Question

if a, b, c are three rational numbers where a=2/3 , b= 4/5 andc = -5/6 verify
a. a+(b+c) =(a+b)+c
(associative property of addition )
b. a×(b×c) =(a×b)×c
(associative property of multiplication)
​

Answer 1

Solution :

When

• a = $\sf\dfrac{2}{3}$

• b = $\sf\dfrac{4}{5}$

• c = $\sf\dfrac{-5}{6}$

1. Associative Property of Addition

$\longrightarrow \sf \: a + (b + c) = (a + b) + c$

$\longrightarrow \sf \: \dfrac{2}{3} + ( \dfrac{4}{5} + \dfrac{ - 5}{6} ) = ( \dfrac{2}{3} + \dfrac{4}{5} ) + \dfrac{ - 5}{6}$

$\longrightarrow \sf \: \dfrac{2}{3} + ( \dfrac{4}{5} - \dfrac{ 5}{6} ) = ( \dfrac{2}{3} + \dfrac{4}{5} ) - \dfrac{ 5}{6}$

$\longrightarrow \sf \: \dfrac{2}{3} + ( \dfrac{24 - 25}{30} )= (\dfrac{10 + 12}{15} )- \dfrac{ 5}{6}$

$\longrightarrow \sf \: \dfrac{2}{3} - \dfrac{1}{30} = \dfrac{22}{15} - \dfrac{ 5}{6}$

$\longrightarrow \sf \: \dfrac{20 -1}{30} = \dfrac{ 44 - 25}{30}$

$\longrightarrow \sf \red{ \dfrac{19}{30} = \dfrac{ 19}{30} }$

• Hence,Verified!

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2. Associative Property of Multiplication :

$\longrightarrow \sf \: a \times( b \times c )=( a \times b) \times c$

$\longrightarrow \sf \: \dfrac{2}{3} \times( \dfrac{5}{6} \times \dfrac{4}{3}) =( \dfrac{2}{3} \times \dfrac{5}{6} ) \times \dfrac{4}{3}$

$\longrightarrow \sf \: \dfrac{2}{3} \times \dfrac{20}{18} = \dfrac{10}{18} \times \dfrac{4}{3}$

$\longrightarrow \sf \: \cancel\dfrac{40}{54} = \cancel\dfrac{40}{54}$

$\longrightarrow \sf \red{ \dfrac{20}{27} = \dfrac{ 20}{27} }$

• Hence,Verified!

Answer 2

Answer:

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