Very few questions are in the NCERT book Chapter 1, Rational Numbers. However, in examples, we have a few questions, but these need to be included in the exercise. We have included 5 additional questions besides the 3 questions in the book. I hope it helps to clear the concept. Please solve the additional questions, too.
NCERT Solutions for Class 8 Maths Exercise 1.1 Chapter 1 Rational Numbers
1. Name the property under multiplication used in each of the following:
Solution:
(i) -4/5 × 1 = 1 × -4/5 = -4/5
This illustrates the Identity Property of Multiplication, which states that any number multiplied by 1 equals the number itself.
(ii) -13/17 × -2/7 = -2/7 × -13/17
This example is about the Commutative Property of Multiplication. As per this property, changing the order of the numbers being multiplied does not change the product.
(iii) -19/29 × 29/-19 = 1
Two rational numbers are inverses of each other. When these numbers are multiplied, they produce 1. It shows Multiplicative Inverse Property. It states that a number times its reciprocal equals 1.
2. Tell what property allows you to compute 1/3 × (6 × 4/5) as (1/3 × 6) × 4/3
Solution:
The property used here is the Associative Property of Multiplication. As per this property the way numbers are grouped in a multiplication problem does not affect the product. Therefore, 1/3 × (6 × 4/5) can be regrouped as (1/3 × 6) × 4/5 without changing the result.
3. The product of two rational numbers is always a ___.
Solution:
The product of two rational numbers is always a rational number.
Rational numbers are numbers that can be expressed as the quotient of two integers. The product of two such quotients is also a quotient of integersand that is what makes it a rational number.
Additional Questions
1. Find the sum of the following rational numbers:
Solution:
Find 5/6 + (-3/8) + (-7/12) + (2/9)
= (5 × 72 + (-3) × 54 + (-7) × 36 + 2 × 48) / 216 (LCM of 6, 8, 12, and 9 is 216)
= (360 – 162 – 252 + 96) / 216
= 42 / 216
= 7/36 (Simplifying the fraction)
2. Calculate the product of these rational numbers:
Solution:
Find -2/3 × 4/5 × -7/9
= (-2 × 4 × -7) / (3 × 5 × 9) (Multiplying numerators and denominators separately)
= 56 / 135
= 56/135
3. Determine the sum of these rational numbers:
Solution:
Find -1/4 + 5/6 + (-3/8) + 7/12
= (-1 × 24 + 5 × 16 – 3 × 12 + 7 × 8) / 48 (LCM of 4, 6, 8, and 12 is 48)
= (-24 + 80 – 36 + 56) / 48
= 76 / 48
= 19/12
4. Find the product of these rational numbers:
Solution:
Find 3/7 × -5/11 × 7/3 × -11/5
= (3 × -5 × 7 × -11) / (7 × 11 × 3 × 5) (Multiplying numerators and denominators separately)
= -1 (All terms cancel out, leaving -1)
= -1
5. Calculate the sum of the following rational numbers:
Solution:
Find -7/10 + 3/4 + (-1/5) + 2/3
= (-7 × 60 + 3 × 50 – 1 × 24 + 2 × 40) / 120 (LCM of 10, 4, 5, and 3 is 120)
= (-420 + 150 – 24 + 80) / 120
= -214 / 120
= -107/60 (Simplifying the fraction)
