Even and Odd Number Properties
Even numbers are numbers that are exactly divisible by 2 (remainder 0). Odd numbers leave a remainder of 1 when divided by 2. In Class 4, you will study the properties of even and odd numbers when they are added, subtracted, or multiplied.
These properties help you predict whether an answer will be even or odd without actually calculating it.
What is Even and Odd Number Properties - Class 4 Maths (Factors and Multiples)?
An even number is any whole number that can be divided by 2 with no remainder. Examples: 0, 2, 4, 6, 8, 10, 12, ...
An odd number is any whole number that leaves a remainder of 1 when divided by 2. Examples: 1, 3, 5, 7, 9, 11, 13, ...
Even numbers end in 0, 2, 4, 6, or 8. Odd numbers end in 1, 3, 5, 7, or 9.
Types and Properties
| Operation | Result | Example |
|---|---|---|
| Even + Even | Even | 4 + 6 = 10 |
| Odd + Odd | Even | 3 + 5 = 8 |
| Even + Odd | Odd | 4 + 3 = 7 |
Properties of Subtraction:
| Operation | Result | Example |
|---|---|---|
| Even − Even | Even | 8 − 4 = 4 |
| Odd − Odd | Even | 9 − 5 = 4 |
| Even − Odd | Odd | 10 − 3 = 7 |
| Odd − Even | Odd | 7 − 2 = 5 |
| Operation | Result | Example |
|---|---|---|
| Even × Even | Even | 4 × 6 = 24 |
| Odd × Odd | Odd | 3 × 5 = 15 |
| Even × Odd | Even | 4 × 3 = 12 |
Solved Examples
Example 1: Example 1: Even + Even
Problem: Is 14 + 26 even or odd?
Solution:
Step 1: 14 is even. 26 is even.
Step 2: Even + Even = Even.
Step 3: Verify: 14 + 26 = 40 (even).
Answer: The sum is even.
Example 2: Example 2: Odd + Odd
Problem: Is 13 + 27 even or odd?
Solution:
Step 1: 13 is odd. 27 is odd.
Step 2: Odd + Odd = Even.
Step 3: Verify: 13 + 27 = 40 (even).
Answer: The sum is even.
Example 3: Example 3: Even + Odd
Problem: Is 18 + 7 even or odd?
Solution:
Step 1: 18 is even. 7 is odd.
Step 2: Even + Odd = Odd.
Step 3: Verify: 18 + 7 = 25 (odd).
Answer: The sum is odd.
Example 4: Example 4: Odd x Odd
Problem: Without calculating, tell whether 15 × 9 is even or odd.
Solution:
Step 1: 15 is odd. 9 is odd.
Step 2: Odd × Odd = Odd.
Step 3: Verify: 15 × 9 = 135 (odd).
Answer: The product is odd.
Example 5: Example 5: Even x Odd
Problem: Is 6 × 11 even or odd?
Solution:
Step 1: 6 is even. 11 is odd.
Step 2: Even × Odd = Even.
Step 3: Verify: 6 × 11 = 66 (even).
Answer: The product is even.
Example 6: Example 6: Subtraction Property
Problem: Is 45 − 17 even or odd?
Solution:
Step 1: 45 is odd. 17 is odd.
Step 2: Odd − Odd = Even.
Step 3: Verify: 45 − 17 = 28 (even).
Answer: The difference is even.
Example 7: Example 7: Word Problem
Problem: Meera has 12 red beads and 9 blue beads. She strings them all together. Will the total number of beads be even or odd?
Solution:
Step 1: 12 is even (red beads). 9 is odd (blue beads).
Step 2: Even + Odd = Odd.
Answer: The total number of beads is odd (12 + 9 = 21).
Example 8: Example 8: Word Problem
Problem: There are 5 rows of chairs with 7 chairs in each row. Is the total number of chairs even or odd?
Solution:
Step 1: Total chairs = 5 × 7.
Step 2: 5 is odd. 7 is odd.
Step 3: Odd × Odd = Odd.
Answer: The total number of chairs is odd (5 × 7 = 35).
Example 9: Example 9: Multiple Operations
Problem: Is (4 + 5) × 3 even or odd?
Solution:
Step 1: 4 + 5 → Even + Odd = Odd. So (4 + 5) = 9 is odd.
Step 2: 9 × 3 → Odd × Odd = Odd.
Answer: The result is odd (9 × 3 = 27).
Key Points to Remember
- Even + Even = Even; Odd + Odd = Even; Even + Odd = Odd.
- Even − Even = Even; Odd − Odd = Even; mixing even and odd in subtraction gives Odd.
- Even × Even = Even; Odd × Odd = Odd; Even × Odd = Even.
- If any factor in a multiplication is even, the product is always even.
- The product of two odd numbers is the only way to get an odd product.
- These rules help you check answers quickly without full calculation.
Practice Problems
- Without calculating, state whether 124 + 87 is even or odd.
- Is 33 x 22 even or odd? Explain using the property.
- Aman has 15 toffees. He buys 8 more. Is his total even or odd?
- Is the sum of three odd numbers even or odd? Give an example.
- Kavi multiplied two numbers and got an odd result. What can you say about the two numbers?
- Find whether 100 - 37 is even or odd without subtracting.
- Is (6 + 9) x (4 + 3) even or odd? Use properties to decide.
Frequently Asked Questions
Q1. What is an even number?
An even number is any whole number divisible by 2 with no remainder. Even numbers end in 0, 2, 4, 6, or 8. Examples: 2, 10, 24, 136.
Q2. What is an odd number?
An odd number is any whole number that leaves a remainder of 1 when divided by 2. Odd numbers end in 1, 3, 5, 7, or 9. Examples: 3, 11, 25, 137.
Q3. Is 0 even or odd?
0 is an even number because it is divisible by 2 with no remainder (0 divided by 2 = 0).
Q4. Why is the sum of two odd numbers always even?
Each odd number can be thought of as an even number plus 1. When you add two odd numbers, the two extra 1s combine to make 2 (an even number), so the total is even. Example: 7 + 5 = 12.
Q5. Can the product of an even and odd number be odd?
No. If any factor is even, the product is always even. The only way to get an odd product is to multiply odd numbers only.
Q6. Is the sum of three odd numbers even or odd?
It is odd. Odd + Odd = Even, then Even + Odd = Odd. Example: 3 + 5 + 7 = 15 (odd).
Q7. How do even-odd properties help in maths?
They help you check whether an answer should be even or odd without doing the full calculation. This is useful for quick verification and error-checking in exams.
Q8. Do these properties work for large numbers?
Yes. The even-odd properties work for all whole numbers, no matter how large. You only need to check the last digit of each number to know if it is even or odd.
Q9. Is this topic part of the NCERT Class 4 syllabus?
Yes. Even and odd number properties are covered in Class 4 under the chapter Factors and Multiples. Students learn the addition, subtraction, and multiplication rules for even and odd numbers.
Related Topics
- Even and Odd Numbers Introduction
- Factors of a Number
- Multiples of a Number
- Common Factors
- Common Multiples
- HCF (Highest Common Factor) Introduction
- LCM (Least Common Multiple) Introduction
- Prime and Composite Numbers
- Sieve of Eratosthenes
- Factors and Multiples Word Problems
- Prime Numbers up to 100
- Factor Pairs
