134 LearnersLast updated on May 26th, 2025
Multiples of 11
In math, multiples are the products we get while multiplying a number with other numbers. Multiples play a key role in construction and design, counting groups of items, sharing resources equally, and managing time effectively. In this topic, we will learn the essential concepts of multiples of 11.
What are the Multiples of 11?
Now, let us learn more about multiples of 11. Multiples of 11 are the numbers you get when you multiply 11 by any whole number, along with zero. Each number has an infinite number of multiples, including a multiple of itself.
In multiplication, a multiple of 11 can be denoted as 11 × n, where ‘n’ represents any whole number (0, 1, 2, 3,…). So, we can summarize that:
Multiple of a number = Number × Any whole number
For example, multiplying 11 × 1 will give us 11 as the product. Multiples of 11 will be larger or equal to 11.
List of First 20 Multiples of 11
Multiples of 11 include the products of 11 and an integer. Multiples of 11 are divisible by 11 evenly. The first few multiples of 11 are given below:
| TABLE OF 11 (1-10) | |
|---|---|
|
11 x 1 = 11 |
11 x 6 = 66 |
|
11 x 2 = 22 |
11 x 7 = 77 |
|
11 x 3 = 33 |
11 x 8 = 88 |
|
11 x 4 = 44 |
11 x 9 = 99 |
|
11 x 5 = 55 |
11 x 10 = 110 |
| TABLE OF 11 (11-20) | |
|---|---|
|
11 x 11 = 121 |
11 x 16 = 176 |
|
11 x 12 = 132 |
11 x 17 = 187 |
|
11 x 13 = 143 |
11 x 18 = 198 |
|
11 x 14 = 154 |
11 x 19 = 209 |
|
11 x 15 = 165 |
11 x 20 = 220 |
Now, we know the first few multiples of 11. They are 0, 11, 22, 33, 44, 55, 66, 77, 88, 99, 110,...
Operations with Multiples of 11
Understanding the multiples of 11 helps solve mathematical problems and boost our multiplication and division skills. When working with multiples of 11, we need to apply it to different mathematical operations such as addition, subtraction, multiplication, and division.
Sum of first 5 Multiples of 11:
11, 22, 33, 44, and 55 are the first five multiples of 11. When multiplying 11 from 1 to 5, we get these numbers as the products. So, the sum of these multiples is:
11 + 22 + 33 + 44 + 55 = 165
When we add the first 5 multiples of 11, the answer will be 165.
Subtraction of first 5 Multiples of 11:
While we do subtraction, it improves our comprehension of how the value decreases when each multiple is subtracted from the previous one. 11, 22, 33, 44, and 55 are the first five multiples of 11. So, let us calculate it as given below:
11 - 22 = -11
-11 - 33 = -44
-44 - 44 = -88
-88 - 55 = -143
Hence, the result of subtracting the first 5 multiples of 11 is -143.
Average of first 5 Multiples of 11:
To calculate the average, we need to identify the sum of the first 5 multiples of 11, and then divide it by the count, i.e., 5. Because there are 5 multiples presented in the calculation. Averaging helps us to understand the concepts of central tendencies and other values. We know the sum of the first 5 multiples of 11 is 165.
11 + 22 + 33 + 44 + 55 = 165
Next, divide the sum by 5:
165 ÷ 5 = 33
33 is the average of the first 5 multiples of 11.
Product of First 5 Multiples of 11:
The product of given numbers is the result of multiplying all of them together. Here, the first 5 multiples of 11 include: 11, 22, 33, 44, and 55. Now, the product of these numbers is:
11 × 22 × 33 × 44 × 55 = 19,404,840
The product of the first 5 multiples of 11 is 19,404,840.
Division of First 5 Multiples of 11:
While we perform division, we get to know how many times 11 can fit into each of the given multiples. 11, 22, 33, 44, and 55 are the first 5 multiples of 11.
11 ÷ 11 = 1
22 ÷ 11 = 2
33 ÷ 11 = 3
44 ÷ 11 = 4
55 ÷ 11 = 5
The results of dividing the first 5 multiples of 11 are: 1, 2, 3, 4, and 5.
Common Mistakes and How to Avoid Them in Multiples of 11
While working with multiples of 11, we make common mistakes. Identifying these errors and understanding how to avoid them can be helpful. Below are some frequent mistakes and tips to avoid them:
Mistake 1
Confusing Multiples with Factors
Sometimes, students get confused between the multiples and factors of 11. A simple trick to differentiate between the two is to remember that multiples are the products of multiplication, while factors are the divisors of the number. Multiples of 11 refer to the products we get while multiplying 11 with other numbers. For example, multiples of 11 include 0, 11, 22, 33, 44, 55, 66, 77, 88, 99, 110….
The factors of 11 are 1 and 11. When 11 is divided by 1 and 11, the remainder will be zero. These are the factors of 11 meaning that these numbers can divide 11 without any remainder.
Factors of 11:
11 ÷ 1 = 11
11 ÷ 11 = 1
Multiples of 11 Examples
Problem 1
In a small town, there is a carousel that has 11 horses. Each week, the carousel owner adds 11 more horses to the ride. How many horses will the carousel have after 5 weeks?
66 horses
Explanation
Each week, 11 horses are added. To find the total number of horses after 5 weeks, we multiply the number of horses added each week by the number of weeks.
Horses added each week = 11
Number of weeks = 5
11 × 5 = 55
Starting with the original 11 horses, we add 55 more:
11 + 55 = 66
So, the carousel will have a total of 66 horses after 5 weeks.
Problem 2
Alyssa is organizing a charity bake sale. She bakes cupcakes in batches where each batch contains the first three multiples of 11 cupcakes. How many cupcakes are there in each batch?
66 cupcakes
Explanation
The first three multiples of 11 are 11, 22, and 33. To find the total number of cupcakes in each batch, we sum these multiples:
11 × 1 = 11
11 × 2 = 22
11 × 3 = 33
11 + 22 + 33 = 66
Therefore, each batch contains 66 cupcakes.
Problem 3
In an art class, students are painting frames. There are 11 frames, and each frame is painted by 11 students. How many students are there in total?
121 students
Explanation
To find the total number of students, we multiply the number of frames by the number of students painting each frame.
Number of frames = 11
Number of students per frame = 11
11 × 11 = 121
Thus, there are a total of 121 students painting the frames.
Problem 4
Lucas is creating a mosaic with tiles. He arranges 7 rows of tiles, with each row containing 11 tiles. How many tiles does Lucas use in total?
77 tiles
Explanation
To find the total number of tiles used, we multiply the number of rows by the number of tiles in each row.
Number of rows = 7
Number of tiles in each row = 11
7 × 11 = 77
So, Lucas uses 77 tiles in total for his mosaic.
Problem 5
Emma is stacking her library with books. She places 11 books on the first shelf, 22 books on the second shelf, and 33 books on the third shelf. How many books are there in total on the three shelves?
66 books
Explanation
The first shelf has 11 books, the second has 22 books, and the third has 33 books. To find the total number of books, we add these amounts:
11 + 22 + 33 = 66
Therefore, there are a total of 66 books on all three shelves.
FAQs on Multiples of 11
1.How do you find the multiples of 11?
2.What is the LCM of 7 and 11?
3.What are the real-life applications of Multiples of 11?
4.Are multiples of 11 finite or infinite?
5.Is there any odd multiples of 11?
Important Glossaries for Multiples of 11
- Multiple: A multiple represents the product of a number that may be multiplied by an integer. For example, multiples of 11 include 11, 22, 33, 44, etc.
- Number pattern: This refers to how numbers are listed. It should follow a certain sequence. Multiples of 11 are the numbers that consist of the number pattern of 11.
- Odd number: An odd number refers to any number that cannot be divided by 2 without leaving a remainder. The last digits of odd numbers are 1, 3, 5, 7, or 9. Some multiples of 11 are odd numbers.
- Divisor: It refers to any number by which another number can be divided without leaving any remainder. 1 and 11 are the divisors of 11.
- LCM (Least Common Multiple): The smallest common multiple of two or more numbers. For example, the LCM of 7 and 11 is 77.
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