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## Math Properties

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**Some rules to live by in Pre - Algebra class and beyond…**Math Properties**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: The Multiplicative Property of Zero**Which of the examples to the left does not demonstrate the**MULTIPLICATIVE PROPERTY of ZERO? 1. 7 x 0 = _____ 2. 3x(0) = _____ 3. -8 x 0 = _____ 4. 35 – (52 + √100) = _____5. 14x (32 – 8 * 4) = _____ 6. 19x (25 – 52) = _____**Number Four (4) WAS NOT the Multiplicative Property of Zero**at work – it was simple subtraction….. MMMUAHAHA!**Any number multiplied by the number zero (0) is:**0 The Multiplicative Property of Zero**Any number added to zero is still the same number it was.**Additive Identity**The Additive Identify Property**Complete each of these examples. Which examples do not demonstrate the Additive Identity Property? 17 + 0 = _____ 45 + (35 * 0) = _____ 77 + (02) = _____ 54 + (17 – 17)5 = _____ -45 + 0 = _____ 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! ! ! ! !**Solve these problems, and determine which two (2) ARE NOT**examples of the Multiplicative Identity Property! • 125 x 1 = _____ • 2 x 51 = _____ • 13 x (45 – 44) = _____ • 63 x 180 = _____ • 14 x √1 = _____ • 5 x 1-2 = _____ 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.**B-B-R-A-A-I-N-S!!!**B-R-R-A-A-I-N-S!!! #2 #6**EXAMPLE A. -6 +6 = 0**• EXAMPLE B. 54 + (-54) = 0 • EXAMPLE C. X + (-X) = 0 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?**Multiplicative Property of Zero**• Additive Inverse • Additive Identity • Multiplicative Identity • 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 Matching Review.**The Multiplicative Inverse Property states that,**“When multiplying a number by its inverse or reciprocal, the product is one.” The Multiplicative Inverse Property**Solve these examples, and identify which of them does**notillustrate the Multiplicative Inverse Property. • 4 x ¼ = _____ • ½ x 2 = _____ • 5 x (-5) = _____ • 15 x ⅟15 = _____ • 1 x 1 = _____ The Multiplicative Inverse - Examples The multiplicative inverse property is the notion that any number multiplied by its inverse – or reciprocal – is one.**Three (3) is not an example of the Multiplicative Inverse,**children. The reciprocal of 5 is 1/5th, not -5! Muawahahahaha!**The Commutative Property of Addition**Changing 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!**Which of the following equations is not true and DOES NOT**demonstrate the commutative property of addition? • 4 + 5 + 7 = 7 + 4 + 5 • 6 + 2 + 14 = 14 + 2 + 6 • (7 + 9 + 6)2 = (9 + 6 + 7)2 • (6 + 72) = (62 + 7) • (72 + √49 + 22) = (22 + 72 + √49) Commutative Property of Addition The Commutative Property of Addition says that changing the order of the terms in an addition problem will not change the sum of the terms.**Listen to me little children, number four (4) was stone cold**lying to yo’ face! Can’t truss it!**The Commutative Property of Multiplication**Changing 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?**Evaluate each of the terms below to determine whether or not**theydemonstrate the commutative property of multiplication. • 4 x5 x 2 ⃝ 2 x 4 x5 • 6 x 2 x3 ⃝ 3 x 2 x 6 • (2 x 3 x 1)2 ⃝ (3 x 1 x 2)2 • (-2) x 4 x 2 x 7 ⃝ 7 x 4 x 2 x (-2) • (3 x √9 x22) ⃝ (22x 3 x √9) • 4 x 2 x (-6) ⃝ (-6) x 4 x 2 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.**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) Associative Properties**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) Associate Property of Addition**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) Associative Property of Multiplication**Negative one hundred five (-105), dude! You know it is so**true, baby! Always!**Commutative Property of Addition B. Commutative Property**of Multiplication • Additive Inverse Property D. Multiplicative Inverse Property • Additive Identity Property F. Multiplicative Identity Property • 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) Matching Review, Number 2**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 The Distributive Property