Question

11 Ifa, b, care three rational numbers where a =
1/4, 16 = 1/2, and c = 2 , verity,
(a) a (b + c) = (a + b) + c
(b) a*b*d) = a*b) C
(Associative property of addition)
(Associative property of multiplication)
​

Answer 1

Answer:

Associative property of rational number under addition is given by following:

a+(b+c)=(a+b)+c

where, a,b and c are rational numbers

Answer 2

Step-by-step explanation:

Given:-

a, b, c are three rational numbers where

a =1/4, b = 1/2, and c = 2.

To find:-

Verify that :

(a) a (b + c) = (a + b) + c

(Associative property of addition)

(b) a*(b*c) = (a*b) c

(Associative property of multiplication)

Solution:-

Given that :

a = 1/4

b = 1/2

c = 2

i) Associative Propert of addition:

LHS :-a+(b+c)

=> (1/4)+[(1/2)+2]

=> (1/4)+(1+4)/2

=> (1/4)+(5/2)

LCM of 4 and 2 = 4

=> (1+10)/4

=> 11/4

LHS = 11/4------------(1)

RHS : (a+b)+c

=> [(1/4)+(1/2)]+2

LCM of 4 and 2 = 4

=> [(1+2)/4]+2

=> (3/4)+2

=> (3+8)/4

=> 11/4

RHS = 11/4 ----------(2)

From (1)&(2)

LHS = RHS

a+(b+c) = (a+b)+c

ii)Associative Property of multiplication:-

LHS:-a(b×c)

=> (1/4)×[(1/2)×2]

=> (1/4)×(2/2)

=> (1/4)×1

=> 1/4

LHS = 1/4 ------------(1)

RHS:(a×b)×c

=>[(1/4)×(1/2)]×2

=> (1/8)×2

=> 2/8

=> 1/4

RHS = 1/4 ------------(2)

From (1)&(2)

LHS = RHS

Verified the given relations in the given problem

Used formulae:-

Associative Property:-

If a ,b, c are three rational numbers then,

• a+(b+c) = (a+b)+c is called Associative Property of addition
• a×(b×c) = (a×b)×c is called Associative Property of multiplication