ncert solutions for class 8 maths chapter 1 deals with Rational Numbers.
chapter 1 maths class 8
chapter 1 maths class 8 deals with Rational Numbers Find ncert solutions for class 8 maths chapter 1 here. In Class 8 maths chapter 1,
NCERT solutions for Class 8 Chapter 1
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Ncert solutions for class 8 maths chapter 1 exercise 1.1
Exercise 1.1
class 8 maths chapter 1 exercise 1.1 (1)
1 Using appropriate properties find:
(i) –( ⅔) × (⅗) +(⁵/₂) –(⅗)×(⅙)
(ii) ( ⅖) × (³/₋₇) –(⅙) ×(³/₂)+(¹/₁₄)×(²/₅)
Solution to class 8 maths chapter 1 exercise 1.1(1)
Solution : (i) – ( ⅔) × (⅗) +(⁵/₂) –(⅗)×(⅙)
= – ( ⅔) × (⅗) –(⅗)×(⅙)+(⁵/₂) [∵Associative property]
= ⅗(– ⅔ –⅙)+ ⁵/₂ [∵ Distributive property]
= ⅗[⁽⁻⁴⁻¹⁾/₆]+⁵/₂ = [³/₅ × (⁻⁵₆)]+(⁵₂)
= ⁻¹/₂ + ⁵/₂ = ⁽⁻¹⁺⁵⁾/ ₂ = ⁴ /₂ =2
(ii) ( ⅖) × (³/₋₇) –(⅙) ×(³/₂)+(¹/₁₄)×(²/₅)
= ( ⅖) × (⁻³/₇) +(¹/₁₄)×(²/₅)–(⅙) ×(³/₂) [∵Associative property]
= ⅖ ×[⁻³/₇+¹/₁₄]–(¹/₄) [∵Distributive property]
=⅖ ×[⁽⁻⁶⁺¹⁾/₁₄] –¼ = ⅖ × (⁻⁵/₁₄) – ¼
= – ⅐ – ¼ =⁽⁻⁴⁻⁷⁾/₂₈ = – ¹¹/₂₈
class 8 maths chapter 1 exercise 1.1 (2)
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
Solution to class 8 maths chapter 1 exercise 1.1(2)
We know that additive inverse of a rational number a/b is (–a/b).
Such that (a/b)+(–a/b)=0
(i) Additive inverse of ²/₈ is – ²/₈
(ii) Additive inverse of –⁵/₉ is ⁵/₉
(iii) Additive inverse of ⁻⁶/₋₅ is – ⁶/₅
(iv) Additive inverse of ²/₋₉is ²/₉
(v) Additive inverse of ¹⁹/₋₆ is ¹⁹/₆
class 8 maths chapter 1 exercise 1.1 (3)
3 Verify – (–x)=x for :
(i)x=¹¹/₁₅ (ii) x=– ¹³/₁₇
Solution to class 8 maths chapter 1 exercise 1.1(3)
Answer: (i) Putting x=¹¹/₁₅ in – (–x)=x
– (– ¹¹/₁₅)=¹¹/₁₅ ⇒ ¹¹/₁₅ = ¹¹/₁₅
LHS=RHS
Hence Verified.
(ii) Putting x= – ¹³/₁₇ in – (–x)=x
– {–(– ¹³/₁₇)}= – ¹³/₁₇ ⇒ – ¹³/₁₇= – ¹³/₁₇
∴ LHS=RHS. Hence Verified.
class 8 maths chapter 1 exercise 1.1 (4)
4 Find the multiplicative inverse of the following.
(i) –13 (ii) – ¹³/₁₉ (iii) ¹/₅(iv) – ⁵/₈ × – ³/₇ (v) –1× – ²/₅ (vi) –1
Solution to class 8 maths chapter 1 exercise 1.1(4)
Answer : We know a multiplicative inverse of a is 1/a, such that a×(1/a)=1
(i) Multiplicative inverse of –13 is – ¹/₁₃
(ii) Multiplicative inverse of – ¹³/₁₉ is – ¹⁹/₁₃
(iii) Multiplicative inverse of ¹/₅ is 5
(iv) Multiplicative inverse of – ⁵/₈ × – ³/₇ =
¹⁵/₅₆ is ⁵⁶/₁₅
(v) Multiplicative inverse of –1× – ²/₅= ²/₅ is ⁵/₂
(vi) Multiplicative inverse of –1 is ¹/ ₋₁= –1
class 8 maths chapter 1 exercise 1.1 (5)
5 Name the property under multiplication used in each of the following:
(i) – ⁴/₅×1=1× –⁴/₅
(ii) –¹³/₁₇ ×– ²/₇ = – ²/₇ × –¹³/₁₇
(iii) –¹⁹/₂₉ × ²⁹/₋₁₉=1
Solution to class 8 maths chapter 1 exercise 1.1(5)
Answer :
(i) 1 is the multiplicative identity.
(ii)Commutative property.
(iii)Multiplicative Inverse property.
class 8 maths chapter 1 exercise 1.1 (6)
6 Multiply ⁶/₁₃ by the reciprocal of ⁻⁷/₁₆
Solution to class 8 maths chapter 1 exercise 1.1(6)
Answer : Reciprocal of ⁻⁷/₁₆ is ¹⁶/₋₇
According to question
⁶/₁₃ × (¹⁶/₋₇)= – ⁹⁶/₉₁
class 8 maths chapter 1 exercise 1.1 (7)
7 Tell what property allows you to compute
⅓ ×(6 × ⁴/₃) as (⅓ × 6)× ⁴/₃
Solution to class 8 maths chapter 1 exercise 1.1(7)
Answer :
By using associative property of multiplication, a×(b ×c) = (a ×b)×c.
class 8 maths chapter 1 exercise 1.1 (8)
8 Is ⁸/₉ the multiplicative inverse of –1¹/₈? Why or why not?
Solution to class 8 maths chapter 1 exercise 1.1(8)
Answer :
Since multiplicative inverse of a is 1/a, such that a×(1/a)=1
(⁸/₉) ×(–1¹/₈) =(⁸/₉) × (⁻⁹₈)= – 1≠1
∴ ⁸/₉ is not the multiplicative inverse of –1¹/₈
class 8 maths chapter 1 exercise 1.1 (9)
9 Is 0.3 is multiplicative inverse of 3⅓? Why or why not?
Solution to class 8 maths chapter 1 exercise 1.1(9)
Answer: Since multiplicative inverse of a is 1/a, such that a×(1/a)=1
∴ 0.3 × 3⅓ = ³/₁₀×¹⁰/₃ =1
∴ Yes, 0.3 is multiplicative inverse of 3⅓
class 8 maths chapter 1 exercise 1.1 (10)
10 Write
(i) The rational number that does not have a reciprocal.
(ii)The rational numbers that are equal to their reciprocals.
(iii) The rational number that is equal to its negative.
Solution to class 8 maths chapter 1 exercise 1.1(10)
Answer : (i) 0
(ii) 1 and –1
(iii) 0
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 1/x, where x ≠ 0 is
______
(v) The product of two rational numbers is always a _____
(vi) The reciprocal of a positive rational number is ______
Solution to class 8 maths chapter 1 exercise 1.1(11)
Answer : (i)No
(ii)1 and –1
(iii) – ⅕
(iv) x
(v)Rational
(vi) positive
Exercise 2
class 8 maths chapter 1 exercise 1.2 (1)
1 Represent these numbers on number line.
(i) ⁷/₄ (ii) – ⁵/₆
Solution to class 8 maths chapter 1 exercise 1.2(1)
(i) ⁷/₄=1¾
Here, P is 1¾=⁷/₄.
(ii) – ⁵/₆
Here, M is – ⁵/₆
solution to class 8 maths chapter 1 exercise 1.2 (2)
2 Represent – ²/₁₁ , – ⁵/₁₁ , –⁹/₁₁ on the number line.
Solution to class 8 maths chapter 1 exercise 1.2(2)
Answer : B= – ²/₁₁ , C= – ⁵/₁₁ , D= – ⁹/₁₁
solution to class 8 maths chapter 1 exercise 1.2 (3)
3 Write five rational numbers which are smaller than 2.
Solution to class 8 maths chapter 1 exercise 1.2(3)
Answer : ⅙ , ⅓ , ½ , – ¼, – ⅕ and so on.
solution to class 8 maths chapter 1 exercise 1.2 (4)
4 Find ten rational numbers between – ⅖ and ½.
Solution to class 8 maths chapter 1 exercise 1.2(4)
Answer : Given rational numbers are –⅖ and ½
Here LCM of 5 and 2 is 10.
∴ – ⅖ × ²/₂= – ⁴/₁₀ and ¹/₂ ×⁵/₅= ⁵/₁₀
Again, – ⁴/₁₀ ײ/₂ = – ⁸/₂₀ and ⁵/₁₀ × ²/₂ =¹⁰/₂₀
∴ Ten rational numbers between – ⅖ and ½
are –⁷/₂₀ , – ⁶/₂₀ , – ⁵/₂₀ , – ⁴/₂₀ , – ³/₂₀ , – ²/₂₀ , – ¹/₂₀ , 0, ¹/₂₀ , ²/₂₀
solution to class 8 maths chapter 1 exercise 1.2 (5)
5 Find five rational numbers between (i) ⅔ and ⅘ (ii) – ³/₂ and ⁵/₃ (iii) ¼ and ½
Solution to class 8 maths chapter 1 exercise 1.2(5)
Answer : (i) ⅔ and ⅘
L.C.M of 3 and 5 is 15
∴ ⅔ × ⁵/₅=¹⁰/₁₅ and ⁴/₅׳/₃=¹²/₁₅
Again ¹⁰/₁₅ × ⁴/₄ = ⁴⁰/₆₀ and ¹²/₁₅ × ⁴/₄ = ⁴⁸/₆₀
∴ Five rational numbers between ⅔ and ⅘ are ⁴¹/₆₀ ,⁴²/₆₀ , ⁴³/₆₀ , ⁴⁴/₆₀ , ⁴⁵/₆₀
(ii) – ³/₂ and ⁵/₃
L.C.M of 2 and 3 is 6.
∴ – ³/₂ × ³/₃= –⁹/₆ and ⁵/₃ ײ/₂=¹⁰/₆
Five rational numbers between –³/₂ and ⁵/₃ are – ⁸/₆ , – ⁷/₆ ,– ⁸/₆ , 0 , ⅙,
(iii) ¼ and ½
L.C.M of 2 and 4 is 4.
∴ ¼ ×¹/₁=¼ and ½ × ²/₂=²/₄
Again, ¼ ×⁸/₈=⁸/₃₂ and ²/₄ ×⁸/₈=¹⁶/₃₂
∴ Five rational numbers between ¼ and ½ are ⁹/₃₂ ,¹⁰/₃₂ ,¹¹/₃₂ ,¹²/₃₂ ,¹³/₃₂
solution to class 8 maths chapter 1 exercise 1.2 (6)
6 Write five rational numbers greater than –2
Solution to class 8 maths chapter 1 exercise 1.2(6)
Answer : Five rational numbers greater than –2 are – ³/₂ ,–1, – ½ , 0, 1
solution to class 8 maths chapter 1 exercise 1.2 (7)
7 Find ten rational numbers between ⅗ and ¾
Solution to class 8 maths chapter 1 exercise 1.2(7)
Answer : L.C.M of 5 and 4 is 20.
∴ ⅗ ×⁴/₄=¹²/₂₀ and ¾ × ⁵/₅=¹⁵/₂₀
Again, ¹²/₂₀ ×⁸/₈ =⁹⁶/₁₆₀ and ¹⁵/₂₀ ×⁸/₈=¹²⁰/₁₆₀
∴ Ten rational numbers between ¼ and ½ are ⁹⁷/₁₆₀ , ⁹⁸/₁₆₀ ,⁹⁹/₁₆₀ ,¹⁰⁰/₁₆₀ ,¹⁰¹/₁₆₀ , ¹⁰²/₁₆₀ , ¹⁰³/₁₆₀ ,¹⁰⁴/₁₆₀ ,¹⁰⁵/₁₆₀ ,¹⁰⁶/₁₆₀