Question

a-- 9/7 b-- -4/2 c -- -1/5

Answer 1

Solution :

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Given :

To prove associative property of integer,.

using a = $\frac{9}{7}$

b = $- \frac{4}{2}$

c = $- \frac{1}{5}$

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Proof :

We know that,

the associative property of integers (Using BODMAS rule,.)

⇒ a + (b + c) = (a + b) + c

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a = $\frac{9}{7}$

b = $- \frac{4}{2}$

c = $- \frac{1}{5}$

⇒ $( \frac{9}{7} + [- \frac{4}{2}] ) + [- \frac{1}{5} ] = \frac{9}{7} +( [- \frac{4}{2}] ) + [- \frac{1}{5} ] )$

We know that,.

+ × - = - ,

Hence,.

⇒ $( \frac{9}{7} - \frac{4}{2}) - \frac{1}{5} = \frac{9}{7} + (- \frac{4}{2}- \frac{1}{5} )$

By cross-multiplication,

We get,

⇒ $( \frac{18}{14} - \frac{28}{14} ) - \frac{1}{5} = \frac{9}{7} + ( -\frac{20}{10} - \frac{2}{10}$

⇒ $( \frac{18 - 28}{14}) - ( \frac{1}{5} ) = \frac{9}{7} + ( \frac{-20-2}{10} )$

⇒ $( \frac{-10}{14}) - ( \frac{1}{5} ) = \frac{9}{7} + ( \frac{-22}{10} )$

⇒ $( \frac{-50}{70}) - ( \frac{14}{70} ) = \frac{90}{70} + ( \frac{-154}{70} )$


⇒ $\frac{-50-14}{70} = \frac{90-154}{70}$

⇒ $\frac{-64}{70} = \frac{-64}{70}$

                           LHS = RHS
 
                          Hence proved,.
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                          Hope it Helps !!

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