Match the columns Column I Column II a . The rational number which is equal to its negative, is i Subtraction b . The rational number which does not have a reciprocal, is ii Division c . The rational numbers which are equal to its reciprocals, are iii Zero d . If zero is excluded from the collection of rational numbers, then the rational numbers are closed under iv One e . Both natural numbers and whole numbers are not commutative under v Negative of one

Rational numbers are those numbers which can be written in p q , where p and q are integers and q ≠ 0 . If x is a rational number, then its reciprocal will be 1 x . The rational number which is equal to its negative, is zero because with zero no sign is used. Hence, a matches with iii The rational number which does not have a reciprocal, is zero, because 1 0 is not defined. Hence, b also matches with iii The rational numbers which are equal to its reciprocals, are 1 and - 1 because, the reciprocals of 1 and - 1 are 1 and - 1 . Hence, c matches with iv and v If zero is excluded from the collection of rational numbers, then the rational numbers are closed under division. Hence, d matches with ii Both natural numbers and whole numbers are not commutative under subtraction because a - b ≠ b - a Hence, e matches with i Therefore, the complete table with correct matches is given below Column I Column II a . The rational number which is equal to its negative, is iii Zero b . The rational number which does not have a reciprocal, is iii Zero c . The rational numbers which are equal to its reciprocals, are iv One v Negative of one d . If zero is excluded from the collection of rational numbers, then the rational numbers are closed under ii Division e . Both natural numbers and whole numbers are not commutative under i Subtraction

E M B I B E

NCERT Practice Workbook Mathematics>Chapter 1 - Rational Numbers>Worksheet 2>Q 2

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The multiplicative identity for rational numbers is

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Important Questions on Rational Numbers

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NCERT Practice Workbook Mathematics>Chapter 1 - Rational Numbers>Worksheet 2>Q 2

For three rational numbers $a, b$ and $c$ , which of the following is correct?

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NCERT Practice Workbook Mathematics>Chapter 1 - Rational Numbers>Worksheet 2>Q 3

An absolute value of a rational number is obtained by taking only the numerical value of that rational number.

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NCERT Practice Workbook Mathematics>Chapter 1 - Rational Numbers>Worksheet 2>Q 3

Rational numbers are not closed under addition and subtraction.

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NCERT Practice Workbook Mathematics>Chapter 1 - Rational Numbers>Worksheet 2>Q 3

Subtraction of rational numbers is commutative.

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NCERT Practice Workbook Mathematics>Chapter 1 - Rational Numbers>Worksheet 2>Q 3

The reciprocal of any rational number is always an integer.

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NCERT Practice Workbook Mathematics>Chapter 1 - Rational Numbers>Worksheet 2>Q 3

The numbers $1$ and $- 1$ are their own reciprocal.

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NCERT Practice Workbook Mathematics>Chapter 1 - Rational Numbers>Worksheet 2>Q 4

Match the columns

Column I	Column II
$a .$ The rational number which is equal to its negative, is	$(i)$ Subtraction
$b .$ The rational number which does not have a reciprocal, is	$(ii)$ Division
$c .$ The rational numbers which are equal to its reciprocals, are	$(iii)$ Zero
$d .$ If zero is excluded from the collection of rational numbers, then the rational numbers are closed under	$(iv)$ One
$e .$ Both natural numbers and whole numbers are not commutative under	$(v)$ Negative of one