Multiples of numbers are the products of that number and another integer. To find the multiples of 11, we would multiply 11 by integers such as 1, 2, 3, 4, and so on. In this guide, we will learn how to find the multiples of 11, including some essential tips and examples.
Multiples of 11: Step-by-Step Guide
Tip #1: Add 11 to any multiple to get the next one
One of the ways to obtain multiples of 11 is to add 11 to any previous multiple. For instance, let’s start with the first few multiples of 11:
11 x 1 = 11
11 x 2 = 22
11 x 3 = 33
Now, if we add 11 to the last obtained multiple 33, we would get the next multiple, which is:
33 + 11 = 44
And if we continue this process, we will obtain more multiples:
11 x 5 = 55
11 x 6 = 66
11 x 7 = 77
And so on.
Tip #2: Use patterns
Another technique to obtain multiples is to look for a pattern in the digits of the multiples. Suppose we list the first ten multiples of 11, we’d have:
11, 22, 33, 44, 55, 66, 77, 88, 99, 110
We can see that each number except the last one consists of two identical digits, and the pairs of digits increase by one as we move down the list. Another pattern is that the first digit of each multiple increases by one, while the second digit decreases by one except the last digit, which resets back to zero before increasing again.
Using these patterns, we can generate many more multiples.
Example 1:
Let’s find the first six multiples of 11
Multiples of 11:
11 x 1 = <>11
11 x 2 = <>22
11 x 3 = <>33
11 x 4 = <>44
11 x 5 = <>55
11 x 6 = <>66
Using Tip #1, we can find the next multiple by adding 11 to 66.
11 x 7 = <>77
Example 2:
Let’s find the first five multiples of 11 using patterns.
Multiples of 11:
11 x 1 = <>11
11 x 2 = <>22
11 x 3 = <>33
11 x 4 = <>44
11 x 5 = <>55
It is easy to notice that each of these numbers consists of two identical digits, and the tens digit increases by one in each step. Therefore, the sixth multiple should be 66, which confirms our finding in Example 1.
Final Thoughts
Finding multiples of a number is essential in mathematics and other fields that require extensive calculations. We can use different strategies to find multiples, including adding the number to its previous multiple or looking for patterns in the digits.
With such techniques, we can easily generate multiples of any number, including 11. As we have seen in this guide, the multiples of 11 always end with a digit of 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9, and the tens digit increases by one in each step.