Question

(1 ) verify the associative property of additionfor the following rational numbers. (b) 4 upon 5, -3 upon 10 , 8 upon 15​

Answer 1

Question

verify the associative property of addition for the following rational numbers. (b) 4/ 5, -3/10 , 8/15

Solution

Associative Property

If a,b and c are two number

So, for associative property for addition it be hold like that

• a + (b +c ) = (a+b) + c

Now, we prove this, by Example

where,

• a = 4/5
• b = -3/10
• c = 8/15

First, Take L.H.S.

==> a + (b +c )

Keep Value of a , b & c

==> (4/5) + [ (-3/10) + (8/15) ]

==> (4/5) + [ (-3*3 + 8 * 2)/30]

==> (4/5) + [ (-9+16)/30]

==> (4/5) + [ 7/30]

==> 4/5 + 7/30

==> (4*6 + 7)/30

==> (24+7)/30

==> 31/30

Now, Take R.H.S.

==> (a+b) + c

keep Value of a , b & c

==> [ (4/5) + (-3/10) ] + (8/15)

==> [ (4*2 - 3)/10 ] + (8/15)

==> [ (8-3)/10] + (8/15)

==> 5/10 + 8/15

==> (5 * 3 + 8*2)/30

==> (15+16)/30

==> 31/30

Here,

• L.H.S = R.H.S.

so, we can say that Associative Property is Satisfied For this Example.

__________________