NCERT Solutions for 8th Class Maths: Chapter 1 Rational Numbers
Page No: 14
Exercise 1.1
1. Using appropriate properties find.
(i) -2/3 × 3/5 + 5/2 - 3/5 × 1/6 (ii) 2/5 × (-3/7) - 1/6 × 3/2 + 1/14 × 2/5
Answer
(i) -2/3 × 3/5 + 5/2 - 3/5 × 1/6
= -2/3 × 3/5 - 3/5 × 1/6 + 5/2 (by commutativity)
= 3/5(-2/3 - 1/6) + 5/2
= 3/5{(-4 - 1)/6} + 5/2
= 3/5(-5/6) + 5/2 (by distributivity)
= -15/30 + 5/2
= -1/2 + 5/2
= 4/2 = 2
(ii) 2/5 × (-3/7) - 1/6 × 3/2 + 1/14 × 2/5
= 2/5 × (-3/7) + 1/14 × 2/5 - (1/6 × 3/2) (by commutativity)
= 2/5(-3/7 + 1/14) - 1/4
= 2/5{(-6 + 1)/14} - 1/4 (by distributivity)
= 2/5(-5/14) - 1/4
= -1/7 - 1/4
= (-4-7)/28
= -11/28
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
Answer
(i) 2/8
Additive inverse = -2/8
(ii) -5/9
Additive inverse = 5/9
(iii) -6/-5 = 6/5
Additive inverse = -6/5
(iv) 2/-9 = -2/9
Additive inverse = 2/9
(v) 19/-6 = -19/6
Additive inverse = 19/6
3. Verify that : -(-x) = x for.
(i) x = 11/15 (ii) x = -13/17
Answer
(i) x = 11/15
The additive inverse of x = 11/15 is -x = -11/15 as 11/15 + (-11/15) = 0
The same equality 11/15 + (-11/15) = 0 , shows that the additive inverse of -11/15 is 11/15 or
-(-11/15) = 11/15 i.e. -(-x) = x
(ii) x = -13/17
The additive inverse of x = -13/17 is -x = 13/17 as (-13/17) + 13/17 = 0
The same equality 13/17 + (-13/17) = 0 , shows that the additive inverse of 13/17 is -13/17 or
-(13/17) = -13/17 i.e. -(-x) = x
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
Answer
The multiplicative inverse of a number is the reciprocal of that number.
(i) -13
Multiplicative inverse = -1/13
(ii) -13/19
Multiplicative inverse = -19/13
(iii) 1/5
Multiplicative inverse = 5
(iv) -5/8 × -3/7 = 15/56
Multiplicative inverse = 56/15
(v) -1 × -2/5 = 2/5
Multiplicative inverse = 5/2
(vi) -1
Multiplicative inverse = -1
5. Name the property under multiplication used in each of the following.
(i) -4/5 × 1 = 1 × -4/5 = -4/5
(ii) -13/17 × -2/7 = -2/7 × -13/17
(iii) -19/29 × 29/-19 = 1
Answer
(i) -4/5 × 1 = 1 × -4/5 = -4/5
Here 1 is the multiplicative identity.
(ii) -13/17 × -2/7 = -2/7 × -13/17
Commutavity
(iii) -19/29 × 29/-19 = 1
Multiplicative inverse
6. Multiply 6/13 by the reciprocal of -7/16.
Answer
Reciprocal of -7/16 = 16/-7
A/q,
6/13 × (Reciprocal of -7/16)
= 6/13 × 16/-7 = 96/-91 = -96/91
7. Tell what property allows you to compute 1/3 × (6 × 4/3) as (1/3 × 6) × 4/3.
Answer
By the property of associativity.
8. Is 8/9 the multiplicative inverse of 
? Why or why not?
Answer
If it will be the multiplicative inverse then their product will be 1.
= -7/8
A/q,
8/9 × -7/8 = -7/9 ≠ 1
Hence, 8/9 is not the multiplicative inverse.
9. Is 0.3 the multiplicative inverse of 
? Why or why not?
Answer
If it will be the multiplicative inverse then their product will be 1.
= 10/3
also, 0.3 = 3/10
A/q,
3/10 × 10/3 = 1
Hence, 0.3 is the multiplicative inverse.
Page No: 15
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.
Answer
(i) 0 is the rational number that does not have a reciprocal.
(ii) 1 and -1 are the rational numbers that are equal to their reciprocals.
(iii) 0 is the rational number that is equal to its negative.
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 ________.
Answer
(i) Zero has no reciprocal.
(ii) The numbers 1 and -1 are their own reciprocals
(iii) The reciprocal of -5 is -1/5.
(iv) Reciprocal of 1/x, where x ≠ 0 is x
(v) The product of two rational numbers is always a rational numbers.
(vi) The reciprocal of a positive rational number is positive rational numbers.
Page No: 20
Exercise 1.2
1. Represent these numbers on the number line. (i) 7/4 (ii) -5/6
Answer
(i) 7/4 on the number line.
Divide line between two natural number in 4 parts. Thus, the rational number 7/4 lies at a distance of 7 points from 0 towards positive number line.
(ii) -5/6 on the number line.
Divide line between two natural number in 6 parts. Thus, the rational number -5/6 lies at a distance of 5 points from 0 towards negative number line.
2. Represent -2/11, -5/11, -9/11 on the number line.
Answer
-2/11, -5/11, -9/11 on the number line.
Divide line between two natural number in 11 parts. Thus, the rational number -2/11, -5/11, -9/11 lie at a distance of 2, 5, 9 points from 0 towards negative number line respectively.
3. Write five rational numbers which are smaller than 2.
Answer
2 can be written as 10/5.
Thus, 5 natural numbers smaller than 2 are:
9/5, 8/5, 7/5, 6/5 and 5/5
4. Find ten rational numbers between -2/5 and 1/2.
Answer
The numbers -2/5 and 1/2 can be written as -8/20 and 10/20
Thus, ten rational numbers between -2/5 and 1/2 are:
-7/20, -6/20, -5/20, -4/20, -3/20, -2/20, -1/20, 0, 1/20 and 2/20
5. Find five rational numbers between.
(i) 2/3 and 4/5 (ii) -3/2 and 5/3 (iii) 1/4 and 1/2
Answer
(i) Five rational numbers between 2/3 and 4/5
The numbers 2/3 and 4/5 can be written as 30/45 and 36/45
Thus, five rational numbers are:
31/45, 32/45, 33/45, 34/45 and 35/45
(ii) Five rational numbers between -3/2 and 5/3
The numbers -3/2 and 5/3 can be written as -9/6 and 10/6
Thus, five rational numbers are:
-8/6, -5/6, -2/6, 0 and 2/6
(iii) Five rational numbers between 1/4 and 1/2
The numbers 1/4 and 1/2 can be written as 7/28 and 14/28
Thus, five rational numbers are:
8/28, 9/28, 10/28, 11/28 and 12/28
6. Write five rational numbers greater than -2.
Answer
-2 can be written as -16/8.
Five rational numbers greater than -2 are:
-15/8, -14/8, -13/8, -12/8 and -11/8
7. Find ten rational numbers between 3/5 and 3/4.
Answer
The numbers 3/5 and 3/4 can be written as 48/80 and 60/80
Thus, ten rational numbers between 3/5 and 3/4 are:
49/80, 50/80, 51/80, 52/80, 53/80, 54/80, 55/80, 56/80, 57/80 and 58/80.
Chapterwise NCERT Solutions for 8th Class Maths
Chapter 1 – Rational Numbers
Chapter 2 – Linear Equations in One Variable
Chapter 3 – Understanding Quadrilaterals
Chapter 4 – Practical Geometry
Chapter 5 – Data Handling
Chapter 6 – Squares and Square Roots
Chapter 7 – Cubes and Cube Roots
Chapter 8 – Comparing Quantities
Chapter 9 – Algebraic Expressions and Identities
Chapter 10 – Visualizing Solid Shapes
Chapter 11 – Mensuration
Chapter 12 – Exponents and Powers
Chapter 13 – Direct and Inverse Proportions
Chapter 14 – Factorization
Chapter 15 – Introduction to Graphs
Chapter 16 – Playing with Numbers
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