Properties of AlgebraProperties of Algebra

Commutative Commutative Property Property

of Additionof Addition Definition – The sum of a group Definition – The sum of a group

of numbers is the same of numbers is the same regardless of the order in which regardless of the order in which

the numbers are arranged.the numbers are arranged.

Example – 7+2=2+7Example – 7+2=2+7 Example – 12+10=10+12Example – 12+10=10+12

Commutative Commutative Property Property

of Multiplicationof Multiplication Definition – The product of a Definition – The product of a

group of numbers is the same group of numbers is the same regardless of the order in which regardless of the order in which

the numbers are arranged.the numbers are arranged.

Example – 3 x 2 = 2 x 3Example – 3 x 2 = 2 x 3 Example – 24 x 11 = 11 x 24Example – 24 x 11 = 11 x 24

Associative Associative Property Property

of Additionof Addition Definition – The sum of a set of Definition – The sum of a set of

numbers is the same no matter numbers is the same no matter how the numbers are grouped.how the numbers are grouped.

Example – 2+(3+4)=(2+3)+4Example – 2+(3+4)=(2+3)+4 Example – Example –

(10+12)+14=10+(12+14)(10+12)+14=10+(12+14)

Associative Associative Property Property

of Multiplicationof Multiplication Definition – The product of a set Definition – The product of a set

of numbers is the same no of numbers is the same no matter how the numbers matter how the numbers

aregrouped.aregrouped.

Example – 5x(3x2)=(5x3)x2Example – 5x(3x2)=(5x3)x2 Example – 12x(16x10) = Example – 12x(16x10) =

(12x16)x10(12x16)x10

Distributive PropertyDistributive Property

Definition – The sum of two Definition – The sum of two addends multiplied by a number addends multiplied by a number is the sum of the product of each is the sum of the product of each addend and the number.addend and the number.

Example – 5(20 + 1)= 5x20+ 5x1Example – 5(20 + 1)= 5x20+ 5x1 Example – 6(7 + 15)= 6x7+ 6x15Example – 6(7 + 15)= 6x7+ 6x15

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Question 1Question 1 What property is shown here?What property is shown here?

34 + 27 = 27 + 3434 + 27 = 27 + 34

A. Commutative Property of AdditionA. Commutative Property of AdditionB. Commutative Property of B. Commutative Property of

MultiplicationMultiplicationC. Associative Property of AdditionC. Associative Property of AdditionD. Associative Property of D. Associative Property of

MultiplicationMultiplication

Answer 1Answer 1 What property is shown here?What property is shown here?

34 + 27 = 27 + 3434 + 27 = 27 + 34

Answer: Answer: A. Commutative Property of AdditionA. Commutative Property of Addition

Question 2Question 2 What property is shown here?What property is shown here?

48 + (73 + 16) = (48 + 73) + 1648 + (73 + 16) = (48 + 73) + 16

A. Commutative Property of AdditionA. Commutative Property of AdditionB. Commutative Property of MultiplicationB. Commutative Property of MultiplicationC. Associative Property of AdditionC. Associative Property of AdditionD. Associative Property of MultiplicationD. Associative Property of Multiplication

Answer 2Answer 2 What property is shown here?What property is shown here?

48 + (73 + 16) = (48 + 73) + 48 + (73 + 16) = (48 + 73) + 1616

Answer: Answer: C. Associative Property of AdditionC. Associative Property of Addition

Question 3Question 3 What property is shown here?What property is shown here?18 x (22 x 49) = (18 x 22) x 4918 x (22 x 49) = (18 x 22) x 49

A. Commutative Property of AdditionA. Commutative Property of AdditionB. Commutative Property of B. Commutative Property of

MultiplicationMultiplicationC. Associative Property of AdditionC. Associative Property of AdditionD. Associative Property of D. Associative Property of

MultiplicationMultiplication

Answer 3Answer 3 What property is shown here?What property is shown here?18 x (22 x 49) = (18 x 22) x 4918 x (22 x 49) = (18 x 22) x 49

Answer: Answer: D. Associative Property of D. Associative Property of

MultiplicationMultiplication

Question 4Question 4 What property is shown here?What property is shown here?

66 x 37 = 37 x 6666 x 37 = 37 x 66

A. Commutative Property of AdditionA. Commutative Property of AdditionB. Commutative Property of B. Commutative Property of

MultiplicationMultiplicationC. Associative Property of AdditionC. Associative Property of AdditionD. Associative Property of D. Associative Property of

MultiplicationMultiplication

Answer 4Answer 4 What property is shown here?What property is shown here?

66 x 37 = 37 x 6666 x 37 = 37 x 66

Answer: Answer: B. Commutative Property of B. Commutative Property of

MultiplicationMultiplication

Question 5Question 5 Which shows the Which shows the

Commutative Property of Commutative Property of Addition?Addition?

A. 7+2+3=3+7+8A. 7+2+3=3+7+8B. 7+(2+3)=(2+2)+7B. 7+(2+3)=(2+2)+7C. 7+2+3=2+3+7C. 7+2+3=2+3+7D. 7+2+3=5+7+2D. 7+2+3=5+7+2

Answer 5Answer 5 Which shows the Which shows the

Commutative Property of Commutative Property of Addition?Addition?

Answer: Answer: C. 7+2+3=2+3+7C. 7+2+3=2+3+7

Question 6Question 6 Which shows the Associative Which shows the Associative

Property of Multiplication?Property of Multiplication?

A. (6 x 5) x 2 = 6 x (5 x 2)A. (6 x 5) x 2 = 6 x (5 x 2)B. 6 x 5 x 2 = 5 x 6 x 2B. 6 x 5 x 2 = 5 x 6 x 2C. 5 x (6 x 2) = 5 x (6 x 2)C. 5 x (6 x 2) = 5 x (6 x 2)D. 5 x 6 x 2 = 6 x 10D. 5 x 6 x 2 = 6 x 10

Answer 6Answer 6 Which shows the Which shows the

Associative Property of Associative Property of Multiplication?Multiplication?

Answer: Answer: A. (6 x 5) x 2 = 6 x (5 x 2)A. (6 x 5) x 2 = 6 x (5 x 2)

Question 7Question 7 Which shows the Which shows the

Commutative Property of Commutative Property of Multiplication?Multiplication?

A. 7 x 8 x 4 = 7 x 16 x 2A. 7 x 8 x 4 = 7 x 16 x 2B. (7 x 8) x 4 = 7 x (2 x 16)B. (7 x 8) x 4 = 7 x (2 x 16)C. 7 x 8 x 4 = 8 x 4 x 7C. 7 x 8 x 4 = 8 x 4 x 7D. 7 x (8 x 4) = (7 x 8) x 4D. 7 x (8 x 4) = (7 x 8) x 4

Answer 7Answer 7 Which shows the Which shows the

Commutative Property of Commutative Property of Multiplication?Multiplication?

Answer: Answer: C. 7 x 8 x 4 = 8 x 4 x 7C. 7 x 8 x 4 = 8 x 4 x 7

Question 8Question 8 Which shows the Associative Which shows the Associative

Property of Addition?Property of Addition?

A. 6 + 9 + 12 = 12 + 6 + 9A. 6 + 9 + 12 = 12 + 6 + 9B. 6 + (9 + 12) = (6 + 9) + 12B. 6 + (9 + 12) = (6 + 9) + 12C. 6 + 9 + 12 = 15 + 12C. 6 + 9 + 12 = 15 + 12D. 6 + (9 + 12) = (9 + 12) + 6D. 6 + (9 + 12) = (9 + 12) + 6

Answer 8Answer 8 Which shows the Which shows the

Associative Property of Associative Property of Addition?Addition?

Answer: Answer: B. 6 + (9 + 12) = (6 + 9) + 12B. 6 + (9 + 12) = (6 + 9) + 12

Question 9Question 9 Which is the best answer for:Which is the best answer for:

62 + (13 + 4) = ______62 + (13 + 4) = ______A. 82A. 82B. 79B. 79C. 74C. 74D. 88D. 88

Answer 9Answer 9 Which is the best answer Which is the best answer

for:for:62 + (13 + 4) = ______62 + (13 + 4) = ______

Answer: Answer: B. 79B. 79

Question 10Question 10 Which is the best answer for:Which is the best answer for:

43 x (2 x 5) = _____43 x (2 x 5) = _____A. 86A. 86B. 345B. 345C. 430C. 430D. 215D. 215

Answer 10Answer 10 Which is the best answer Which is the best answer

for:for:43 x (2 x 5) = _____43 x (2 x 5) = _____

Answer: Answer: C. 430C. 430