Question 3
The numerical expression $\frac{3}{8} + \frac{(- 5)}{7} = \frac{- 19}{56}$ 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.

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Solution

We have,
$\frac{3}{8} + (\frac{(- 5)}{7}) = \frac{- 19}{56}$

which shows that rational numbers are closed under addition.

$[∵ \frac{3}{8} a n d \frac{- 5}{7} a r e r a t i o n a l n u m b e r s a n d t h e i r a d d i t i o n i s \frac{- 19}{56} w h i c h i s a l s o a r a t i o n a l n u m b e r]$

Hence, option (a) is correct.

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Similar questions

Question 5
$- \frac{3}{8} + \frac{1}{7} = \frac{1}{7} + (\frac{- 3}{8})$ is an example to show that
(a) addition of rational numbers is commutative.
(b) rational numbers are closed under addition.
(c) addition of rational number is associative.
(d) rational numbers are distributive under addition

Question 4
Which of the following is not true?
(a) rational numbers are closed under addition.
(b) rational numbers are closed under subtraction.
(c) rational numbers are closed under multiplication.
(d) rational numbers are closed under division.

Q. Question 77
Rational numbers are closed under addition and multiplication but not under subtraction.

Q. Rational numbers are not closed under ___.

Q. Question 104
Give one example each to show that the rational numbers are closed under addition, subtraction and multiplication. Are rational numbers closed under division? Give two examples in support of your answer.

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Question 3 The numerical expression 38+(−5)7=−1956 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.

We have, 38+((−5)7)=−1956 which shows that rational numbers are closed under addition. [∵38 and −57 are rational numbers and their addition is −1956 which is also a rational number] Hence, option (a) is correct.