Properties of Real Numbers Commutative Associative Distributive Identity
Properties of Real Numbers Commutative Associative Distributive Identity + × Inverse + ×
Commutative Properties Changing the order of the numbers in + or x will not change the result. Commutative Property of Addition states: 2 + 3 = 3 + 2 or a + b = b + a. Commutative Property of Multiplication states: 4 • 5 = 5 • 4 or ab = ba.
Associative Properties Changing the grouping of the numbers in + or x will not change the result. Associative Property of Addition states: 3 + (4 + 5)= (3 + 4)+ 5 or a + (b + c)= (a + b)+ c Associative Property of Multiplication states: (2 • 3) • 4 = 2 • (3 • 4) or (ab)c = a(bc)
Distributive Property Multiplication distributes over addition. x x
Additive Identity Property There exists a unique number 0 such that zero preserves identities under addition. a + 0 = a and 0 + a = a In other words adding zero to a number does not change its value.
Multiplicative Identity Property There exists a unique number 1 such that the number 1 preserves identities under multiplication. a ∙ 1 = a and 1 ∙ a = a In other words multiplying a number by 1 does not change the value of the number.
Additive Inverse Property For each real number a there exists a unique real number –a such that their sum is zero. a + (-a) = 0 In other words opposites add to zero.
Multiplicative Inverse Property For each real number a there exists a unique real number product is 1. such that their
Let’s play “Name that property!”
State the property or properties that justify the following. 3+2=2+3 Commutative Property
State the property or properties that justify the following. 10(1/10) = 1 Multiplicative Inverse Property
State the property or properties that justify the following. 3(11 – 10) = 33 – 30 Distributive Property
State the property or properties that justify the following. 3 + (4 + 5) = (3 + 4) + 5 Associative Property
State the property or properties that justify the following. (5 + 2) + 9 = (2 + 5) + 9 Commutative Property
1. 3+7=7+3 Commutative Property of Addition
2. 8+0=8 Identity Property of Addition
3. 6 • 4=4 • 6 Commutative Property of Multiplication
4. 17 + (-17) = 0 Inverse Property of Addition
5. 2(5) = 5(2) Commutative Property of Multiplication
6. (2 + 1) + 4 = 2 + (1 + 4) Associative Property of Addition
7. even + even = even Closure Property
8. 3(2 + 5) = 3 • 2 + 3 • 5 Distributive Property
9. 6(7 • 8) = (6 • 7)8 Associative Property of Multiplication
10. 5 • 1=5 Identity Property of Multiplication
11. 1 5/ + 0 = 7 1 5/ 7 Identity Property of Addition
12. 6(3 – 2) = 18 – 12 Distributive Property
13. 2+3=3+2 Commutative Property of Addition
14. ab = ba Commutative Property of Multiplication
15. a+0=a Identity Property of Addition
16. a(bc) = (ab)c Associative Property of Multiplication
17. a • 1 = a Identity Property of Multiplication
18. a +b = b + a Commutative Property of Addition
19. a(b + c) = ab + ac Distributive Property
20. a + (b + c) = (a +b) + c Associative Property of Addition
21. a + (-a) = 0 Inverse Property of Addition
HOMEWORK TIME! Week: 5 Assignment: Identifying Properties Due Date: A day: 08/25/17 - Friday B day: 08/24/17 - Thursday
- Slides: 36