Math Properties

Some rules to live by in Pre - Algebra class and beyond…

The Multiplicative Property of Zero

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:

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?

Number Four (4) WAS NOT the

Multiplicative Property of Zero at work – it was simple subtraction…..

MMMUAHAHA!

The Multiplicative Property of Zero

Any number multiplied by the number zero (0) is:

0

Additive IdentityAny number added to zero is still the same number it was.

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 = _____

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! ! ! ! !

Multiplicative Identity

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 = _____

#2

#6

B-B-R-A-A-I-N-S!!!

B-R-R-A-A-I-N-S!!!

The Additive Inverse Property

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

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

The Multiplicative Inverse Property

The Multiplicative Inverse Property

The Multiplicative Inverse Property states that,

“When multiplying a number by its inverse or reciprocal, the product is one.”

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 = _____

Three (3) is not an

example of the

Multiplicative Inverse,

children. The reciprocal of 5 is 1/5th, not

-5! Muawahahah

aha!

The Commutative Property of Multiplication and Addition

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!

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)

Listen to me little

children, number four (4) was stone cold lying to

yo’ face! Can’t truss

it!

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?

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

The Associative Properties of Multiplication and Addition

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)

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)

Twenty (20),

baby! Wassu

p!

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)

Negative one hundred five (-105), dude! You know it is so true, baby!

Always!

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)

The Distributive Property

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