NCERT Exercise 3.2 Solution Class 6 Math
Question (1) What is the sum of any two
(a) Odd numbers?
Answer: The sum of two odd numbers are even numbers.
Example
(i) 1 and 3 are two odd numbers.
And their sum = 1 + 3 = 4
Here the sum of 1 and 3 is equal to 4, which is an even number.
(ii) 5 and 7 are two odd numbers.
And, their sum = 5 + 7 = 12
Here the sum of 5 and 7 is equal to 7, which is an even number.
(b) Even Numbers?
Answer The sum of two even numbers is always even numbers.
Example
(i) 2 and 4 are two even numbers
And their sum = 2 + 4 = 6
Here, the sum of two even numbers, 2 and 4 is equal to 6, which is an even number.
(ii) 10 and 12 are two even numbers
And their sum = 10 + 12 = 22
Here, the sum of two even numbers, 10 and 12 is equal to 22, which is an even number.
Question (2) State whether the following statements are True or False:
(a) The sum of three odd numbers is even.
Answer: False.
Explanation
The sum of three odd numbers is always an odd number.
Example (i)
1, 3, and 5 are three odd numbers.
And, sum of 1, 3, and 5
= 1 + 3 + 5 = 9
Here, the sum of three odd numbers 1, 3, and 5 is equal to 9 which is an odd number.
Example (ii)
7, 9, and 13 are three odd numbers.
And, sum of 7, 9, and 13
= 7 + 9 + 13 = 29
Here, the sum of three odd numbers 7, 9, and 13 is equal to 29 which is an odd number.
(b) The sum of two odd numbers and one even number is even.
Answer: True
Explanation
The sum of two odd numbers is always an even number, and the sum of two even numbers is always an even number. Hence, the sum of three odd numbers is always an even number.
Example (i): Let two odd numbers 1 and 3, and an even number 4
Thus, sum of all these three numbers, 1, 3, and 4
= 1 + 3 + 4 = 8
Here, 8 is an even number.
Thus, sum of two odd numbers 1 and 3 and one even number 4 is equal to 8 which is an even number.
Example (ii): Let two odd numbers 5 and 7, and an even number 12
Thus, sum of all these three numbers, 5, 7, and 12
= 5 + 7 + 12 = 24
Here, 24 is an even number.
Thus, sum of two odd numbers 5 and 7 and one even number 12 is equal to 24 which is an even number.
Thus, sum of two odd numbers and one even number is always an even number.
(c) The product of three odd numbers is odd.
Answer: True.
ExplanationThe product of odd numbers is always odd.
The product of two odd numbers is always an odd number. And when we multiply this odd number with another odd number, we get an odd number. Thus, product of odd numbers is always odd.
Example
(i) 3 × 5 = 15
Here 3 and 5 are odd numbers, and the product of these numbers, 15 is also an odd number.
(ii) 7 × 21 = 147
Here 7 and 21 are odd numbers, and the product of these numbers, 147 is also an odd number.
(d) If an even number is divided by 2, the quotient is always odd.
Answer: False
Explanation
(i) 2 is the smallest even number. And when 2 is divided by 2 it gives 1 which is an odd number.
That is, 2 ÷ 2 = 1
(ii) 4 is an even number.
4 ÷ 2 = 2
When 4, an even number is divided by 2 it gives 2, an even number.
(iii) 4 is an even number.
10 ÷ 2 = 5
When 10, an even number is divided by 2 it gives 5, an odd number.
(e) All prime numbers are odd.
Answer: False
Explanation
Two is the smallest prime number and is an even number.
All other prime numbers except 2 are odds.
(f) Prime numbers do not have any factors.
Answer False
Explanation
Numbers which have only two factors, 1 and the number itself, are known as Prime Numbers.
(g) Sum of two prime numbers is always even.
Answer False
Two (2) is the smallest prime number and it is an even number.
When any prime number is added with 2, it gives an odd number.
Thus, the given statement, "Sum of two prime numbers is always even," is False.
(h) 2 is the only even prime number.
Answer True
Explanation
The number which is exactly divisible by 2 is called an even number.
2 is a prime number and is divisible by 2, thus it is an even number.
All prime numbers except 2 are odd numbers.
Thus, the given statement, "2 is the only even prime number," is ture.
(i) All even numbers are composite numbers.
Answer False.
Explanation
The numbers can be divided in two categories on the basis of their divisibility by 2, these categories are Prime Numbers and Even Numbers.
The numbers which has only two factors, 1 and the number themselves, are called Prime Numbers.
And, the numbers which has more than two factors, are known as Composite Numbers.
Thus, the given statement, "All even numbers are composite numbers," is false.
(j) The product of two even numbers is always even.
Answer True.
Example
(i) 2 × 4 = 6
Here, 2 and 4 are even numbers and their product 6 is also an even number.
(ii) 8 × 100 = 800
Here, 8 and 100 are even numbers and their product 100 is also an even number.
Thus, the given statement, "The product of two even numbers is always even," is true.