 Properties of odd and even numbers

Lesson Look back to where we first investigated odd and even numbers.

Even numbers

A number is even if it can be equally split (divided) into $2$2 groups without a remainder.

So our pattern of even numbers goes $2,4,6,8,10,12$2,4,6,8,10,12 and keeps on going and going!

This means we start at $2$2 and jump $2$2 spaces each time.

Odd numbers

Odd numbers are the opposite of even numbers. Odd numbers cannot be divided into $2$2 groups- there's always an odd one out!

So our pattern of odd numbers goes $1,3,5,7,9,11$1,3,5,7,9,11 and keeps on going.

This means we start at $1$1 and jump forward $2$2 spaces each time.

A special case

Zero is not odd or even.

Looking at odd and even numbers together

Below are numbers from $1$1 to $20$20. The blue numbers are odd and the green numbers are even.

1  2  3   6  7  8  9  10  11  12  13  14  15  16  17  18  19  20

See how the numbers change from odd to even one by one?

Is it odd or even?

If it can be evenly divided by $2$2, it's even. If not, then it's odd.

Properties of odd and even numbers

When we add and subtract with odd and even numbers we notice some rules.

If we add or subtract two even numbers our answer is always even.

For example: $10-6=4$106=4

If we add or subtract two odd numbers our answer is always even.

For example: $5+7=12$5+7=12

If we add or subtract an odd and even number our answer is always odd.

For example: $14-5=9$145=9

Remember!

Two even numbers added, or subtracted, will equal an even number.

Two odd numbers added, or subtracted, will equal an even number.

Adding, or subtracting, an odd and even number will equal an odd number.

Examples

Question 1

Is $52$52 odd or even?

Do: $52\div2=26$52÷​2=26, plus $52$52 ends in a $2$2, so it is even.

Question 2

Is $397$397 odd or even?

Do: This number ends in a $7$7 (and can't be divided by $2$2) so it's odd.

Question 3

Write the smallest four digit odd number.

Do: The smallest four digit number we could write would be $1000$1000 but it's even. So to find the smallest odd number we would add one so our answer would be $1001$1001.

Completing the sequence

You may also be asked to complete a sequence of odd or even numbers.

Examples

question 1

Write the next three odd numbers after $297$297.

Think: To find the next odd number after an odd, I would jump to places: $297+2=299$297+2=299. Continue doing this to get the other two.

Do: $299$299, $301$301 and $303$303

question 2

Write the next three even numbers after $583$583.

Think: The next even number after $583$583 would be $584$584 (because we are jumping from an odd to an even number). Then we go back to jumping by two.

Do: $584$584, $586$586 and $588$588.

Question 3

Write the odd number that comes before $17$17.

Question 4

1. What is $5+7$5+7?

2. What is $7+15$7+15?

3. What is $15+5$15+5?

4. Were the answers to the last three questions odd or even?

Even

A

Odd

B

Even

A

Odd

B
5. This happens all of the time. In fact, every time we add two odd numbers together, the answer is always even!

So, which of the following pairs of numbers will be even when added together?

$73+85$73+85

A

$99+86$99+86

B

$73+99$73+99

C

$85+86$85+86

D

$73+85$73+85

A

$99+86$99+86

B

$73+99$73+99

C

$85+86$85+86

D

question 5

The following questions are all about adding odd and even numbers together.

1. What is $8+7$8+7?

2. What is $11+8$11+8?

3. What is $12+11$12+11?

4. Were the answers to the last three questions odd or even?

Even

A

Odd

B

Even

A

Odd

B
5. This happens all of the time. In fact, every time we add an odd and even number together, the answer is always odd!

So, which of the following pairs of numbers will be odd when added together?

$33+47$33+47

A

$78+52$78+52

B

$47+52$47+52

C

$33+78$33+78

D

$33+47$33+47

A

$78+52$78+52

B

$47+52$47+52

C

$33+78$33+78

D