answer the question questions questions
Answers
Step-by-step explanation:
Given :-
a) 3/2 , 1/4 , 7/6
b) -2/5 , 3/10 , -1/15
c) 8/3 , 7/2 , -4/3
To find :-
Verify Associative Property of addition for the given rational numbers ?
Solution :-
We know that
If a , b, c are three rational numbers then (a+b)+c = a+(b+c) is called Associative Property of addition in rational numbers.
a)
Given rational numbers are 3/2 , 1/4 , 7/6
Let a = 3/2 , b = 1/4, c = 7/6
(a+b)+c = [(3/2)+(1/4)]+(7/6)
LCM of 2 and 4 = 4
=> [{(3×2)+(1×1)}/4] +(7/6)
=> [(6+1)/4]+(7/6)
=> (7/4)+(7/6)
LCM of 4 and 6 = 12
=> [(7×3)+(7×2)]/12
=> (21+14)/12
=> 35/12
(a+b)+c = 35/12 -------------------(1)
a+(b+c) = (3/2)+[(1/4)+(7/6)]
LCM of 4 and 6 = 12
=> (3/2)+[{(1×3)+(7×2)}/12]
=> (3/2)+[(3+14)/12]
=> (3/2)+(17/12)
LCM of 2 and 12 = 12
=> [(3×6)+(17×1)]/12
=> (18+17)/12
=> 35/12
a+(b+c) = 35/12 -------------------(2)
From (1)&(2)
(a+b)+c = a+(b+c)
___________________________
b)
Given rational numbers are -2/5 , 3/10, -1/15
Let a = -2/5 , b = 3/10, c = -1/15
(a+b)+c = [(-2/5)+(3/10)]+(-1/15)
LCM of 5 and 10 = 10
=> [{(-2×2)+(3×1)}/10] +(-1/15)
=> [(-4+3)/10]+(-1/15)
=> (-1/10)+(-1/15)
LCM of 10 and 15 = 30
=> [(-1×3)+(-1×2)]/30
=> (-3-2)/30
=> -5/30
=> -1/6
(a+b)+c = -1/6 -------------------(1)
a+(b+c) = (-2/5)+[(3/10)+(-1/15)]
LCM of 10 and 15 = 30
=> (-2/5)+[{(3×3)+(-1×2)}/30]
=> (-2/5)+[(9-2)/30]
=> (-2/5)+(7/30)
LCM of 5 and 30 = 30
=> [(-2×6)+(7×1)]/30
=> (-12+7)/30
=> -5/30
=> -1/6
a+(b+c) = -1/6 -------------------(2)
From (1)&(2)
(a+b)+c = a+(b+c)
____________________________
c)
Given rational numbers are 8/3, 7/2, -5/3
Let a = 8/3 , b = 7/2, c = -4/3
(a+b)+c = [(8/3)+(7/2)]+(-4/3)
LCM of 3 and 2 = 6
=> [{(8×2)+(7×3)}/6] +(-4/3)
=> [(16+21)/6]+(-4/3)
=> (37/6)+(-4/3)
=> (37/6)-(4/3)
LCM of 6 and 3 = 6
=> [(37×1)+(-4×2)]/6
=> (37-8)/6
=> 29/6
(a+b)+c = 29/6 -------------------(1)
a+(b+c) = (8/3)+[(7/2)+(-4/3)]
LCM of 2 and 3 = 6
=> (8/3)+[{(7×3)+(-4×2)}/6]
=> (8/3)+[(21-8)/6]
=> (8/3)+(13/6)
LCM of 3 and 6 = 6
=> [(8×2)+(13×1)]/6
=> (16+13)/6
=> 29/6
a+(b+c) = 29/6 -------------------(2)
From (1)&(2)
(a+b)+c = a+(b+c)
Verified the given relations in the given problem.
Used formulae:-
Associative Property of addition:-
If a , b, c are three rational numbers then (a+b)+c = a+(b+c) is called Associative Property of addition in rational numbers.
Step-by-step explanation:
Given :-
a) 3/2 , 1/4 , 7/6
b) -2/5 , 3/10 , -1/15
c) 8/3 , 7/2 , -4/3
To find :-
Verify Associative Property of addition for the given rational numbers ?
Solution :-
We know that
If a , b, c are three rational numbers then (a+b)+c = a+(b+c) is called Associative Property of addition in rational numbers.
a)
Given rational numbers are 3/2 , 1/4 , 7/6
Let a = 3/2 , b = 1/4, c = 7/6
(a+b)+c = [(3/2)+(1/4)]+(7/6)
LCM of 2 and 4 = 4
=> [{(3×2)+(1×1)}/4] +(7/6)
=> [(6+1)/4]+(7/6)
=> (7/4)+(7/6)
LCM of 4 and 6 = 12
=> [(7×3)+(7×2)]/12
=> (21+14)/12
=> 35/12
(a+b)+c = 35/12 -------------------(1)
a+(b+c) = (3/2)+[(1/4)+(7/6)]
LCM of 4 and 6 = 12
=> (3/2)+[{(1×3)+(7×2)}/12]
=> (3/2)+[(3+14)/12]
=> (3/2)+(17/12)
LCM of 2 and 12 = 12
=> [(3×6)+(17×1)]/12
=> (18+17)/12
=> 35/12
a+(b+c) = 35/12 -------------------(2)
From (1)&(2)
(a+b)+c = a+(b+c)
___________________________
b)
Given rational numbers are -2/5 , 3/10, -1/15
Let a = -2/5 , b = 3/10, c = -1/15
(a+b)+c = [(-2/5)+(3/10)]+(-1/15)
LCM of 5 and 10 = 10
=> [{(-2×2)+(3×1)}/10] +(-1/15)
=> [(-4+3)/10]+(-1/15)
=> (-1/10)+(-1/15)
LCM of 10 and 15 = 30
=> [(-1×3)+(-1×2)]/30
=> (-3-2)/30
=> -5/30
=> -1/6
(a+b)+c = -1/6 -------------------(1)
a+(b+c) = (-2/5)+[(3/10)+(-1/15)]
LCM of 10 and 15 = 30
=> (-2/5)+[{(3×3)+(-1×2)}/30]
=> (-2/5)+[(9-2)/30]
=> (-2/5)+(7/30)
LCM of 5 and 30 = 30
=> [(-2×6)+(7×1)]/30
=> (-12+7)/30
=> -5/30
=> -1/6
a+(b+c) = -1/6 -------------------(2)
From (1)&(2)
(a+b)+c = a+(b+c)
____________________________
c)
Given rational numbers are 8/3, 7/2, -5/3
Let a = 8/3 , b = 7/2, c = -4/3
(a+b)+c = [(8/3)+(7/2)]+(-4/3)
LCM of 3 and 2 = 6
=> [{(8×2)+(7×3)}/6] +(-4/3)
=> [(16+21)/6]+(-4/3)
=> (37/6)+(-4/3)
=> (37/6)-(4/3)
LCM of 6 and 3 = 6
=> [(37×1)+(-4×2)]/6
=> (37-8)/6
=> 29/6
(a+b)+c = 29/6 -------------------(1)
a+(b+c) = (8/3)+[(7/2)+(-4/3)]
LCM of 2 and 3 = 6
=> (8/3)+[{(7×3)+(-4×2)}/6]
=> (8/3)+[(21-8)/6]
=> (8/3)+(13/6)
LCM of 3 and 6 = 6
=> [(8×2)+(13×1)]/6
=> (16+13)/6
=> 29/6
a+(b+c) = 29/6 -------------------(2)
From (1)&(2)
(a+b)+c = a+(b+c)
Verified the given relations in the given problem.
Used formulae:-
Associative Property of addition:-
If a , b, c are three rational numbers then (a+b)+c = a+(b+c) is called Associative Property of addition in rational numbers.