.in/reader036/viewer/2022062814/56816783550346895ddc94dc/html5/thumbnails/6.jpg)
The Multiplicative Property of Zero
Any number multiplied by the number zero (0) is:
0
![Page 7: Math Properties](https://reader036.vdocument.in/reader036/viewer/2022062814/56816783550346895ddc94dc/html5/thumbnails/7.jpg)
Additive IdentityAny number added to zero is still the same number it was.
![Page 8: Math Properties](https://reader036.vdocument.in/reader036/viewer/2022062814/56816783550346895ddc94dc/html5/thumbnails/8.jpg)
The Additive Identify PropertyComplete each of these examples. Which examples do not demonstrate the Additive Identity Property?
1. 17 + 0 = _____
2. 45 + (35 * 0) = _____
3. 77 + (02) = _____
4. 54 + (17 – 17)5 = _____
5. -45 + 0 = _____
6. 35x + (7 – 7)2 = _____
![Page 9: Math Properties](https://reader036.vdocument.in/reader036/viewer/2022062814/56816783550346895ddc94dc/html5/thumbnails/9.jpg)
They are all examples of the Additive Identity
Property, silly little children!!!
B-R-A-A-I-N-S-S! ! ! !
B-R-A-A-I-N-S-S! ! ! ! !
B-R-A-A-I-N-S-S! ! ! ! !
![Page 10: Math Properties](https://reader036.vdocument.in/reader036/viewer/2022062814/56816783550346895ddc94dc/html5/thumbnails/10.jpg)
Multiplicative Identity
![Page 11: Math Properties](https://reader036.vdocument.in/reader036/viewer/2022062814/56816783550346895ddc94dc/html5/thumbnails/11.jpg)
The Multiplicative Identity Property The multiplicative identify property is the very simple notion that any number multiplied by the number one is still that number.
Solve these problems, and determine which two (2) ARE NOT examples of the Multiplicative Identity Property!
1. 125 x 1 = _____
2. 2 x 51 = _____
3. 13 x (45 – 44) = _____
4. 63 x 180 = _____
5. 14 x √1 = _____
6. 5 x 1-2 = _____
![Page 12: Math Properties](https://reader036.vdocument.in/reader036/viewer/2022062814/56816783550346895ddc94dc/html5/thumbnails/12.jpg)
#2
#6
B-B-R-A-A-I-N-S!!!
B-R-R-A-A-I-N-S!!!
![Page 13: Math Properties](https://reader036.vdocument.in/reader036/viewer/2022062814/56816783550346895ddc94dc/html5/thumbnails/13.jpg)
The Additive Inverse Property
![Page 14: Math Properties](https://reader036.vdocument.in/reader036/viewer/2022062814/56816783550346895ddc94dc/html5/thumbnails/14.jpg)
The Additive Inverse of a Number The Additive Inverse property is defined in this manner:
When adding a number to its negative or its opposite, the result is zero!
The additive inverse of seven (7), for example, is negative seven (-7). 7 + (-7) = 0. Right?
EXAMPLE A. -6 +6 = 0
EXAMPLE B. 54 + (-54) = 0 EXAMPLE C. X + (-X) = 0
![Page 15: Math Properties](https://reader036.vdocument.in/reader036/viewer/2022062814/56816783550346895ddc94dc/html5/thumbnails/15.jpg)
Matching Review.
A. Multiplicative Property of ZeroB. Additive InverseC. Additive IdentityD. Multiplicative IdentityE. Multiplicative Inverse
_____1. 563 x 580 = 563 _____2. 56 + (-56) = 0
_____3. 2 x ½ = 1 _____4. 114 x (7-7)3 = 0
_____5. 67 x 1 = 67 _____6. 13 + (35 x 0) = 13
![Page 16: Math Properties](https://reader036.vdocument.in/reader036/viewer/2022062814/56816783550346895ddc94dc/html5/thumbnails/16.jpg)
The Multiplicative Inverse Property
![Page 17: Math Properties](https://reader036.vdocument.in/reader036/viewer/2022062814/56816783550346895ddc94dc/html5/thumbnails/17.jpg)
The Multiplicative Inverse Property
The Multiplicative Inverse Property states that,
“When multiplying a number by its inverse or reciprocal, the product is one.”
![Page 18: Math Properties](https://reader036.vdocument.in/reader036/viewer/2022062814/56816783550346895ddc94dc/html5/thumbnails/18.jpg)
The Multiplicative Inverse - ExamplesThe multiplicative inverse property is the notion that any number multiplied by its inverse – or reciprocal – is one.
Solve these examples, and identify which of them does not illustrate the Multiplicative Inverse Property.
1. 4 x ¼ = _____
2. ½ x 2 = _____
3. 5 x (-5) = _____
4. 15 x ⅟15 = _____
5. 1 x 1 = _____
![Page 19: Math Properties](https://reader036.vdocument.in/reader036/viewer/2022062814/56816783550346895ddc94dc/html5/thumbnails/19.jpg)
Three (3) is not an
example of the
Multiplicative Inverse,
children. The reciprocal of 5 is 1/5th, not
-5! Muawahahah
aha!
![Page 20: Math Properties](https://reader036.vdocument.in/reader036/viewer/2022062814/56816783550346895ddc94dc/html5/thumbnails/20.jpg)
The Commutative Property of Multiplication and Addition
![Page 21: Math Properties](https://reader036.vdocument.in/reader036/viewer/2022062814/56816783550346895ddc94dc/html5/thumbnails/21.jpg)
The Commutative Property of AdditionChanging the order of the terms used when multiplying or adding does not change the product or sum. So whether you add two (2) pumpkins + four (4) pumpkins or four (4) pumpkins + two (2) pumpkins, there’s still six (6) pumpkins up in here!
![Page 22: Math Properties](https://reader036.vdocument.in/reader036/viewer/2022062814/56816783550346895ddc94dc/html5/thumbnails/22.jpg)
Commutative Property of AdditionThe Commutative Property of Addition says that changing the order of the terms in an addition problem will not change the sum of the terms.
Which of the following equations is not true and DOES NOT demonstrate the commutative property of addition?
1. 4 + 5 + 7 = 7 + 4 + 5
2. 6 + 2 + 14 = 14 + 2 + 6
3. (7 + 9 + 6)2 = (9 + 6 + 7)2
4. (6 + 72) = (62 + 7)
5. (72 + √49 + 22) = (22 + 72 + √49)
![Page 23: Math Properties](https://reader036.vdocument.in/reader036/viewer/2022062814/56816783550346895ddc94dc/html5/thumbnails/23.jpg)
Listen to me little
children, number four (4) was stone cold lying to
yo’ face! Can’t truss
it!
![Page 24: Math Properties](https://reader036.vdocument.in/reader036/viewer/2022062814/56816783550346895ddc94dc/html5/thumbnails/24.jpg)
The Commutative Property of MultiplicationChanging the order of the terms used when multiplying or adding does not change the product or sum. So whether you multiply two (2) pumpkins times three (3) columns of pumpkins or three (3)pumpkins times two (2) rows pumpkins, it still six (6) pumpkins up in here! See?
![Page 25: Math Properties](https://reader036.vdocument.in/reader036/viewer/2022062814/56816783550346895ddc94dc/html5/thumbnails/25.jpg)
Commutative Property of Multiplication
The Commutative Property of Multiplication says that changing the order of the terms in a multiplication problem will not change the product of the terms.
Evaluate each of the terms below to determine whether or not they demonstrate the commutative property of multiplication.
1. 4 x 5 x 2 ⃝ 2 x 4 x 5
2. 6 x 2 x 3 ⃝ 3 x 2 x 6
3. (2 x 3 x 1)2 ⃝ (3 x 1 x 2)2
4. (-2) x 4 x 2 x 7 ⃝ 7 x 4 x 2 x (-2)
5. (3 x √9 x 22) ⃝ (22 x 3 x √9)
6. 4 x 2 x (-6) ⃝ (-6) x 4 x 2
![Page 26: Math Properties](https://reader036.vdocument.in/reader036/viewer/2022062814/56816783550346895ddc94dc/html5/thumbnails/26.jpg)
The Associative Properties of Multiplication and Addition
![Page 27: Math Properties](https://reader036.vdocument.in/reader036/viewer/2022062814/56816783550346895ddc94dc/html5/thumbnails/27.jpg)
Associative Properties
Associative Property of Addition Associative Property of Multiplication
The property which states that for all real numbers a, b, and c, their sum is always the same, regardless of their grouping:
(a + b) + c = a + (b + c)
Example: (2 + 3) + 4 = 2 + (3 + 4)
When three or more numbers are multiplied, the product is the same regardless of the grouping of the factors.
(a * b) * c = a * (b * c)
Example: (2 * 3) * 4 = 2 * (3 * 4)
![Page 28: Math Properties](https://reader036.vdocument.in/reader036/viewer/2022062814/56816783550346895ddc94dc/html5/thumbnails/28.jpg)
Associate Property of Addition
Prove that the Associative Property of Addition is true by solving for both sides of these equations.
(7 – 3) + (5 + 11) = (-3 + 11) + (7 + 5) or
(5 – 3) + (11 + 7) = (7 – 3) + (5 + 11) or
(-3 + 7) + (11 + 5) = (11 – 3) + (5 + 7)
![Page 29: Math Properties](https://reader036.vdocument.in/reader036/viewer/2022062814/56816783550346895ddc94dc/html5/thumbnails/29.jpg)
Twenty (20),
baby! Wassu
p!
![Page 30: Math Properties](https://reader036.vdocument.in/reader036/viewer/2022062814/56816783550346895ddc94dc/html5/thumbnails/30.jpg)
Associative Property of Multiplication
Prove that the Associative Property of Multiplication is true by solving for both sides of these equations.
[7 x (-3)] x (5 x 1) = [(-3) x 1)] x (7 x 5) or
[5 x (– 3)] x (1 x 7) = [7 x (– 3)] x (5 x 1) or
[(-3) x 7)] x (1 x 5) = [1 x (– 3)] x (5 x 7)
![Page 31: Math Properties](https://reader036.vdocument.in/reader036/viewer/2022062814/56816783550346895ddc94dc/html5/thumbnails/31.jpg)
Negative one hundred five (-105), dude! You know it is so true, baby!
Always!
![Page 32: Math Properties](https://reader036.vdocument.in/reader036/viewer/2022062814/56816783550346895ddc94dc/html5/thumbnails/32.jpg)
Matching Review, Number 2
A. Commutative Property of Addition B. Commutative Property of Multiplication C. Additive Inverse Property D. Multiplicative Inverse PropertyE. Additive Identity Property F. Multiplicative Identity Property G. Associative Property of Addition H. Associative Property of Multiplication
_____1. 34 x 1 = 34 _____2. 15 + 0 = 15
_____3. 5 + 6 + 11 = 6 + 11 + 5 _____4. 19 + 4 + 6 = 6 + 19 + 4
_____5. 4 x ¼ = 1 _____6. 8 + (-8) = 0
_____7. (5 + 6) + 11 = (5 + 11) + 6 _____8. 5 (6 * 4) = 4 (5 * 6)
![Page 33: Math Properties](https://reader036.vdocument.in/reader036/viewer/2022062814/56816783550346895ddc94dc/html5/thumbnails/33.jpg)
The Distributive Property
![Page 34: Math Properties](https://reader036.vdocument.in/reader036/viewer/2022062814/56816783550346895ddc94dc/html5/thumbnails/34.jpg)
The Distributive Property
Let’s learn about the Distributive Property by checking out a super-sweet video and quiz game hosted by the website below:
http://www.glencoe.com/sec/math/brainpops/00112041/00112041.html