Question

if a,b,c are three rational numbers where a = 2/3
b = 4/5 and C= - 5/6 verify.
1. a +( b + c) = (a+b)+c (associative property of addition)

2. a×(b×c)=(a×b)×c
(associative property of multiplication)​

Answer 1

Answer is in the attachment provided hope it helps

Answer 2

Answer:

Step-by-step explanation:

Given,

a = $\frac{2}{3}$,  b = $\frac{4}{5}$, c = $\frac{-5}{6}$

1) Associative property of addition

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

LHS = a +( b + c)

Substituting the values of a,b,c we get

=  $\frac{2}{3}$ + ($\frac{4}{5}$ + $\frac{-5}{6}$ )

Solving the operation in the bracket, we get

=  $\frac{2}{3}$ + $\frac{24 -25}{30}$

= $\frac{2}{3}$ +  $\frac{-1}{30}$

= $\frac{20 -1}{30}$

= $\frac{19}{30}$

RHS = (a+b)+c

= ( $\frac{2}{3}$ +$\frac{4}{5}$) +  $\frac{-5}{6}$

=$\frac{10+12}{15}$ + $\frac{-5}{6}$

=$\frac{22}{15}$ +  $\frac{-5}{6}$

= $\frac{44 - 25}{30}$

= $\frac{19}{30}$

Hence we have,

LHS  = RHS

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

The associative property of addition of rational numbers is verified

2)a×(b×c)=(a×b)×c

LHS = a×(b×c)

=  $\frac{2}{3}$  × ($\frac{4}{5}$ × $\frac{-5}{6}$)

= $\frac{2}{3}$ ×  $\frac{-2}{3}$

= $\frac{-4}{9}$

RHS = (a×b)×c

= ( $\frac{2}{3}$  ×$\frac{4}{5}$) ×  $\frac{-5}{6}$

= $\frac{8}{15}$ ×  $\frac{-5}{6}$

= $\frac{-4}{9}$

∴ LHS = RHS

a×(b×c)=(a×b)×c

Associative property of multiplication of rational numbers is verified

#SPJ2