 # 1.01 Odd and even numbers

Lesson

## Ideas

Can you identify numbers as odd or even?

Even numbers can be divided by 2 evenly. This means that we can equally share the number and have nothing left over. Odd numbers cannot be divided by 2 evenly; they have a left over of 1.

### Examples

#### Example 1

Is 115 odd or even?

Worked Solution
Create a strategy

Check if the last digit is even or odd.

Apply the idea

Odd numbers end in 1, \, 3, \, 5, \, 7, and 9. Even numbers end in 0, \, 2, \, 4, \, 6, and 8.

115 is odd because its last digit is 5.

115 is odd.

Idea summary

Even numbers can be divided by 2 evenly. Odd numbers cannot be divided by 2 evenly; they have a left over of 1.

## Properties of even and odd numbers

When we add and subtract odd and even numbers, we can work out whether our answer will be odd or even. Let's learn how.

### Examples

#### Example 2

a

What is 5+7?

Worked Solution
Create a strategy

On a number line, start with the bigger number and count to the right by the smaller number.

Apply the idea

Locate where 7 is on the number line. We can find 5 + 7 by jumping from 7 to the right by 5:

5 + 7 = 12

b

What is 7+15?

Worked Solution
Create a strategy

On a number line, start with the bigger number and count to the right by the smaller number.

Apply the idea

Locate where 15 is on the number line. We can find 7 + 15 by jumping from 15 to the right by 7:

7 + 15 = 22

c

What is 15+5?

Worked Solution
Create a strategy

On a number line, start with the bigger number and count to the right by the smaller number.

Apply the idea

Locate where 15 is on the number line. We can find 15 + 5 by jumping from 15 to the right by 5:

15 + 5 = 20

d

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

Worked Solution
Create a strategy

Check if the last digit of each number is even or odd.

Apply the idea

In parts (a) and (b) the answers were 12 and 22, which end with 2. So both answers are even.

In part (c) the answer is 20 and its last digit is 0. So it is also even.

e

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?

A
73+85
B
99+86
C
73+99
D
85+86
Worked Solution
Create a strategy

Choose the options in which the numbers are both odd.

Apply the idea

Options A and C are the correct answers because 73+85 and 73+99 are pairs of odd numbers.

#### Example 3

a

What is 4+6?

Worked Solution
Create a strategy

On a number line, start with the bigger number and count to the right by the smaller number.

Apply the idea

Locate where 6 is on the number line. We can find 4 + 6 by jumping from 6 to the right by 4:

4 + 6 = 10

b

What is 6+10?

Worked Solution
Create a strategy

On a number line, start with the bigger number and count to the right by the smaller number.

Apply the idea

Locate where 10 is on the number line. We can find 6 + 10 by jumping from 10 to the right by 6:

6 + 10 = 16

c

What is 10+4?

Worked Solution
Create a strategy

On a number line, start with the bigger number and count to the right by the smaller number.

Apply the idea

Locate where 10 is on the number line. We can find 10 + 4 by jumping from 10 to the right by 4:

10 + 4 = 14

d

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

Worked Solution
Create a strategy

Check if the last digit of each number is even or odd.

Apply the idea

In part (a) the answer is 10 and its last digit is 0. So it is even.

In part (b) the answer is 16 and its last digit is 6. So it is even.

In part (c) the answer is 14 and its last digit is 4. So it is even.

e

Every time we add two even numbers together, the answer is always even.

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

A
38+24
B
38+22
C
24+71
D
71+22
Worked Solution
Create a strategy

Choose the options in which the numbers are both even.

Apply the idea

Options A and B are the correct answers because 38+24 and 38+22 are pairs of even numbers.

Idea summary

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.

### Outcomes

#### VCMNA151

Investigate and use the properties of odd and even numbers