Multiples of 11: Master the Magic Patterns and Fast Tricks!

Multiples of a number are the products obtained by multiplying that number by natural numbers like 1, 2, 3, and so on. Following this mathematical principle, multiples of 11 are generated by multiplying 11 by integers, resulting in a predictable and symmetrical sequence: 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, and beyond.

In this guide, our Math Team will provide a comprehensive overview of multiples of 11, including their unique visual patterns, the ‘alternating sum’ divisibility rule, and practical solved examples. Whether you are a student looking to sharpen your mental math skills or a parent seeking to strengthen your child’s number sense, this resource will clarify how to identify and master multiples of 11 with ease and logic.

What Are Multiples of 11?

In simple terms, multiples of 11 are the products of 11 and any whole number. If you can divide a number by 11 and get a clean result with no remainder, that number is a multiple of 11.

Think of it as “skip counting” by 11. Each time you add another group of 11, you reach the next multiple.

• 11×1=11
• 11×2=21
• 11×3=33

The 1-99 Pattern: The “Twin” Numbers

For the first nine multiples, the pattern is incredibly easy to spot. These are what we call “twin numbers.” When you multiply 11 by any single-digit number (1 through 9), you simply repeat that digit twice!

• 11, 22, 33, 44, 55, 66, 77, 88, 99.

Look at the digits: they are identical! This visual symmetry makes multiples of 11 the favorite of many young mathematicians.

The Ultimate Trick: The Divisibility Rule

What if you see a huge number like 2,728? How can you tell if it belongs to the 11 family without using a calculator? At our class, we often teach the “Alternating Sum Test” or “Divisibility Rule for 11”

Let’s act like a math detective and follow these steps:

1. Identify the positions: Look at the digits from right to left.
   eg: In 2,728, the digits are 8 (1st), 2 (2nd), 7 (3rd), and 2 (4th).
2. Add the odd-position digits: 8+7=15
3. Add the even-position digits: 2+2=4
4. Subtract the smaller sum from the larger sum: 15-4=11
5. Check the result: If the result is 0 or a multiple of 11 (like 11, 22, 33), then the original number is a multiple of 11!

Let’s look at this picture for another exemple:

Conclusion: Since 11 is a multiple of 11, 2,728 is too! Discovering these “hidden codes” is how we build strong logic skills.

The Magic of 11: How to Multiply Any Number by 11 in Seconds

We all know the easy part: 11x 3 is 33 and 11x 8 is 88. But what happens when you need to calculate 

11 x 45, or even 11×1,234?

Most people reach for a calculator, but with a simple mental math trick, you can solve these problems faster than you can type them in. Here is how to master the multiples of 11.

1. The Basic Trick: Two-Digit Numbers

For most two-digit numbers, the “Split and Sum” method is your best friend.

The Rule: Split the two digits apart, add them together, and stick the sum in the middle.

Example: 25×11

1. Split the digits 2 and 5: 2-5
2. Add them together: 2+5=7
3. Place the 7 in the middle: 275

2. The “Carry Over” Rule

Sometimes, the two digits add up to a number greater than 9. In this case, you simply “carry the one.”

Example: 85×11

1. Split the digits 8 and 5: 8 _ 5
2. Add them together: 8+5=138+5=13
3. The Trick: You can’t put 13 in the middle. Keep the 3 in the middle and add the 1 to the first digit (8+18+1).
4. Result: 935

3. Level Up: Multiplying Large Numbers

This trick even works for huge numbers! The rule here is: “Keep the ends, add the neighbors.”

Example: 1,234×11

1. Write down the last digit of the number: 4
2. Add the neighbors from right to left:
   • 3+4=7
   • 2+3=5
   • 1+2=3
3. Write down the first digit: 1
4. Put it all together: 13,574

Why Does This Work?

It’s not magic—it’s algebra! Multiplying a number by 11 is the same as multiplying it by (10+1)(10+1).

When you do 25×11, you are really doing (25×10)+(25×1)(25×10)+(25×1)

• 250+25=275

The “middle number” in the trick is simply the result of the two numbers overlapping when you add them up.

Practice Makes Perfect

Try these in your head right now:

• 35×11=？
• 62×11=？
• 77×11=？ (Careful with the carry!)

Answers: 385, 682, 847.

Next time you see a multiple of 11, don’t fear the math. Embrace the magic!

Multiples of 11 Complete List (First 20)

Here is a quick reference table for the first 20 multiples of 11:

Mathematical Properties: Odd and Even

Notice something interesting in the list above? The multiples of 11 alternate between odd and even numbers:

• 11 (Odd)
• 22 (Even)
• 33 (Odd)
• 44 (Even)

This happens because 11 itself is an odd number. When you multiply an odd number by an even number, you get an even result. This is a great way for students to check their work quickly!

Wukong Math Insight: Patterns vs. Memorization

Why do we spend time learning these tricks instead of just memorizing the table? Take our student of Wukong, Leo, for example. Leo used to struggle with long division. However, once he learned to “see” the patterns in multiples of 11, his confidence soared.

At Wukong Math Class, we emphasize heuristic education—the art of discovery. When a child understands why a pattern exists, they aren’t just doing math; they are developing Number Sense. Logic is a muscle, and patterns are the weights that make it stronger!

Conclusion

Mastering multiples of 11 is like having a superpower. It helps with mental math, fractions, and complex problem-solving. By looking for the “twins” in small numbers and using the “alternating sum” for big ones, your child can conquer any math challenge.

Ready to unlock more math mysteries? Join a Wukong Math trial class today and watch your child fall in love with the logic behind the numbers!

Multiplication Tables

Multiplication Tables From 1-24

This collection of multiplication resources is designed to support mastery of Common Core State Standards for Operations and Algebraic Thinking. Specifically, it aligns with CCSS.MATH.CONTENT.3.OA.C.7, which requires students to fluently multiply and divide within 100, and 4.OA.B.4, focusing on factors and multiples. By exploring these tables, learners develop the algebraic foundation necessary for mental math fluency and higher-level problem solving.

FAQs About Multiples of 11

Nathan | WuKong Math Teacher

Nathan, a graduate of the University of New South Wales, brings over 9 years of expertise in teaching Mathematics and Science across primary and secondary levels. Known for his rigorous yet steady instructional style, Nathan has earned high acclaim from students in grades 1-12. He is widely recognized for his unique ability to blend academic rigor with engaging, interactive lessons, making complex concepts accessible and fun for every student.