Identifying Even Numbers

Is 48 an even or odd number?

Look at the last digit: The last digit of 48 is 8 = Last digit: 8

Check if it's in the even list: Even digits are 0, 2, 4, 6, 8. Is 8 in this list? = Yes, 8 is even

Conclusion: Since 48 ends in 8, it is even = 48 is even

Answer: 48 is an **even** number because it ends in 8.

Identifying Odd Numbers

Is 73 an even or odd number?

Look at the last digit: The last digit of 73 is 3 = Last digit: 3

Check if it's in the odd list: Odd digits are 1, 3, 5, 7, 9. Is 3 in this list? = Yes, 3 is odd

Conclusion: Since 73 ends in 3, it is odd = 73 is odd

Answer: 73 is an **odd** number because it ends in 3.

Division Test for Even Numbers

Show that 26 is even by dividing by 2.

Divide by 2: $26 \div 2 = 13$ = Result: 13

Check for remainder: $13 \times 2 = 26$ (exact) = No remainder

Conclusion: 26 divides evenly by 2, so it is even = 26 is even

Answer: $26 \div 2 = 13$ with no remainder, so 26 is **even**.

Adding Even and Odd Numbers

What happens when you add an even number and an odd number?

Try an example: $4 + 5 = 9$ = Even + Odd = 9 (odd)

Try another example: $6 + 3 = 9$ = Even + Odd = 9 (odd)

Try one more: $10 + 7 = 17$ = Even + Odd = 17 (odd)

Find the pattern: Every time we add even + odd, we get odd = Pattern: Even + Odd = Odd

Answer: **Even + Odd = Odd** (always!)

Mistake: Thinking 0 is neither even nor odd

Why: Zero can be confusing because it's special in many ways.

Correct: 0 IS even! It divides by 2 with no remainder: $0 \div 2 = 0$

Mistake: Looking at the first digit instead of the last

Why: It's easy to read left-to-right and check the wrong digit.

Correct: Always check the LAST digit. For 52, check 2 (not 5). For 87, check 7 (not 8).

Mistake: Thinking bigger numbers must be even

Why: Large numbers seem more "complete" but size doesn't matter.

Correct: Any size number can be even or odd. 1,000,001 is odd. 2 is even.

Fair Sharing

When dividing things between 2 people, even numbers split perfectly.

You have 14 candies to share with your friend. $14 \div 2 = 7$ each. Fair!

Pairing Objects

Even numbers pair up perfectly. Odd numbers always have one left alone.

8 socks make 4 complete pairs. 9 socks make 4 pairs with 1 sock left over.

Q: Is zero even or odd?

A: Zero is EVEN. It divides by 2 with no remainder ($0 \div 2 = 0$), and it fits the pattern: ..., $-4$, $-2$, 0, 2, 4, ...

Q: Are negative numbers even or odd?

A: Yes! Negative numbers can be even or odd too. $-4$ is even (ends in 4), and $-7$ is odd (ends in 7).

Q: What happens when you multiply even and odd numbers?

A: Even $\times$ anything = Even. Odd $\times$ Odd = Odd. So $3 \times 4 = 12$ (even), $3 \times 5 = 15$ (odd).