Numbers can be divided into two main categories: even and odd. Knowing the difference helps in math problems, counting, and everyday situations like sharing items equally.

Even Numbers

• Definition: Numbers that can be split into two equal groups with nothing left over.
• Examples: 2, 4, 6, 8, 10, 12, 14, …
• How to Spot Them: Even numbers always end with 0, 2, 4, 6, or 8.

Examples:

• 8 ÷ 2 = 4 (no remainder → even)
• 14 ÷ 2 = 7 (no remainder → even)

Let’s take a closer look at the number 8 to understand why it’s even.

1. Dividing into Equal Groups

• Imagine you have 8 apples 🍎🍎🍎🍎🍎🍎🍎🍎.
• If you split them into two equal groups, you get:
  • Group 1: 🍎🍎🍎🍎
  • Group 2: �🍎🍎🍎
• Each group has 4 apples, with none left over.
• Since they divide perfectly, 8 is even.

2. Checking the Last Digit

• Even numbers always end in 0, 2, 4, 6, or 8.
• The number 8 ends with 8, so it must be even.

3. Dividing by 2 (No Remainder)

• 8 ÷ 2 = 4 (exact division, no remainder).
• If a number divides cleanly by 2, it’s even.

Odd Numbers

• Definition: Numbers that cannot be split into two equal groups—there’s always one left over.
• Examples: 1, 3, 5, 7, 9, 11, 13, …
• How to Spot Them: Odd numbers always end with 1, 3, 5, 7, or 9.

Examples:

• 7 ÷ 2 = 3 with 1 left → odd
• 11 ÷ 2 = 5 with 1 left → odd

Let’s explore the number 7 in detail to understand exactly what makes it odd.

1. The Leftover Test (Most Fundamental Definition)

• Scenario: You have 7 apples 🍎🍎🍎🍎🍎🍎🍎
• Try to split them equally between 2 people:
  • First person gets 3 apples: 🍎🍎🍎
  • Second person gets 3 apples: 🍎🍎🍎
  • Leftover apple: 🍎
• Conclusion: Since there’s 1 apple remaining, 7 cannot be divided into two equal whole numbers. This makes it odd.

2. The Last Digit Rule (Quick Identification)

• Odd numbers always end with 1, 3, 5, 7, or 9.
• 7 ends with 7 → immediately tells us it’s odd.
• Other examples:
  • 23 (ends with 3 → odd)
  • 105 (ends with 5 → odd)
  • 1,009 (ends with 9 → odd)

3. The Division Test (Mathematical Proof)

• When we divide 7 by 2:
  • 7 ÷ 2 = 3 with a remainder of 1
• Key point: Odd numbers always have a remainder of 1 when divided by 2.
• Compare to even numbers:
  • 8 ÷ 2 = 4 (no remainder → even)
  • 7 ÷ 2 = 3 R1 (remainder → odd)

Practice:

1. Which of the following numbers are even?

3, 4, 16, 27, 55

Answer: 4 and 16, because the last digit of each number is an even number.

2. Which of the following numbers are odd?

7, 15, 24, 36, 88

Answer: 77 and 15, because the last digit of each number is an odd number.

Solve the following exercises:

Circle ⭕ for odd, box ▢ for even:

1. 2 ▢ ⭕
2. 5 ▢ ⭕
3. 8 ▢ ⭕
4. 1 ▢ ⭕
5. 4 ▢ ⭕

Pattern Hint: Alternate between odd and even starting from 2.
Answer: 2(e), 5(o), 8(e), 1(o), 4(e)

Write “O” for odd, “E” for even:

1. 14 → ___
2. 27 → ___
3. 30 → ___
4. 63 → ___
5. 98 → ___

Bonus: What’s the pattern?
Answer: E, O, E, O, E (alternating)

Complete the sequence and label (O/E):

105 (O), 108 (), 111 (), ___ (), ___ ()

16 (E), 19 (), 22 (), ___ (), ___ ()

Clue: First sequence +3, second sequence +3.
Answer: 1. 19(O), 22(E), 25(O), 28(E) / 2. 108(E), 111(O), 114(E), 117(O)

So, to see which number is even or odd, we look at the last digit of each number, if it is 0, 2, 4, 6 or 8, then the number is even, and if it is 1, 3, 5, 7 or 9 , then the number is odd.