NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev

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Class 8 : NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev

The document NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev is a part of the Class 8 Course Class 8 Mathematics by VP Classes.
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Ques 1: Fill in the blanks in the following table:

Numbers
Closed under

Addition
Subtraction
Rational numbersYesYes
Integers.....Yes
Whole numbers ..........
Natural numbers.....No


Numbers
Closed under

Multiplication
Division
Rational numbers....No
 Integers.....No
Whole numbers Yes.....
Natural numbers..........


Ans: Using the closure property over addition, subtraction, multiplication, and division for rational numbers, integers, whole-numbers, and natural numbers, we have:

Numbers
Closed under

AdditionSubtraction
Rational numbersYesYes
IntegersYesYes
Whole numbersYesNo
Natural numbersYesNo


Numbers
Closed under

MultiplicationDivision
Rational numbersYesNo
IntegersYesNo
Whole numbersYesNo
Natural numbersYesNo


Ques 2: Complete the following table:

Numbers
Commutative for

AdditionSubtraction
Rational numbersYes.....
Integers.....No
Whole numbers..........
Natural numbers..........


Numbers
Commutative for

MultiplicationDivision
Rational numbers..........
Integers..........
Whole numbersYes.....
Natural numbers.....No


Ans:

Numbers
Commutative for

AdditionSubtraction
Rational numbersYesNo
IntegersYesNo
Whole numbersYesNo
Natural numbersYesNo


Numbers
Commutative for

MultiplicationDivision
Rational numbersYesNo
IntegersYesYes
Whole numbersYesYes
Natural numbersYesYes


Ques 3: Complete the following table:

Numbers
Associative for

AdditionSubtraction
Rational numbers........
Integers........
Whole numbersYes....
Natural numbers....No


Numbers
Associative for

MultiplicationDivision
Rational numbers....No
Integers........
Whole numbersYes....
Natural numbers........

Ans: 

Numbers
Associative for

AdditionSubtraction
Rational numbersYesNo
IntegersYesNo
Whole numbersYesNo
Natural numbersYesNo


Numbers
Associative for

MultiplicationDivision
Rational numbersYesNo
IntegersYesNo
Whole numbersYesNo
Natural numbersYesNo


Ques 4: If a property holds for rational numbers, will it also hold for integers? For whole Numbers? Which will? Which will not?
Ans: 
(i) Any property which is true for rational numbers is also true for integers except for any integers ‘a’ and ‘b’, (a ÷ b) is not necessarily an integer.
(ii) All properties which are true for rational numbers are also true for whole numbers also except:
(a) For ‘a’ and ‘b’ being whole numbers, (a – b) may not be a whole number.
(b) For ‘a’ and ‘b’ being whole numbers (b ≠ 0), a ÷ b may not be the whole number.
Ques 5: Find using distributive property:

NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev
NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev

Ans: 
NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev
NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev
NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev
NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev (∵ LCM of 12 and 9 is 36)
NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev


EXERCISE 1.1
Ques 1. 
Using appropriate properties find:
NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev
NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev
Ans: NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev(Using commutative property)

NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev
NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev (Using distributive property)
NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev
NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev
NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev (Using commutative property)
NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev (Using distributive property)
NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev

Ques 2. Write the additive inverse of each of the following:

(i) 2/8
(ii) -5/9
(iii) -6/-5
(iv) 2/-9
(v) 19/-6

Ans. Concept: The negative of a rational number is called additive inverse. 

Sr. No.
Rational number
Additive inverse
(i)
NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev
NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev
(ii)
NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev
NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev
(iii)
-6/-5 = 6/5
NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev
(iv)
NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev
NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev
(v)
NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev
NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev

 

Ques 3. Verify that –(–x) = x for:

NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev

Ans. 
(i) Given, x = 11/15
⇒ (-x) = -11/15

⇒ -(-x) = -(-11/15) = 11/15
Therefore, -(-x) = x

(ii) Given, x = -13/17
⇒ (-x) = -13/17

⇒ -(-x) = -(-13/17) = 13/17
Therefore, -(-x) = x

Ques 4. Find the multiplicative inverse of the following:
NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev

Ans:

Sr. No.
 Rational number
 Multiplicative inverse
(i)
–13
-1/13
(ii)
-13/19
-19/13
(iii)
1/55
(iv)
  NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev
56/15
(v)
NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev
5/2
(vi)
-1
-1


Ques 5: Name the property under multiplication used in each of the following:
NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev
NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev
NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev

Ans:

Sr. No.
Multiplication
Property used
(i)
NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev
 1 is the multiplicative identity
(ii)
NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev
 Commutative property
(iii)
NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev
 Multiplicative inverse


Ques 6: Multiply NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev by the reciprocal of   NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev
Ans: As,
 Reciprocal of NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev

NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev
NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev 

Ques 7: Tell what property allows you to compute  NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev
Ans: When rational numbers are rearranged between one or more same operations and still their result does not change then we say that they follow the associative property for that operation. Thus, given equation follows the associative property.

Ques 8: Is  8/9 the multiplicative inverse of NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev Why or why not?
Ans: Since,
  NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev  [Which is not equal to 1]

∴ 8/9 is not the multiplicative inverse of NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev

Ques 9: Is 0.3 the multiplicative inverse of NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev? Why or why not?
Ans: Since,
 NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev
0.3 х 10/3 = 1

Therefore, 0.3 is the multiplicative inverse of 10/3.

Ques 10: Write: 
(i) The rational number that does not have reciprocal. 
(ii) The rational numbers that are equal to their reciprocals. 
(iii) The rational number that is equal to its negative.
Ans:
(i) The rational number zero (0) does not have a reciprocal.
(ii) The rational numbers 1 and (–1) are equal to their reciprocals respectively.
(iii) Zero (0) is the rational number that is equal to its negative.

Ques 11: Fill in the blanks:
(i) Zero has ______ reciprocal.
(ii) The numbers ______ and ______ are their own reciprocals.
(iii) The reciprocal of –5 is ______.
(iv) Reciprocal of 
NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev, where x ≠ 0 is ______.
(v) The product of two rational numbers is always a ______.
(vi) The reciprocal of a positive rational number is ______.

Ans:
(i) Zero has no reciprocal. 

(ii) The numbers 1 and –1 are their own reciprocals.
(iii) The reciprocal of –5 is 
NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev
(iv) The reciprocal of  1/x , where x ≠ 0 is x.
(v) The product of two rational numbers is always a rational number.
(vi) The reciprocal of a positive rational number is positive.

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