Even and Odd numbers: Overview, Questions, Preparation

A number represents some value or quantity. Numbers are of different types, including whole numbers, natural numbers, imaginary numbers, and real numbers. We also categorise them as even and odd numbers.

We represent the set of all even numbers as {2k: k ϵ Z} and the set of all odd numbers as {2k + 1: k ϵ Z}.

We can infer that even numbers are integers of the form n = 2k, where ‘k’ is also an integer. And odd numbers are integers that exist in the form n = 2k +1. However, both even and odd numbers are only for integers and not for non-integers, such as fractions or decimal numbers.

A number is even or odd if it has the following properties.

1. When we add two even numbers, the resulting number will always be an even number.
2. Likewise, when we add two odd numbers, the resulting number will always be an even number.
3. Even numbers should be divisible by ‘two,’ leaving ‘zero’ as the remainder.
4. Similarly, a number is odd if it isn’t completely divisible by ‘two,’ leaving a remainder.

An even number ends with the digits, 0, 2, 4, 6, 8, while an odd number ends with the digits, 1, 3, 5, 7, 9. From this, we come to know that ‘zero’ is also an even number.

Also, decimals cannot be odd or even numbers as they are not whole numbers.

Even and Odd Numbers for Class 10

Odd and even numbers are a part of the chapter ‘Number System’ in Class 10. The chapter carries 6 marks in the exam.

1.     What are the sums of two odd and even numbers?

 When we add two odd numbers, it always results in an even number.

For example, 1 + 3 = 4, which is an even number.

Similarly, adding two even numbers always results in an even number.

For instance, 2 + 4 = 6, which is an even number.

2.     Express the following as the sum of three odd prime numbers.

 21, 31, 61, 53. 

Solution:

21 = 3 + 7 + 11.

Similarly, 31 = 3 + 11 + 17.

Likewise, 61 = 19 + 29 + 13.

And, 53 = 13 + 17 + 23

3.     Express each number that you find below as the sum of two even numbers. 

44, 36, 24, 18

Solution:

44 = 20 + 24.

Similarly, 36 = 20 + 16.

Likewise, 24 = 10 +14.

And, 18 = 10 + 8

Q: How to identify if a number is even or odd?

Q: What are odd composite numbers?

Q: What is the product of two odd numbers?

Q: What is the product of two even numbers?

Q: Why are decimals not odd or even numbers?