Question

6 . Verify the following (5/4 + - 1/2) + - 3/2 = 5/4 + (- 1/2 + - 3/2)

Answer 1

★ How to do :-

Here, we are given with some rational numbers on LHS and the same three rational numbers on the LHS. But in the LHS, the first two numbers are grouped by bracket whereas on RHS, the last two numbers are grouped by bracket. In any question, if we find this type of method then this is known as the associative property. This property is only used by addition or multiplication. It cannot be used for subtraction and division. If we use same three rational numbers on LHS and RHS in addition or multiplication of associative property we always get the result as both the sides of the statement's answer will be same whereas this cannot happen in the case of subtraction or division. So, let's solve!!

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➤ Solution :-

${\sf \bigg( \dfrac{5}{4} + \dfrac{(-1)}{2} \bigg) + \dfrac{(-3)}{2} = \dfrac{5}{4} + \bigg( \dfrac{(-1)}{2} + \dfrac{(-3)}{2} \bigg)}$

Let's solve the LHS and RHS separately.

LHS :-

${\sf \leadsto \bigg( \dfrac{5}{4} + \dfrac{(-1)}{2} \bigg) + \dfrac{(-3)}{2}}$

LCM of 4 and 2 is 4.

${\sf \leadsto \bigg( \dfrac{5}{4} + \dfrac{(-1) \times 2}{2 \times 2} \bigg) + \dfrac{(-3)}{2}}$

Multiply the numerators and denominators of second fraction.

${\sf \leadsto \bigg( \dfrac{5}{4} + \dfrac{(-2)}{4} \bigg) + \dfrac{(-3)}{2}}$

Write the second number with one sign.

${\sf \leadsto \bigg( \dfrac{5 - 2}{4} \bigg) + \dfrac{(-3)}{2}}$

Subtract the numbers in the bracket.

${\sf \leadsto \dfrac{3}{4} + \dfrac{(-3)}{2}}$

LCM of 4 and 2 is 4.

${\sf \leadsto \dfrac{3}{4} + \dfrac{(-3) \times 2}{2 \times 2}}$

Multiply the numerators and denominators of second fraction.

${\sf \leadsto \dfrac{3}{4} + \dfrac{(-6)}{4}}$

Write the second number with own sign.

${\sf \leadsto \dfrac{3 + (-6)}{4} = \dfrac{3 - 6}{4}}$

Subtract the numbers to get the value of LHS.

${\sf \leadsto \dfrac{(-3)}{4} \: --- LHS}$

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RHS :-

${\sf \leadsto \dfrac{5}{4} + \bigg( \dfrac{(-1)}{2} + \dfrac{(-3)}{2} \bigg)}$

Let's add the numbers in the bracket.

${\sf \leadsto \dfrac{5}{4} + \bigg( \dfrac{(-1) + (-3)}{4} \bigg)}$

Write the second number with one sign.

${\sf \leadsto \dfrac{5}{4} + \bigg( \dfrac{(-1) - 3}{2} \bigg)}$

Subtract the numbers in bracket.

${\sf \leadsto \dfrac{3}{4} + \dfrac{(-4)}{2}}$

LCM of 4 and 2 is 4.

${\sf \leadsto \dfrac{3}{4} + \dfrac{(-4) \times 2}{2 \times 2}}$

Multiply the numerators and denominators of second fraction.

${\sf \leadsto \dfrac{3}{4} + \dfrac{(-8)}{4}}$

Write the second number with one sign.

${\sf \leadsto \dfrac{3 + (-8)}{4} + \dfrac{3 - 8}{4}}$

Subtract the numbers to get the value of RHS.

${\sf \leadsto \dfrac{(-5)}{4} \: --- RHS}$

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Let's compare the answers of LHS and RHS.

Comparison :-

${\sf \leadsto \dfrac{(-3)}{4} \: and \: \dfrac{(-5)}{4}}$

As we can see that they aren't equal. So,

${\sf \leadsto \dfrac{(-3)}{4} \neq \dfrac{(-5)}{4}}$

So,

${\sf \leadsto LHS \neq RHS}$

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${\red{\underline{\boxed{\bf So, \: the \: values \: of \: LHS \: and \: RHS \: aren't \: equal.}}}}$