Question

Verify the following and state the property used.

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Answer 1

it is accositive property

Answer 2

Solution :-

Associative law of addition used in this statement.

$\bf\boxed {(a + b) + c = a + (b + c)}$

Verification-

LHS-

$\bf {( \frac{ - 1}{2} + \frac{3}{7} ) + ( \frac{ - 4}{3} )}$

$\sf {= > \frac{ - 1}{14} + ( \frac{ - 4}{3} )}$

$\sf { = > \frac{ - 3 + ( - 56)}{42} }$

$\sf { = > \frac{ - 3 - 56}{42} = \frac{ - 59}{42}}$

In left hand side, we got the answer = -59/42

RHS -

$\bf { \frac{ - 1}{2} + ( \frac{3}{7} + ( \frac{ - 4}{3} ))}$

$\sf { = > - \frac{ - 1}{2} + ( \frac{ - 19}{21} )}$

$\sf { = > \frac{ - 21 + ( - 38)}{42} }$

$\sf { = > \frac{ - 21 - 38}{42} = \frac{ - 59}{42} }$

In RHS we also got the anwer -59/42

$\sf {RHS = LHS}$

$\sf { \frac{ - 59}{42} = \frac{ - 59}{42}}$

Hence, verified!!!

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Properties of addition of rational numbers -

• Closure Property - The sum of two rational number is always a rational number.

• Commutative Property

[a/b + c/d = c/d + a/b]

• Associative Property

[ a/b + ( c/d + e/f) = (a/b + c/d) + e/f ]

• Property of zero ( additive identity)

The sum of any rational number a and 0 is the rational number itself.

That means, for any rational number 'a' ,

a +0=0+a = a.

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