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**

Exercises and solutions of chapter 1 maths class 8 available here so students can read online view.

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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 ×²/₂ = – 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 ⁴/₅×³/₃=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 ×²/₂=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