Question

Question 2 State whether the following statements are True or False: (a) The sum of three odd numbers is even. (b) The sum of two odd numbers and one even number is even. (c) The product of three odd numbers is odd. (d) If an even number is divided by 2, the quotient is always odd. (e) All prime numbers are odd. (f) Prime numbers do not have any factors. (g) Sum of two prime numbers is always even. (h) 2 is the only even prime number. (i) All even numbers are composite numbers. (j) The product of two even numbers is always even.

Class 6 - Math - Playing with Numbers Page 53

Answer 1

Odd numbers:

A number not divisible by 2 is odd number. All numbers 1 , 3 ,5 ,7 & 9 in the unit's place are called odd numbers.

Even numbers:

A number divisible by 2 is called even number. All the numbers 0, 2, 4, 6 , 8 in the unit's place are called even numbers..

Prime numbers:

Numbers that have only two factors 1 and the number itself are prime numbers.

Composite numbers:

Numbers that have more than two factors are called composite numbers.

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Solution:

a) False

Because the sum of three odd numbers always odd. E.g 3+5+7=15
& 7+ 5+ 9= 21

b) True

Because the sum of two odd numbers and one even number is always an even number.
For e.g
3(odd)+ 5(odd)+4(even)= 12(even)

c) True

Because product of three odd numbers is always odd.

For e.g
3×5×7=105(odd)

d) False

Because if an even number is divided by 2 the quotient is always an even number.
For e.g
36/2= 18(even)

e) False

Because 2 is only even prime number so all prime numbers are not odd.

f) False

Because prime numbers have two factors which are 1 & number itself.
For e.g

3 is a prime number & has two factors 1 & 3.

g) False

Because sum of two prime numbers is either odd or even.

For e.g
2+3= 5(odd)
5+7=12(even)

h) True.

Because 2 is the only even prime number.

i) False

Because all even numbers are not composite numbers.

For e.g
2 has the factors 1 & 2 only so it is a prime number but not a composite number.

j) True

Because a product of two even number is always even.

For e g.

2×4= 8,. 4× 4=16

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Hope this will help you...

Answer 2

Answer:

1. False
2. True
3. True
4. False
5. False
6. False
7. False
8. True
9. False
10. True