Question

(–4/9- 3/4)+2/12 , -4/9- ( 3/4+ 2/12)
Find the rational number in each pair and examine if they are equal or not ​

Answer 1

★ How to do :-

Here, we are given with three fractions to add and subtract with them. On the other side we are given with the same theree rational numbers. We are asked to find the answer of both the sides and we should examine wether the obtained answers are equal to each other or not. This concept is called as associative property on which in LHS, we group the first two numbers and on the RHS, we group the second two numbers and vise versa. If the obtained answers are same, then we can consider that this is the property of associative. So, let's solve!!

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➤ Solution :-

${\tt \leadsto \bigg( \dfrac{(-4)}{9} - \dfrac{3}{4} \bigg) + \dfrac{2}{12} \neq \dfrac{(-4)}{9} - \bigg( \dfrac{3}{4} + \dfrac{2}{12} \bigg)}$

Let's solve the LHS and RHS separately.

LHS :-

${\tt \leadsto \bigg( \dfrac{(-4)}{9} - \dfrac{3}{4} \bigg) + \dfrac{2}{12}}$

First, solve the brackets.

LCM of 9 and 4 is 36.

${\tt \leadsto \bigg( \dfrac{(-4) \times 4}{9 \times 4} - \dfrac{3 \times 9}{4 \times 9} \bigg) + \dfrac{2}{12}}$

Multiply the numerators and denominators in bracket.

${\tt \leadsto \bigg( \dfrac{(-16)}{36} - \dfrac{27}{36} \bigg) + \dfrac{2}{12}}$

Subtract those fractions now.

${\tt \leadsto \bigg( \dfrac{-16 - 27}{36} \bigg) + \dfrac{2}{12}}$

Write the resulting fraction.

${\tt \leadsto \dfrac{(-43)}{36} + \dfrac{2}{12}}$

LCM of 36 and 12 is 36.

${\tt \leadsto \dfrac{(-43)}{36} + \dfrac{2 \times 3}{12 \times 3}}$

Multiply the numerators and denominators of second fraction.

${\tt \leadsto \dfrac{(-43)}{36} + \dfrac{6}{36}}$

Add the fractions now.

${\tt \leadsto \dfrac{(-43) + 6}{36} = \dfrac{(-37)}{36} \: \: - - - \sf LHS}$

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RHS :-

${\tt \leadsto \dfrac{(-4)}{9} - \bigg( \dfrac{3}{4} + \dfrac{2}{12} \bigg)}$

Solve the brackets first.

LCM of 4 and 12 is 12.

${\tt \leadsto \dfrac{(-4)}{9} - \bigg( \dfrac{3 \times 3}{4 \times 3} + \dfrac{2}{12} \bigg)}$

Write the resulting fractions.

${\tt \leadsto \dfrac{(-4)}{9} - \bigg( \dfrac{9}{12} + \dfrac{2}{12} \bigg)}$

Add the fractions in bracket.

${\tt \leadsto \dfrac{(-4)}{9} - \bigg( \dfrac{9 + 2}{12} \bigg)}$

Write the resulting fractions.

${\tt \leadsto \dfrac{(-4)}{9} - \dfrac{11}{12}}$

LCM of 9 and 12 is 36.

${\tt \leadsto \dfrac{(-4) \times 4}{9 \times 4} - \dfrac{11 \times 3}{12 \times 3}}$

Multiply the numbers on numerator and denominator.

${\tt \leadsto \dfrac{(-16)}{36} - \dfrac{33}{36}}$

Subtract the fractions now.

${\tt \leadsto \dfrac{(-16) - 33}{36}}$

Write the resulting fraction.

${\tt \leadsto \dfrac{(-49)}{36} \: \: - - - \sf RHS}$

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Now, we can see whether they are equal or not.

${\tt \leadsto \dfrac{(-37)}{36} \neq \dfrac{(-49)}{36}}$

So,

$\sf \leadsto LHS \neq RHS$

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$\red{\underline{\boxed{\bf So, \: they \: aren't \: equal}}}$