Question

Verify the following property of rational numbers for x = 1/2, y = 3/4 and z = 5/6 :-

a) X + y = y + x
b) X (y + Z) = x * y + x * z

Answer 1

Answer:

x+y::::

a) 1/2+3/4= (L.C.M= 4)

So, 1/2+3/4= 2/4+3/4=

5/4

y+x::::::

3/4+1/2= (L.C.M=4)

So, 3/4+1/2= 3/4+ 2/4=

5/4

Hence, Verified

It's commutative property under addition.

b)

1/2(3/4+5/6)= 1/2×3/4+ 1/2×5/6

L.H.S= 1/2×3/4+ 1/2×5/6

= 3/8+ 5/12

= 19/24

OR

1/2× 3/4+5/6= 1/2 ×19/12

= 19/24

R.H.S = 1/2×3/4+1/2×5/6

= 3/8+ 5/12 (L.C.M = 24)

= 19/24

Hence, verified

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