Property
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PROPERTIES OF THE OPERATION OF INTEGERS I.
COMMUTATIVE PROPERTY Given a = 3, b = -2, and c = 7 1. Commutative Property of Addition Fill in the blank by the right number i. a+b=3+…=… ii. b + a = (-2) + … = … So a+b=b+… iii. a+c=…+…=… iv. c+a=…+…=… So a + c = c + … v. b+c=…+…=… vi. c+b=…+…=… So b + c = … + … 2. Commutative Property of Multiplication Fill in the blank by the right number i. axb=3x…=… ii. b x a = (-2) x … = … So axb=bx… iii. axc=…x…=… iv. cxa=…x…=… So a x c = … x … v. bxc=…x…=… vi. cxb=…x…=… So b x c = … x …
II.
ASSOCIATIVE PROPERTY Given a = 4, b = 5, and c = -3 1. Associative Property of Addition Fill in the blank by the right number i. (a + b) + c = (… + 5) + … = … ii. (a + c) + b = (4 + …) + … = … iii. (b + c) + a = (… + …) + … = … So (a + b) + c = (a + …) + … = (… + …) + … 2. Associative Property of Multiplication Fill in the blank by the right number i. (a x b) x c = (4 x 5) x … = 20 x … = … ii. (a x c) x b = (… x (-3)) x … = … x … = …
iii.
III.
(b x c) x a = (… x …) x … = … x … = … So (a x b) x c = (… + …) x … = (… x …) x …
DISTRIBUTIVE PROPERTY Given a = 5, b = 2, and c = 4 1. Distributive Property Over Addition Fill in the blank by the right number i. a x (b + c) = 5 x ( 2 + 4) = 5 x … = … ii. (a x b) + (a x c) = (5 x 2) + (… x …) = … + … = … So a x (b + c) = (a x b) + (… x …) iii. b x (a + c) = 2 x (… + …) = 2 x … = iv. (b x a) + (b x c) = (2 x …) + (… x …) = … + … = … So b x (a + c) = (b x …) + (… x …) 2. Distributive Property Over Subtraction Fill in the blank by the right number i. a x (c - b) = 5 x ( 4 - 2) = 5 x … = … ii. (a x c) - (a x b) = (5 x …) - (… x …) = … - … = … So a x (b - c) = (a x b) - (… x …) iii. c x (a - b) = … x ( … - …) = 4 x … = … iv. (c x a) - (c x b) = (4 x …) - (… x …) = … - … = … So c x (a - b) = (… x …) - (… x …)
Conclusion The properties of the Integers are: 1. Commutative Property i. …………………………………….. ii. …………………………………….. 2. Associative Property i. ………………………………………. ii. ………………………………………. 3. Distributive Property i. ……………………………………… ii. ………………………………………
COMMUTATIVE PROPERTY Given a = 3, b = -2, and c = 7 1. Commutative Property of Addition Fill in the blank by the right number i. a+b=3+…=… ii. b + a = (-2) + … = … So a+b=b+… iii. a+c=…+…=… iv. c+a=…+…=… So a + c = c + … v. b+c=…+…=… vi. c+b=…+…=… So b + c = … + … 2. Commutative Property of Multiplication Fill in the blank by the right number i. axb=3x…=… ii. b x a = (-2) x … = … So axb=bx… iii. axc=…x…=… iv. cxa=…x…=… So a x c = … x … v. bxc=…x…=… vi. cxb=…x…=… So b x c = … x …
II.
ASSOCIATIVE PROPERTY Given a = 4, b = 5, and c = -3 1. Associative Property of Addition Fill in the blank by the right number i. (a + b) + c = (… + 5) + … = … ii. (a + c) + b = (4 + …) + … = … iii. (b + c) + a = (… + …) + … = … So (a + b) + c = (a + …) + … = (… + …) + … 2. Associative Property of Multiplication Fill in the blank by the right number i. (a x b) x c = (4 x 5) x … = 20 x … = … ii. (a x c) x b = (… x (-3)) x … = … x … = …
iii.
III.
(b x c) x a = (… x …) x … = … x … = … So (a x b) x c = (… + …) x … = (… x …) x …
DISTRIBUTIVE PROPERTY Given a = 5, b = 2, and c = 4 1. Distributive Property Over Addition Fill in the blank by the right number i. a x (b + c) = 5 x ( 2 + 4) = 5 x … = … ii. (a x b) + (a x c) = (5 x 2) + (… x …) = … + … = … So a x (b + c) = (a x b) + (… x …) iii. b x (a + c) = 2 x (… + …) = 2 x … = iv. (b x a) + (b x c) = (2 x …) + (… x …) = … + … = … So b x (a + c) = (b x …) + (… x …) 2. Distributive Property Over Subtraction Fill in the blank by the right number i. a x (c - b) = 5 x ( 4 - 2) = 5 x … = … ii. (a x c) - (a x b) = (5 x …) - (… x …) = … - … = … So a x (b - c) = (a x b) - (… x …) iii. c x (a - b) = … x ( … - …) = 4 x … = … iv. (c x a) - (c x b) = (4 x …) - (… x …) = … - … = … So c x (a - b) = (… x …) - (… x …)
Conclusion The properties of the Integers are: 1. Commutative Property i. …………………………………….. ii. …………………………………….. 2. Associative Property i. ………………………………………. ii. ………………………………………. 3. Distributive Property i. ……………………………………… ii. ………………………………………
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