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

Class 8 Mathematics by Full Circle

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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 Full Circle.
All you need of Class 8 at this link: Class 8

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 numbers
YesYes
Integers
YesYes
Whole numbersYesNo
Natural numbersYesNo


Numbers
Closed under

MultiplicationDivision
Rational numbers
YesNo
Integers
YesNo
Whole numbersYesNo
Natural numbersYesNo


Ques 2: Complete the following table:

Numbers
Commutative for

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


Numbers
Commutative for

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


Ans:

Numbers
Commutative for

AdditionSubtraction
Rational numbers
YesNo
Integers
YesNo
Whole numbersYesNo
Natural numbersYesNo


Numbers
Commutative for

MultiplicationDivision
Rational numbers
YesNo
Integers
YesYes
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 numbers
YesNo
Integers
YesNo
Whole numbersYesNo
Natural numbersYesNo


Numbers
Associative for

MultiplicationDivision
Rational numbers
YesNo
Integers
YesNo
Whole numbersYesNo
Natural numbersYes
No


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 commutativity)

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


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

NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev
(ii) ∵ x =  NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev
NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev

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

Ans:

Sr. No.
Rational number
Additive inverse
(i)
–13
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)
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: ∵ 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: In computing  NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev  we use the associativity. 


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

[∵ The product of NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev and its multiplicative inverse must be equal to 1]


Ques 9: Is 0.3 the multiplicative inverse of NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev? Why or why not?
Ans: ∵ NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRevand, multiplicative inverse of   NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev


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) ∵ [A rational number] + [Negative of the rational number] = 0
∴ [0] + [0] = 0
So, Negative of 0 is 0.
Hence, 0 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.

REMEMBER

The additive inverse has the same numerator and denominator as the number but has the opposite sign whereas a reciprocal has the same sign as the number but numerator and denominator are interchanged.


REPRESENTATION OF RATIONAL NUMBERS ON THE NUMBER LINE

We can also represent a rational number on a number line. In a rational number, the numeral below the bar (denominator), tells the number of equal parts into which the first unit has been divided. The numeral above the bar (numerator) tells ‘how-many’ of these parts are considered.
Ques 1: To represent 4/7, we divide the distance between 0 and 1 in 7 equal parts such that the 1st marking represents 1/7 , i.e. one out of seven equal parts.

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

Similarly, 2nd marking represents 2/7
3rd marking represents 3/7
4th marking represents 4/7
5th marking represents 5/7
6th marking represents 6/7
7th marking represents 7/7 (i.e. 1)

Thus, the 4th marking represents the rational number 4/7

Ques 2: Let us represent  NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev  on the number line. In this case we divide the distance between 0 and (–1) into 7 equal parts and then consider 2 parts out them.

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

Thus, the second marking on the left of 0, represents the rational number NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev

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