Download Properties of Numbers

Properties of Numbers
Name ________________________
Standard: Algebra and Functions 1.3 - Simplify numerical expressions by applying properties of rational
numbers (e.g., identity, inverse, distributive, associative, commutative) and justify the process used.
Part 1 - Commutative, Associative, and Identity Properties
Commutative Property of Addition
Commutative Property of Multiplication
Associative Property of Addition
Associative Property of Multiplication
Additive Identity (Identity Prop. of Addition)
Multiplicative Identity (Identity Prop. of multiplication)
a+b=b+a
ab=ba
(a + b) + c = a + (b + c)
(a  b)  c = a  (b  c)
a+0=a
a1=a
Commutative – Order does not matter in addition (a + b = b + a)
or multiplication (a  b = b  a)
Associative – Grouping does not matter in repeated addition (a + b) + c = a + (b + c) or
repeated multiplication (a  b)  c = a  (b  c)
Identity – Adding 0 to any number or multiplying 1 to any number gets that same number.
0+a=a
1a=a
When would you EVER use properties? Suppose you’re at Rose and Mike’s down the
street and you have three items you want to buy that cost 1.65, 0.85, and 0.35. You only
have three dollars and want to know how much everything will cost. You don’t have a
calculator, pencil, or paper so you’ll have to add it all up in your head. You can use the
properties! Fancy that.
1.65 + 0.85 + 0.35 = ???
= 0.85 + 1.65 + 0.35
= 0.85 + (1.65 + 0.35)
= 085 + 2.00
= 2.85
Use the Commutative Property to change the order
Use the Associative Property to change the grouping
Add within the paranthesis
Your $3 should cover the cost (as long as there is no tax!)
Part 2 - Distributive and Inverse Properties
Distributive Property – Multiply each number inside the parentheses with the number
outside the parenthesis.
a(b + c) = ab + ac
(b + c) = ba + ca
a(b – c) = ab – ac
(b – c)a = ba – ca
Inverse Property of Addition (additive inverse) – The sum of an integer and its opposite
is zero.
1 + (–1) = 0
–1 + 1 = 0
Inverse Property of multiplication (multiplicative inverse) – When you multiply
reciprocals, their product is 1.
2

1
=1
2
A. Commutative Property of Addition
B. Commutative Property of Multiplication
C. Associative Property of Addition
D. Associative Property of Multiplication
E. Additive Identity (Identity Prop. of Addition)
F. Multiplicative Identity (Identity Prop. of multiplication)
a+b=b+a
ab=ba
(a + b) + c = a + (b + c)
(a  b)  c = a  (b  c)
a+0=a
a1=a
Properties of Numbers (Part 1)
Write the letter of the property shown.
1. (12r)s = 12(rs) ______
2. 6  1 = 6 ______
3. (9 + 7) + 6 = 9 + (7 + 6) ______
4. (3 + 2)(4 + 5) = (4 + 5)(3 + 2) ______
5. (6x)y = 6(xy) ______
6. (1 + 2)(3 + 4) = (3 + 4)(1 +2) ______
7. 6 + 0 = 6 ______
8. 6  3  2 = 3  6  2 ______
9. Which equation shows the Associative Property of Addition?
A. 8 + 6 + 7 = 8 + 7 + 6
B. 10 + 5 + 15 + 6 = 10 + (5 + 15) + 6
C. 9 + 0 + (–1) = 9 + (–1)
D. 17  (–2)  1  9 = 17  (–2)  9
10. Which property is used in the equation 12 + x + 9 = x + 12 + 9?
A. Commutative Property of Addition
B. Commutative Property of Multiplication
C. Associative Property of Addition
D. Additive Identity Property
Properties of Numbers (Part 2)
Multiply using the Distributive Property.
1. 7(3n + 2) ______
2. 4(c + 7)
3. (3x + 1)2 ______
4. Which product equals 3a – 12?
A. 4(a – 3)
B. (3 – t)4
C. (4 – t)3
D. 3(a – 4)
5. Which property does 3 + (–3) show?
A. Commutative Property of Addition
B. Associative Property of Addition
C. Inverse Property of Addition
D. Commutative Property of Multiplication
6. Which operation will change the value of any nonzero number?
A. adding zero
B. multiplying by zero
C. multiplying by one
D. dividing by one
7. Which property is used in the equation 12(x + 4) = 12x + 48?
A. Associative Property of Addition
B. Commutative Property of Addition
C. Distributive Property
D. Reflexive Property
8. Which expression is equivalent to 3x – 3y?
A. 3xy
B. 3(x – y)
C. 3x – y
D. x – 3y
9. Which of the flowing equations illustrates the inverse property of multiplication?
1
A. 5  1
5
B. 5  1 = 5
C. 5  0 = 0
D. 5  5 = 25

Answers
Part 1
1. D
2. F
3. C
4. B
5. D
6. B
7. E
8. B
9. B
10. A
Part 2
1.
2.
3.
4.
5.
6.
7.
8.
9.
21n + 14
4c + 28
6x + 2
D
C
B
C
B
A