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The numerical expression (3/8) + (-5/7) = (-19/56) shows that

(a) rational numbers are closed under addition.

(b) rational numbers are not closed under addition.

(c) rational numbers are closed under multiplication.

(d) addition of rational numbers is not commutative.

Answer:

(a) rational numbers are closed under addition.

Because, (3/8) + (-5/7)

Take the LCM of the denominators of the given rational numbers.

LCM of 8 and 7 is 56

Express each of the given rational numbers with the above LCM as the common denominator.

Now,

(3/8)= [(3×7)/ (8×7)] = (21/56)

(-5/7)= [(-5×8)/ (7×8)] = (-40/56)

Then,

= (21/56) + (-40/56) … [∵ denominator is same in both the rational numbers]

= (21 - 40)/56

= (-19/56)

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