# Multiples of 11

Eleven is the smallest non-repeating two-digit number and the first two-digit prime

number. In Pythagorean numerology, the number 11 has a negative connotation since it is placed between the two promising and significant numbers – 10 and 12.

While 10 symbolizes completeness and perfection, 11, on the other hand, represented exaggeration, indulgence, and human sin. It was also regarded as a symbol of internal strife and insurrection.

For some, the “11^{th} hour” implies a sense of urgency because the clock is approaching twelve o’clock – which can mean that this is the final hour to complete tasks.

On the brighter side, the number 11 became somewhat famous because of the American show called “Stranger Things,” wherein one of the characters was named “Eleven.”

Eleven may have a negative implication for some people, but it is still an interesting and important number to take note of. Do you want to journey with us to see how beautiful and meaningful the multiples of 11 are? Hop on as we learn exciting stuff about this remarkable number!

## Multiples of 11 are 11, 22, 33, 44, 55, 66, 77 …

One thing that we are most certain about multiples of 11 is that they will always be a whole number. They result from any natural numbers multiplied by 11, which can be expressed as** 11 n**. It is a sequence wherein the difference between two consecutive numbers is 11.

Multiples of 11 can be a positive or negative number – since any integer that we are going to pair with 11 can be either positive or negative. We just have to take note that a multiple of 11 cannot have a fractional factor and should always have a zero remainder.

Are you know getting excited on know how to find multiples of 11?

## How to find the multiples of 11?

**Skip counting** and **multiplication** can be used to determine the multiples of 11.

Now, let’s try to find the first five multiples of 11 using skip counting.

Skip counting is done by repeatedly adding 11 as many times as necessary.

To find the first five multiples of 11 using skip counting, we are going to start the count at 11. Then, adding 11 to 11 will give us 22.

If we continue doing this process, we will have the sequence 11, 22, 33, 44, and 55 as the first five multiples of 11.

On the other hand, we can use a different approach where we just multiply 11 to any positive and negative integer.

Suppose we are asked to get the 17^{th} multiple of 11. By multiplication method, we will have the process $$11 \times 17 = 187$$. Therefore, the 17^{th} multiple of 11 is 187.

More so, if we are told to find the negative 156^{th} multiple of 11, it is easier to use the multiplication method instead of skip counting.

Thus, using multiplication, $$11 \times (-156) = -1,716$$.

Therefore, the negative 156^{th} multiple of 11 is –1,716.

Now, let’s take a look at this table.

n^{th} Multiple | Skip Counting | Multiplication |
---|---|---|

1 |
11 |
11 x 1 = 11 |

2 |
11 + 11 = 22 |
11 x 2 = 22 |

3 |
11 + 11 + 11 = 33 |
11 x 3 = 33 |

4 |
11 + 11 + 11 + 11 = 44 |
11 x 4 = 44 |

5 |
11 + 11 + 11 + 11 + 11 = 55 |
11 x 5 = 55 |

This table shows that no matter what method you use, you will always come up with the same results.

## Did you know that…

When a multiple of 11 is reversed, the new number is also a multiple of 11!

Now, let’s see if this is true. 836 is a multiple of 11. If we reverse the number, we will now have 638. If we divide 638 by 11, we will have $$68\;\div\;11=\;58$$. This is so cool, right?

Let’s see if this will work on larger numbers. Suppose 1,095,127 is a multiple of 11; reversing the number will give us 7,215,901. Now, if we divide it by 11, we will get the result

$$7,215,901\;\div\;11\;=\;655,991$$.

What an incredible and mind-blowing discovery, right?

## List of First 30 multiples of 11

We know that there are is an infinite number, and so do the multiples of 12. The following shows a list of the first 30 multiples of 12 generated by multiplying 12 by numbers ranging from 1 to 30.

Product of 11 and a positive counting number | Multiples of 11 |
---|---|

$$11\times1$$ | 11 |

$$11\times2$$ | 22 |

$$11\times3$$ | 33 |

$$11\times4$$ | 44 |

$$11\times5$$ | 55 |

$$11\times6$$ | 66 |

$$11\times7$$ | 77 |

$$11\times8$$ | 88 |

$$11\times9$$ | 99 |

$$11\times10$$ | 110 |

$$11\times11$$ | 121 |

$$11\times12$$ | 132 |

$$11\times13$$ | 143 |

$$11\times14$$ | 154 |

$$11\times15$$ | 165 |

$$11\times16$$ | 176 |

$$11\times17$$ | 187 |

$$11\times18$$ | 198 |

$$11\times19$$ | 209 |

$$11\times20$$ | 220 |

$$11\times21$$ | 231 |

$$11\times22$$ | 242 |

$$11\times23$$ | 253 |

$$11\times24$$ | 264 |

$$11\times25$$ | 275 |

$$11\times26$$ | 286 |

$$11\times27$$ | 297 |

$$11\times28$$ | 308 |

$$11\times29$$ | 319 |

$$11\times30$$ | 330 |

If you take a closer look at how the result and the counting number relate to each other, you will notice that the units digit of the positive counting number is the same as the units digit of the result.

$$11 \times 8 = 88$$

$$11 \times19 = 209$$

$$11 \times24 = 264$$

Can you see any other pattern that will help us easily distinguish that a number is a multiple of 11?

## Solving problems involving multiples of 11

Finding multiples of 11 isn’t that quite challenging, right? Now, let’s relate what we’ve learned about multiples of 11 by solving these real-life situation problems.

### Problem #1

Alexa is tasked to count all the collected blueberries of her family. There are six baskets of blueberries. The first basket contains 11 blueberries; the second one has 22 blueberries, and so on. How many blueberries did Alexa’s family collect?

For us to know the total number of blueberries Alexa’s family has collected, we should take note that the six baskets contain blueberries that are in the sequence of multiples of 11. Thus, the five baskets have 11, 22, 33, 44, 55, and 66 blueberries.

Now, all we need to do is add all the blueberries inside the baskets. Thus,

**11 + 22 + 33 + 44 + 55 + 66 = 231**

Therefore, Alexa’s family was able to gather **231 blueberries**.

Are you getting the hang of it already? That’s good as we are going to try to solve

another problem.

### Problem #2

Sabrina is preparing herself for a math competition. She has 65 days to do training and practice. She pledges to train herself to do mental math every day.

On her first day, she plans to solve 11 problems; 22 on the following day, 33 on the third day, and so on. How many math problems does Sabrina need to practice before her competition?

We need to find the number of math problems Sabrina needs to solve on her 65^{th} day of training. In the given problem, we can take note that the math problems are increasing by 11 every single day.

Thus, we can say that it is in the sequence of multiples of 11.

Now, to get the number of problems she needs to solve on the 65^{th} day, we will multiply 65 by 11. Hence, $$65 \times 11 = 715$$.

Therefore, Sabrina needs to solve **715 math problems** using mental math. That’s a lot of math problems in a day, but we will surely root for Sabrina to win that competition!

Now, we are also rooting for you that you can ace these three practice exercises!