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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

Solution:

3/8 and -5/7 are rational numbers. Adding two rational numbers results in a rational number.

Let us verify it. 3/8 + (-5/7) = 3/8 - 5/7

21/56 - 40/56 = -19/56

The sum of two rational numbers is a rational number. Thus we conclude that rational numbers are closed under addition.

✦ Try This: Are the rational numbers closed under subtraction? Justify with an example.

Consider two rational numbers ⅔ and ⅘. Let us subtract them.

2/3 - 4/5 = 10/15 - 12/15 = -2/15 which is again a rational number.

Consider two rational numbers -1/7 and 3/4. Let us subtract them.

-1/7 - 3/4 = -4/28 - 21/28 = -25/28 which is again a rational number.

Thus we conclude that the rational numbers are closed under subtraction.

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 1

NCERT Exemplar Class 8 Maths Chapter 1 Problem 3

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

Summary:

The numerical expression 3/8 + (-5/7) = -19/56 shows that (a) rational numbers are closed under addition

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