116 LearnersLast updated on July 23rd, 2025
Missing Numbers
We often come across number sequences with missing values. To find the unknown number, we first need to identify the pattern in the sequence. Solving such problems helps students strengthen their understanding of mathematical concepts like addition, subtraction, and multiplication. In this article, we will learn how to find missing numbers mathematically.
What are Missing Numbers?
Missing numbers in a sequence or series can be found by identifying the pattern followed. These missing numbers are required to complete the sequence correctly. Practicing missing numbers helps reinforce multiplication tables and arithmetic operations. Moreover, this activity helps students develop their mental math abilities.
What Are the Methods for Representing Missing Numbers?
The different kinds of activities to solve missing numbers are mentioned below:
- Pictorial representation
- Series representation
- Table representation
- Fill in the blanks in between calculations
How to Find Missing Numbers in Series?
The missing numbers in a series or sequence are presented in a fill-in-the-blanks format. We solve equations involving one or more missing numbers by identifying the pattern they follow. Let’s now look at number sequences from 1 to 10, 1 to 20, and 1 to 50, which helps in easily memorizing counting numbers.
Missing Numbers from 1 to 10
The counting numbers from 1 to 10 are listed with blanks.
- Given: 1, __, 3, 4, 5, 6, __, __, 9, 10
- Answer: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
Missing Numbers from 1 to 20
Recall the numbers from 1 to 20 and fill in the blanks.
- Given: 1, __, 3, 4, 5, 6, __, __, 9, 10, 11, __, 13, __, 15, 16, __, __, 19, 20
- Answer: 1, 2, 3, 4, 5, 6, 7 , 8 , 9, 10, 11, 12, 13, 14 , 15, 16, 17 , 18 , 19, 20.
Missing Numbers from 1 to 50
We now memorize the counting numbers from 1 to 50 and complete the blanks given below.
- Given: 1,__, 3, 4, 5, 6,__, __, 9, 10, 11, __, 13, __, 15, 16, __, __, 19, 20, 21, 22, 23, __, __, 26, 27,__, 29,__, 31,__, 33, 34,__, 36,__, __, __, 40, 41, 42, 43, 44,__, 46, , 48,__, 50.
- Answer: 1, 2, 3, 4, 5, 6, 7 , 8 , 9, 10, 11, 12, 13, 14 , 15, 16, 17 , 18 , 19, 20, 21, 22, 23, 24 , 25 , 26, 27, 28 , 29, 30 , 31, 32 , 33, 34, 35 , 36, 37 , 38 , 39 , 40, 41, 42, 43, 44, 45 , 46, 47 , 48, 49 , 50.
How to Find Missing Numbers in Addition and Subtraction?
Let’s solve the following number sequences one by one to find the missing numbers:
Examples:
- ___ + 5 = 9 → 4 + 5 = 9
We find the number by subtracting 5 from 9. The sum of 5 and 4 gives 9.
- 1 –1 = ___ → 1 – 1 = 0
Subtract 1 from 1 to get the result.
- 10 – ___ = 4 → 10 – 6 = 4
Subtract 4 from 10 to get the missing number (6).
- 7 + 4 = ___ → 7 + 4 = 11
Add 7 and 4 to get the missing number (11).
- 18 + ___ = 20 → 18 + 2 = 20
Subtract 18 from 20 to get the missing number (2).
- ___ – 3 = 2 → 5 – 3 = 2
Add 3 and 2 to get the missing number (5).
How to Find Missing Numbers in Multiplication and Division?
We will now solve missing number sequences involving multiplication and division.
- 6 × 2 = ___ → 6 × 2 = 12
Multiply the numbers 6 and 2 to get the product 12.
- 2 × ___ = 8 → 8 ÷ 2 = 4
Here, the multiplier is missing, therefore we have to divide the product by multiplicand. so, divide 8 by 2 to get the result of 4.
- ___ × 5 = 40 → 40 ÷ 5 =8
Divide 40 by 5 to get the missing number (8).
- 20 ÷ 2 = ___ → 20 ÷ 2 = 10
Divide 20 by 2 to get 10 as the quotient.
- 32 ÷ __ = 4 → 32 ÷ 4 = 8
If a number divides 32, it results 4, in another way round, if we divide 32 by 4, we will get the missing number. In this case, 8 is the missing number.
- __ ÷ 3 = 3 → 9 ÷ 3 = 3
Here, the dividend is missing. We are given both the divisor and the quotient, so to find the dividend, multiply them. Here, 9 is the missing number.
How to Find Missing Numbers - Before and After
We will now discuss the ways to find the missing numbers before and after a given number. Let’s look at some examples:
- ,6, .
The number before 6 is 5, and after 6 is 7. So the series is 5, 6, 7.
- , 15, .
The number before 15 is 14, and after 15 is 16. So the series is 14, 15, 16.
- , 40, .
The number before 40 is 39 and after 40 is 41. So the series is 39, 40, 41.
- , 20 .
The number before 20 is 19 and after 20 is 21. So the series is 19, 20, 21.
Tips and Tricks for Solving Missing Numbers
Solving missing numbers equations is a great way to learn numbers and patterns. Here are a few tips and tricks to help you master them efficiently:
- Observe if the numbers in the sequence are increasing or decreasing.
- Always use the opposite operations when working with missing number equations, i.e., if a number is missing in addition, use subtraction.
- Creating a number line helps in visualizing the sequence correctly.
- Guess the missing numbers and check if they fit in the given sequence
- In case of missing multiple numbers, always solve one at a time.
Real-life Applications of Missing Numbers
Missing numbers are essential in various fields. Understanding how to solve missing numbers helps children develop key life skills. Here are a few real-life examples of missing numbers:
- Solving missing numbers helps us make financial decisions, such as finding missing values in taxes, expenses, or discounts.
- We apply formulas to solve unknown values in scientific experiments.
- Students can build their logical reasoning by solving unknown values in puzzles.
- Data analysts can predict future trends based on past data.
- It helps us in estimating the arrival or departure time of a journey when one is missing.
Common Mistakes and How to Avoid Them in Missing Numbers
Finding missing numbers can significantly help children develop their problem-solving skills. However, students often make mistakes when finding unknown numbers. Here are a few such common mistakes and the ways to avoid them
Mistake 1
Overlooking the Pattern in the Sequence
While solving the missing numbers in the sequence, students frequently overlook the pattern.
For finding a pattern, students should understand the progression, whether the number is increasing or decreasing or is it some other operation. So it is important for students to apply most of the mathematical operations on such sequences to understand the progression.
Mistake 2
Forgetting the Inverse Operation
Skipping the step of performing inverse operations when finding missing numbers can lead to incorrect results.
To find a missing number in an addition problem, use subtraction, and for a multiplication problem, use division.
Mistake 3
Not Reviewing the Answer
When filling in missing numbers, students randomly guess the answer without checking it.
Always check whether the assumed answer follows the pattern of the given series.
Mistake 4
Misapplying Even or Odd Number Rules
Some students might fill in odd numbers in an even number series, or vice versa.
Double-check whether the sequence includes odd or even numbers before finding the missing numbers.
Mistake 5
Confusion Between Mathematical Operations
Students might try to solve missing number equations using incorrect operations.
Always identify the pattern and determine whether addition, subtraction, multiplication, or division should be applied.
Solved Examples of Missing Numbers
Problem 1
Alice had some money, from which she spent $240 and now has $560 left. How much did she have initially?
Alice initially had $800.
Explanation
We find the initial amount of money, we use the equation:
Total amount – Spent amount = The amount left
Consider the initial amount Alice had as Y
Y – 240 = 560
Adding 240 to both sides:
Y = 560 + 240
Y = 800
Therefore, the amount Alice had is $800.
Problem 2
Find the before and after missing numbers of 15 in the series: 5,__, 15, __, 25.
The before and after missing numbers of 15 are 10 and 20, respectively.
Explanation
We first identify the pattern:
The pattern shows that the numbers increase by 5 each time:
5 + 5 = 10
10 + 5 = 15
15 + 5 = 20
20 + 5 = 25
Now, fill in the missing numbers:
The number before 15 is 10
The number after 15 is 20
So, the complete series is 5, 10, 15, 20, 25.
Problem 3
A bus stops at stop 6, then stop___, then 8. Find the missing stop.
The missing stop is Stop 7.
Explanation
Identify the pattern that the given numbers follow:
The difference between 6 and 8 is:
8 – 6 = 2
So, the numbers increase by 1 stop at a time: 6, 7, 8.
The number between 6 and 8 is:
6 + 1 = 7
So, the missing stop is Stop 7.
Problem 4
A mother is 38 years old, her daughter is __ years old, and their age difference is 27 years. Find the daughter’s age.
The daughter’s age is 11.
Explanation
Given that,
Mother’s age = 38 years
Age difference = 27 years
Let daughter’s age be X
We form an equation to determine the value of X:
Daughter’s age = Mother’s age – Age difference
X = 38 – 27 = 11
Therefore, the daughter’s age is 11.
Problem 5
A company produced ____ items in 30 days at a rate of 10 items per day. Determine the number of items produced in total?
The company produced 300 items in 30 days.
Explanation
Given that,
Rate of production = 10 items per day
Total days = 30
Total items produced = X
We form the equation:
Total items = Rate per day × Total days
X = 10 × 30 = 300
Therefore, the company produced 300 items in 30 days.
FAQs on Missing Numbers
1.Define missing numbers.
2.How can we determine a missing number in addition?
3.How can we find a missing number in division?
4.Cite one real-life example of missing numbers.
5.How can children in United Arab Emirates use numbers in everyday life to understand Missing Numbers?
6.What are some fun ways kids in United Arab Emirates can practice Missing Numbers with numbers?
7.What role do numbers and Missing Numbers play in helping children in United Arab Emirates develop problem-solving skills?
8.How can families in United Arab Emirates create number-rich environments to improve Missing Numbers skills?
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
