Verify the following
(a)Closure property for multiplication and addition if a= 25 and b = 78.
(b)Associative property for multiplication and addition if a = 13,b = 17 and c= 40
(c)Distributive property of multiplication over addition if a = 63. b= 92 and c= 46
(d)Commutative property for multiplication and addition if a = 700 and b = 999
Answers
Step-by-step explanation:
(a) Closure property for addition states that the sum of any two integers a and b will also be an integer : a + b = 25 + 78 = 103, which is an integer.
Closure property for multiplication states that the product of any two integers a and b will also be an integer : ab = 25*78 = 1950, which is an integer.
(b) Associative property for multiplication states that if there are any three integers a, b and c then, (a * b) * c = a * (b * c) :
(13*17)*40 = 221*40 = 8840
13*(17*40) = 13*680 = 8840, so both are equal.
Associative property for addition states that if there are any three integers a, b and c then, (a + b) + c = a + (b + c) :
(13 + 17) + 40 = 30 + 40 = 70
13 + (17 + 40) = 13 + 57 = 70, so both are equal.
(c) Distributive property of multiplication over addition states that if there are integers a,b and c then a(b + c) = ab + ac :
63 * (92 + 46) = 63 * 138 = 8694 = 63 * 92 + 63*46
(d) Commutative property for multiplication states that a*b = b*a
700*999 = 699300 = 999*700
Commutative property for addition states that a + b = b + a
700 + 999 = 1699 = 999 + 700
Step-by-step explanation:
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