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

Name the property used in the following. 2 3 × 5 × 6 7 = 2 3 × 5 × 6 7

The property of associativity is closed under the set of rational numbers. That makes the operation order independent. For three rational numbers say a , b and c , multiplication follows the associativity property. i.e. a × b × c = a × b × c . Given, 2 3 × 5 × 6 7 = 2 3 × 5 × 6 7 . Here, the result of rational numbers is same even changing the order of the numbers. Hence, in the given question, associativity property is used.

Name the property used in the following. 4 5 × - 3 5 × 1 2 = 4 5 × - 3 5 × 1 2

The property of associativity is closed under the set of rational numbers. That makes the operation order independent. For three rational numbers say a , b and c , multiplication follows the associativity property. i.e. a × b × c = a × b × c . Given, 4 5 × - 3 5 × 1 2 = 4 5 × - 3 5 × 1 2 Hence, in the given question, associativity property is used.

Name the property used in the following. 1 2 × 1 5 + - 1 7 = 1 2 × 1 5 + 1 2 × - 1 7

For three rational numbers, say a , b and c , the distributive property of multiplication over addition is given by a b + c = a × b + a × c The distributive property states that multiplying a sum by a number gives the same result as multiplying each addend by the number and then adding the products together. Given, 1 2 × 1 5 + - 1 7 = 1 2 × 1 5 + 1 2 × - 1 7 Hence, in the given question, distributive property is used.

Name the properties used in the following. - 2 9 + 0 = 0 + - 2 9 = - 2 9

If 0 is added to a rational number x or x is added to 0 , then the value of the rational number remains same. i.e. a + 0 = 0 + a = a Here, 0 is known as the additive identity. Hence, in the given question, - 2 9 + 0 = 0 + - 2 9 = - 2 9 , So, the property used in the given question is additive identity. We know that, two rational numbers a and b are said to in commutative, if a + b = b + a . Given, - 2 9 + 0 = 0 + - 2 9 = - 2 9 . Here, result is same even after changing the order of the numbers. So, the property used in the given question is commutative. Hence, the properties used are additive identity and commutativity.

E M B I B E

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

Subject Experts Solutions for Chapter: Rational Numbers, Exercise 2: Worksheet 2

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Subject Experts Mathematics Solutions for Exercise - Subject Experts Solutions for Chapter: Rational Numbers, Exercise 2: Worksheet 2

Attempt the practice questions on Chapter 1: Rational Numbers, Exercise 2: Worksheet 2 with hints and solutions to strengthen your understanding. NCERT Practice Workbook Mathematics solutions are prepared by Experienced Embibe Experts.

Questions from Subject Experts Solutions for Chapter: Rational Numbers, Exercise 2: Worksheet 2 with Hints & Solutions

EASY

8th CBSE

IMPORTANT

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

The reciprocal of any rational number is always an integer.

HARD

8th CBSE

IMPORTANT

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