Multiples and square numbers
When dealing with multiplication, it is important to know the meaning of multiples and square numbers.
Multiples
A multiple of a number can be divided exactly by that number. So for example, 12 is a multiple of 2, 3, 4 and 6, because:
2 × 6 = 12
4 × 3 = 12
Activity 9: Looking for multiples
Look at the following row of numbers, and then answer the questions below.
12, 17, 300, 24, 30, 39, 2000, 100, 45, 52, 80, 50, 450
Which of these numbers are multiples of 2?
Which of these numbers are multiples of 3?
Which of these numbers are multiples of 5?
Which of these numbers are multiples of 10?
Which of these numbers are multiples of 50?
Which of these numbers are multiples of 100?
Which of these numbers are multiples of 1000?
Answer
1. 12, 24, 30, 50, 52, 80, 100, 300, 450, 2000 are multiples of 2.
· 2 × 6 = 12
· 2 × 12 = 24
· 2 15 = 30
· 2 × 25 = 50
· 2 × 26 = 52
· 2 × 40 = 80
· 2 × 50 = 100
· 2 × 150 = 300
· 2 × 225 = 450
· 2 × 1000 = 2000
2. 12, 24, 30, 39, 45, 300 and 450 are multiples of 3.
· 3 × 4 = 12
· 3 × 8 = 24
· 3 × 10 = 30
· 3 × 13 = 39
· 3 × 15 = 45
· 3 × 100 = 300
· 3 × 150 = 450
3. 30, 45, 50, 80, 100, 300, 450 and 2000 are multiples of 5.
· 5 × 6 = 30
· 5 × 9 = 45
· 5 × 10 = 50
· 5 × 16 = 80
· 5 × 20 = 100
· 5 × 60 = 300
· 5 × 90 = 450
· 5 × 400 = 2000
4. 30, 50, 100, 300, 450, 2000 are multiples of 10.
· 10 × 3 = 30
· 10 × 5 = 50
· 10 × 8 = 80
· 10 × 10 = 100
· 10 ×30 = 300
· 10 × 45 = 450
· 10 × 200 = 2000
5. 50, 100, 300, 450 and 2000 are multiples of 50.
· 50 × 1 = 50
· 50 × 2 = 100
· 50 × 6 = 300
· 50 × 9 = 450
· 50 × 40 = 2000
6. 100, 300 and 2000 are multiples of 100.
· 100 × 1 = 100
· 100 × 3 = 300
· 100 × 20 = 2000
7. 2000 is a multiple of 1000: 1000 × 2 = 2000
Square numbers
A square number is made when you multiply any whole number by itself. For example:
1 × 1 = 1
2 × 2 = 4
3 × 3 = 9
Hint: Square numbers are commonly shown as: 12 (meaning 1 × 1), 22 (meaning 2 × 2), 32 (meaning 3 × 3), etc.
Activity 10: Identifying square numbers
You have been given the square numbers up to 3. Following the pattern, what are the square numbers from 4 to 12?
Answer
The answers are as follows:
4 × 4 = 16
5 × 5 = 25
6 × 6 = 36
7 × 7 = 49
8 × 8 = 64
9 × 9 = 81
10 × 10 = 100
11 × 11 = 121
12 × 12 = 144