What are Whole Numbers?
Whole numbers are counting numbers such as 0, 1, 2, 3…
Whole numbers can be represented on a number line as:
What is the Number Pattern of Whole Numbers?
In mathematics, whole numbers are written in a set sequence. The sequence brings out a relationship between the numbers in the sequence. So the whole numbers are related due to a particular rule or pattern, called the number pattern of whole numbers. We can observe the first few numbers written in the sequence and identify the rule that is being followed.
Now let’s take a look at a few examples of number patterns to clearly understand this concept.
Number Pattern of Even Numbers
Even numbers are numbers such as 0, 2, 4, 6, 8 ….
To represent even numbers on a number line, we mark ‘0’ on the number line and then mark the even numbers that follow.
Let’s observe the first few numbers, 0, 2, 4, 6, … and identify the pattern followed here.
0 + 2 = 2
2 + 2 = 4
4 + 2 = 6
6 + 2 = 8
We can observe that 2 is added to 0 to get 2, then to 2 to get 4 and so on. Hence, we can see a constant addition of 2 starting from 0 as the pattern or rule followed in the case of even numbers.
Patterns of Odd Numbers
Odd numbers are numbers such as 1, 3, 5, 7, … To represent odd numbers on a number line, we mark ‘1’ on the number line and then mark the odd numbers that follow.
Let’s observe the first few numbers, 1, 3, 5, 7, … and identify the pattern followed here.
1 + 2 = 3
3 + 2 = 5
5 + 2 = 7
7 + 2 = 9
We can observe that 2 is added to 1 to get 3, then to 3 to get 5 and so on. Hence, we can see a constant addition of 2 starting from 1 as the pattern or rule followed when we look at odd numbers.
Solved Examples
Example 1: Find the next number of the given number pattern: 6, 17, 28, 39, 50, ___, …
Solution:
Let’s observe the first few numbers and then identify the rule followed.
6 + 11 = 17
17 + 11 = 28
28 + 11 = 39
39 + 11 = 50
We can see that 11 has been constantly added to the previous number, in other words, the difference between consecutive numbers is 11. So the next number will be 11 more than the previous number.
Hence, the next number = 50 + 11 = 61
Example 2: Describe the pattern given below and find the missing numbers: 6, 8, 10, ___, 14, ___, 18
Solution:
Observe the first few numbers and identify the rule followed. We can solve this in two ways.
Method 1: Pattern of constant addition.
6 + 2 = 8
8 + 2 = 10
10 + 2 = 12
12 + 2 = 14
14 + 2 = 16
16 + 2 = 18
In the pattern we can see that 2 is added to each preceding number to get the succeeding number.
So the missing numbers are: 12 and 16
Method 2: Pattern of multiples
6 = 2 \(\times\) 3
8 = 2 \(\times\) 4
10 = 2 \(\times\) 5
12 = 2 \(\times\) 6
14 = 2 \(\times\) 7
16 = 2 \(\times\) 8
18 = 2 \(\times\) 9
In the pattern we can see that the numbers are consecutive multiples of 2 starting from 6.
So, the missing numbers are: 12 and 16
Example 3: Tom earns the same amount of money each week. The amount of money (in dollars) earned after 2 weeks, 4 weeks and 6 weeks is as follows: 16, 32 and 48. If the pattern continues, how much money will he earn after 10 weeks?
Solution:
The weeks are: 2, 4 and 6
2 + 2 = 4
4 + 2 = 6
So, the pattern followed to represent weeks is a constant addition of 2.
The amount earned during these weeks: 16, 32 and 48
16 + 16 = 32
32 + 16 = 48
So, the pattern followed to represent the amount earned is a constant addition of 16.
Therefore, using a table to depict the above we can find the amount earned after 10 weeks.
So we can see that the amount earned after 10 weeks is $80.
Let’s take a look at another way to solve this.
Income earned in 2 weeks = 16
Income earned in 1 week = \(\frac{16}{2}\) = 8
We know that Tom earns the same amount every week.
Therefore, income earned after 10 weeks = 10 \(\times\) 8 = 80
Therefore, Tom earns $80 after 10 weeks
Natural numbers are numbers such as 1, 2, 3, …. Whole numbers are numbers such as 0, 1, 2, … So whole numbers comprise 0 as the start of the series, and the set of natural numbers has 1 starting the series.It must be noted that natural numbers belong to the set of whole numbers.
Whole numbers are numbers such as 0, 1, 2, 3, …. As we can see the numbers are constantly increasing by 1. Therefore, the number pattern to represent whole numbers is the addition of 1 starting from 0.
Let’s use an example to understand the concept.
Multiples of 5: 5, 10, 15, 20, 25…. We can see that on adding 5 to the preceding number we get the next number. Therefore, consecutive multiples can be represented using an addition pattern.