Question

verify x+(y+z)=(x+y)+z if x=3/4,y=5/6 and z=-7/8.​

Answer 1

Step-by-step explanation:

Given -

x = 3/4

y = 5/6

z = -7/8

To show -

x + (y + z) = (x + y) + z

Now,

= 3/4 + [5/6 + (-7/8)] = (3/4 + 5/6) + (-7/8)

= 3/4 + (5/6 - 7/8) = (3/4 + 5/6) - 7/8

= 3/4 + (20-21/24) = (9+10/12) - 7/8

= 3/4 + (-1/24) = (19/12) - 7/8

= 3/4 - 1/24 = 19/12 - 7/8

= 18-1/24 = 38-21/24

= 17/24 = 17/24

LHS = RHS

Hence,

Proved..

Answer 2

Given:

• Value of x = ¾

• Value of y = ⅚

• Value of z = -⅞

To Prove:

✪x+(y+z) = (x+y)+z

Proof:

$x + ( y + z) = (x + y) + z$

$\bigstar \: Putting \: the \: values$

$\rightarrow \: \frac{3}{4} + ( \frac{5}{6} + ( - \frac{7}{8} )) = ( \frac{3}{4} + \frac{5}{6} ) + ( - \frac{7}{8} )$

$\rightarrow \frac{3}{4} + ( \frac{20 - 21}{24} ) = (\frac{18 + 20}{24} ) + ( - \frac{7}{8} )$

$\rightarrow \: \frac{3}{4} + ( - \frac{1}{24} ) = \frac{38}{24} + (- \frac{7}{8} )$

$\rightarrow \frac{18 - 1}{24} = \frac{38 - 21}{24}$

$\rightarrow \: \frac{17}{24} = \frac{17}{24}$

$\bold{L.H.S = R.H.S }$

knowledge Enhancer

✪ Properties of Additional of Rational numbers:

Property 1 .

• Closure: a/b + c/d is a rational number .

Property 2.

• Commutative property = a/b + c/d = c/d + a/b , two rational numbers can be added in any order.