Whether we are at home, school or the market, maths is an integral art of life, something which comes handy everyday in our daily lives. Therefore, it is important that children understand basic maths concepts from an early age. But it is not just something that they can read and understand, like a story. Maths involves various formulas and derivations, which can only be understood if you understand, practice and apply them in daily life.
In this article, we have covered one such mathematical concept – consecutive integers or consecutive numbers for kids. We have covered some examples below as well to make the learning process easy for children. Let’s begin.
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What Are Consecutive Numbers?
Let’s take a look at consecutive numbers meaning for children.
Consecutive numbers are the numbers that follow each other in a pattern or regular counting order. These numbers can be written in a series where the difference between the two numbers is fixed, and no number is skipped in between. Consecutive numbers follow each other in order from the smallest to the largest number and generally have a difference of 1 between two numbers.
Examples Of Consecutive Numbers
To understand more about consecutive numbers, let’s explore the examples given below.
- Consecutive digits between 1 to 10 with a difference of 1 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
- Consecutive numbers between 70 to 80 with a difference of 2 are 70, 72, 74, 76, 78, and 80.
- Consecutive integers from – 1 to 9 with a difference of 1 are -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
Even, Odd And Natural Numbers As Consecutive Numbers
Let’s read about even, odd and natural numbers with consecutive numbers.
1) Consecutive Natural Numbers With Example
Consecutive whole numbers begins with 0. Natural numbers are whole numbers excluding 0. Natural numbers are used for counting and ordering.
The natural numbers are written in the following way:
N = {1, 2, 3, 4, 5, 6, 7, 8, 9, ……}
Therefore, consecutive natural numbers are the continuous numbers or the ones that continuously follow each other in a particular order, which is from the smallest number to the largest number.
Example: The consecutive natural numbers from 5 to 10 are 5, 6, 7, 8, 9, and 10.
2) Consecutive Even Numbers With Example
Even numbers are the numbers that end in 0, 2, 4, 6, and 8.
Let’s take a look at the example given below to understand consecutive even numbers.
We will write the even numbers from 2 to 12 in ascending order. They are 2, 4, 6, 8, 10, and 12 when written from the smallest one to the largest.
We can observe that the difference between any predecessor-successor number is 2. Therefore, these numbers form consecutive even numbers.
3) Consecutive Odd Numbers With Example
Odd numbers are numbers which are not completely divisible by 2. These typically end with 1, 3, 5, 7 and 9.
Let’s take a look at the example given below to understand consecutive odd numbers.
We will write the odd numbers from 3 to 9 in ascending order. They are 3, 5, 7, 9 when written from the smallest to the largest.
We can see observe the difference between any predecessor-successor number is 2. Therefore, these numbers form consecutive odd numbers.
Consecutive Numbers In Maths
It is important to teach kids what consecutive numbers in maths stand for. We have discussed the properties and formulas of consecutive numbers below to help your child get a clear idea about consecutive numbers.
What Are The Properties Of Consecutive Numbers?
Now that your child knows about consecutive numbers, let’s read the following points to know the properties of consecutive numbers.
- The difference between any predecessor-successor pair is fixed and uniform in consecutive numbers. So, if we denote the first number as n, then the consecutive numbers in the series will be n, n+1, n+2, n+3, n+4, n+5 and so on.
- Any two consecutive odd numbers have a difference of 2. For example, 5 and 7 are two consecutive odd numbers, their difference = 7 – 5 = 2.
- Any two consecutive even numbers have a difference of 2. For example, 8 and 10 are two consecutive even numbers. Their difference = 10 – 8 = 2.
- If ‘n’ is an odd number, then the sum of ‘n’ consecutive numbers will be divisible by ‘n’. For example, the sum of these three consecutive numbers is 4+5+6=15 and 15 is divisible by 3.
Formula Of Consecutive Number
Let’s read the formula of consecutive numbers to teach kids.
For a number n, the next two consecutive numbers will be (n + 1) and (n + 2).
- The formula for adding n consecutive numbers = [a + (a + 1) + (a + 2) + …. {a + (n-1)}]. Therefore, the sum of n consecutive numbers or sum of n terms of arithmetic progression) = (n/2) × (first number + last number).
- The formula of even consecutive numbers = 2n, 2n+2, 2n+4, 2n+6,…
- The formula of odd consecutive numbers = 2n+1, 2n+3, 2n+5, 2n+7,…
Solved Examples Of Consecutive Numbers
1. What are the consecutive numbers in maths for natural numbers between 1 and 20?
Solution: The consecutive numbers for the natural numbers between 1 and 20 are as follows:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20.
2. Write the consecutive even integers between 70 and 80.
Solution: The consecutive even integers between 70 and 80 are as follows:
70, 72, 74, 76, 78, 80.
3. Find the sum of these two consecutive numbers: 5 and 6.
Solution: Here, the sum of two consecutive numbers is 5+6 = 11.
4. Write the consecutive odd integers between 11 and 33.
Solution: The consecutive odd integers between 11 and 33 are as follows:
11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33.
Practice Problems On Consecutive Numbers
1. What are the consecutive odd numbers between 11 to 21?
Answer: The consecutive odd numbers between 11 and 21 are: 11, 13, 15, 17, 19, 21.
2. What are the 3 consecutive integers that are even starting from the number 6?
Answer: The three consecutive integers that are even starting from the number 6 are: 6, 8, and 10.
3. Find the missing number in the series: 2, 4, 6, 8, _, 12, 14, 16.
Answer: The difference between predecessor-successor pairs in this series is 2. The predecessor of the missing number is 8, and the successor of the missing number is 12.
The missing number is = predecessor + difference = 8 + 2= 10.
Alternatively, the missing number is = successor – difference = 12 – 2= 10.
Thus, the missing number in the series is 10.
Important Points Regarding Consecutive Numbers That Need To Be Remembered
Below is a list of some important points that children should remember about consecutive numbers.
- If you need to find the missing numbers in a series, first write the numbers in ascending order and then find the difference between any predecessor-successor pair.
- For three numbers in an arithmetic progression with a common difference of 1, we can define these numbers as {n, n + 1, n+2}, where ‘n’ is a number.
- When we denote the first number as n, then the consecutive numbers in that series will be n+1, n+2, n+3, n+4, n+5 and so on.
- When we denote the first integer as n, the consecutive odd or consecutive even integers will be n+2, n+4, n+6, n+8, n+10 and so on.
- For any odd consecutive number, the general formula = 2n+1 (where ‘n’ = any integer).
- For any even consecutive number, the general formula = 2n (where ‘n’ = any integer).
Remember that it will take your little one some time to understand the concept of consecutive numbers fully. Make sure they practice the practical problems mentioned above in the article, and they will slowly but surely learn this concept.
Also Read:
Missing Numbers for Preschoolers and Kids
Number Recognition for Preschool Children
Before, After and In-Between Numbers for Kindergarteners
