Definition properties rules and solved examples of even and odd numbers
A number can be considered even or odd. Even numbers are numbers ending in 0, 2, 4, 6, or 8, and odd numbers ending in 1, 3, 5, 7, or 9.
The Even and Odd Numbers
What are Odd and Even Numbers?
If you've ever had this question or if you don't understand what it means, you need to know that a number can be classified as even or odd. Even numbers are those divisible by 2. That is if we divide a number by 2 and the remainder of the division is zero, it is an even number. A number is considered odd if it is not divisible by 2, that is if we divide that number by 2 and it leaves a remainder equal to 1. In the article, below see the even and odd numbers charts.
Properties of Even and Odd Numbers
An integer can be either even or odd.
Even numbers are divisible by 2.
Odd numbers are not divisible by 2.
The unit of even numbers is equal to 0, 2, 4, 6, or 8.
The unit of odd numbers is equal to 1, 3, 5, 7, or 9.
Two even integers added together result in an even number.
Two odd integers are added together to make an even number.
An even number is produced when two even integers are multiplied.
Two odd integers multiplied together result in another odd number.
Even Number
A number is classified as even if it is divisible by 2, that is if we can divide it into two equal parts.
For example, if there are 6 marbles, it is possible to divide them between two people so that none are left, leaving 3 marbles for one person and 3 for the other. So 6 is an even number.
The Even Numbers Example
In general, an even number is one whose unit is equal to 0, 2, 4, 6, or 8. Watch:
The number 534 is even, as its unit is 4.
The number 1023 is not even, as its unit is 3.
Even Numbers Less than 100
See below for all even numbers less than 100.
Even Numbers Less than 100
Odd Number
A number is classified as odd if it is not divisible by 2. That is, by dividing this number by 2, we will find a remainder equal to 1.
For example, if we are going to divide 11 marbles between 2 people, we will give 5 marbles to each one and there will be 1 marble left.
Example of Odd Numbers
In general, an odd number is one whose unit is equal to 1, 3, 5, 7, or 9. Watch:
The number 245 is odd, as its unit is 5.
The number 2024 is not odd, as its unit is 4.
Odd Numbers Less than 100
See below for all odd numbers less than 100.
The Odd Numbers Less than 100
Solved Examples
Q1. The sum of four odd numbers is equal to:
Ans: When we add the odd numbers two by two, we find two numbers that are even. When we add these two even numbers together, we will find an even number. Therefore, the sum of four odd numbers is equal to an even number, as the sum of two odd numbers is an even number and the sum of two even numbers is an even number.
Q2. Matheus lives in the third apartment on the 26th floor of a building. To speak with Matheus, the doorman calls number 2603, which is Matheus' apartment. Analysing this number, is it even or odd?
Ans: Number 2603 is an odd number. To know if it is odd, just look at the unit place of this number, which is equal to 3. Numbers ending in 3 are always odd.
Practice on Your Own
Q1. What is the Smallest Positive Even Number and an Odd Number?
Ans: Smallest positive numbers that are even and odd are 2 and 1, respectively.
Q2. Write all the even numbers from 1 – 50.
Ans: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50.
Tips on Even and Odd Numbers that help Students to learn
While counting the numbers, the alternating number starting from one will always be odd while the alternating number starting from 2 will always be an even number.
One of the easy ways to find out regarding the even and off is by checking whether it is divisible by 2 or not.
Non-integer numbers will neither be odd nor even which includes decimals, fraction numbers, and even infinity.
The set of odd and even numbers can be determined by taking a look at the one's place and the number present there as well.
Every odd number will consist of the letter “e” in it.
Summary
The article describes what is odd and even numbers. Even numbers are those that have the number two as a multiple, or what is the same, that have a perfect half. If we take an even number and divide it in half, it will give us two equal parts. This means that all even numbers have two equal halves.
On the other hand, odd numbers are those that do not have equal halves, that is, if they are divided by two, one part will be greater than the other, or they will have decimals to their credit.
FAQs on Understanding Even and Odd Numbers in Maths
1. What are even and odd numbers?
An even number is a whole number divisible by 2, while an odd number is a whole number not divisible by 2.
- Even numbers end in 0, 2, 4, 6, 8.
- Odd numbers end in 1, 3, 5, 7, 9.
- Examples: 8 is even (8 ÷ 2 = 4), 7 is odd (7 ÷ 2 leaves remainder 1).
2. How do you identify if a number is even or odd?
You can identify an even or odd number by checking its last digit.
- If the last digit is 0, 2, 4, 6, or 8 → the number is even.
- If the last digit is 1, 3, 5, 7, or 9 → the number is odd.
3. What is the formula for even and odd numbers?
An even number can be written as 2n, and an odd number can be written as 2n + 1, where n is an integer.
- Example of even: If n = 5, then 2n = 10.
- Example of odd: If n = 5, then 2n + 1 = 11.
4. What happens when you add two even numbers?
When you add two even numbers, the result is always even.
- Example: 6 + 8 = 14 (even).
- Reason: 2a + 2b = 2(a + b), which is divisible by 2.
5. What happens when you add two odd numbers?
When you add two odd numbers, the result is always even.
- Example: 5 + 7 = 12 (even).
- Reason: (2a + 1) + (2b + 1) = 2(a + b + 1).
6. What happens when you add an even and an odd number?
When you add an even number and an odd number, the result is always odd.
- Example: 4 + 9 = 13 (odd).
- Reason: 2a + (2b + 1) = 2(a + b) + 1.
7. Are zero and negative numbers even or odd?
Zero is an even number, and negative numbers follow the same even-odd rules as positive numbers.
- 0 ÷ 2 = 0, so 0 is even.
- −4 is even because it is divisible by 2.
- −7 is odd because it is not divisible by 2.
8. How do you check if a large number is even or odd?
To check if a large number is even or odd, look only at its units digit.
- If the last digit is 0, 2, 4, 6, or 8 → even.
- If the last digit is 1, 3, 5, 7, or 9 → odd.
9. What is the difference between even and odd numbers?
The main difference is that even numbers are divisible by 2, while odd numbers are not.
- Even numbers can be split into two equal groups.
- Odd numbers always leave a remainder of 1 when divided by 2.
- Examples: 12 (even), 15 (odd).
10. What are some real-life examples of even and odd numbers?
Even and odd numbers appear in everyday counting and grouping situations.
- Even example: 10 apples can be divided equally between 2 people.
- Odd example: 7 chairs cannot be split equally into two equal rows.
- House numbers and jersey numbers are often classified as even or odd.
