Maths Facts
Why 11 times table repeats digits at first
Show 11 × 2 through 11 × 9 with tens and ones.
Quick answer
The 11 times table repeats digits at first because when you multiply 11 by a single-digit number, you get a two-digit number where both digits are the same as that single-digit number. For example, 11 × 3 = 33.Learning outcome
By the end of this page, you will understand why the 11 times table repeats digits for the first few numbers, and you will be able to use this pattern to multiply by 11 quickly. Success signs:- You can explain why 11 × 2 = 22, 11 × 3 = 33, and so on.
- You can use this pattern to solve multiplication problems with 11.
- You can show how this pattern works with larger numbers too.
- You can check your answers using repeated addition or arrays.
Why this matters
Understanding patterns in the 11 times table helps you learn multiplication faster. It’s like a secret trick that makes maths fun and easy! When you know this pattern, you can quickly work out things like how many cookies you need if you have 11 trays with 7 cookies on each tray. This skill will help you in school and in real life when you're shopping, cooking, or playing games.How it works
Let’s break it down step by step. First, let’s look at what happens when we multiply 11 by single-digit numbers (from 1 to 9): 1. 11 × 1 = 11 2. 11 × 2 = 22 3. 11 × 3 = 33 4. 11 × 4 = 44 5. 11 × 5 = 55 6. 11 × 6 = 66 7. 11 × 7 = 77 8. 11 × 8 = 88 9. 11 × 9 = 99 This pattern happens because: - When you multiply 11 by a single-digit number, you're really making that number appear twice. - You can think of it as 11 × n = n × (10 + 1) = n × 10 + n × 1 = 10n + n = n0 + n = nn. So, 11 × 4 = 40 + 4 = 44. This is a helpful shortcut for the first few numbers in the 11 times table.Examples you can see
Let’s look at a few examples you can imagine or draw. Example 1: Counting in groups Imagine you have 11 boxes, and each box has 5 toys. How many toys are there altogether? - 11 × 5 = 55 toys - You can think of it as 5 groups of 11, or 11 groups of 5. - This gives you 55 toys. Example 2: Drawing arrays Draw a grid with 11 rows and 6 columns. - Each row has 6 items. - Total = 11 × 6 = 66 items. - You can see that 66 has the same digits (6 and 6). Example 3: Real-world situation You are helping your parent set up chairs for a party. - You have 11 rows of chairs. - Each row has 7 chairs. - How many chairs are there in total? - 11 × 7 = 77 chairs. - This shows the same digit (7) twice. Example 4: Repeated addition If you want to find 11 × 4: - Add 11 four times: 11 + 11 + 11 + 11 = 44 - Or think of it as 4 + 4 = 8, then 40 + 4 = 44 - This is why 11 × 4 = 44Try it as a mini adventure
Adventure: The Mystery of the Magic 11s You are a detective solving a mystery in a maths kingdom. In this kingdom, all numbers are magical, and the 11s are especially powerful. You must discover why 11 × 2 = 22, 11 × 3 = 33, and so on. Step 1: Collect 11 apples and put them into 2 groups. - How many apples in total? 11 + 11 = 22 - So 11 × 2 = 22 Step 2: Now, take 11 marbles and split them into 3 groups. - How many marbles in total? 11 + 11 + 11 = 33 - So 11 × 3 = 33 Step 3: Keep going with 11 × 4, 11 × 5, and 11 × 6. - 11 × 4 = 44 - 11 × 5 = 55 - 11 × 6 = 66 Step 4: Now, you find a clue that says, “The magic only works for single-digit numbers.” - Test 11 × 10 = 110 - Why is it different now? Because 10 is not a single digit. This adventure shows that the pattern works only when multiplying by single-digit numbers.Common mistakes
- Mistake: Thinking 11 × 10 = 110, and expecting the same pattern. Why it happens: The pattern only works for single-digit numbers. Fix: Remember that 11 × 10 = 110 because 10 is not a single digit.
- Mistake: Believing 11 × 7 = 77 is a trick that works for all numbers. Why it happens: Confusing the pattern with other multiplication facts. Fix: Practice with different numbers to see the pattern only applies to 11 × 1 to 11 × 9.
- Mistake: Adding 11 to itself instead of multiplying. Why it happens: Not understanding multiplication as repeated addition. Fix: Use arrays or drawings to show that 11 × 3 means 3 groups of 11.
Parent and carer guide
Parents and carers can help children learn this pattern by:- Using real-life examples like 11 trays with 4 cookies each to show 11 × 4 = 44.
- Encouraging children to draw arrays or use physical objects like counters or blocks.
- Playing a quick game where you ask, “What is 11 × 6?” and see if they say 66 without counting.
- Practising the pattern with different numbers to show it only works for 1 to 9.
- Reinforcing that 11 × 10 = 110 and not 110, so the pattern doesn’t work beyond single digits.
Practice questions
- What is 11 × 2?
- What is 11 × 5?
- What is 11 × 7?
- What is 11 × 9?
- Why doesn’t the pattern work for 11 × 10?
- 22
- 55
- 77
- 99
- Because 10 is not a single-digit number, so the pattern of repeating digits doesn’t apply.
FAQ
Why does 11 × 2 = 22, 11 × 3 = 33, and so on?
This happens because when you multiply 11 by a single-digit number, you're really just repeating that digit twice. For example, 11 × 3 means 3 groups of 11, which is 33.
Does this pattern work for all numbers?
No, it only works for 11 × 1 to 11 × 9. When you get to 11 × 10, the pattern stops because 10 is not a single digit.
Can I use this trick to multiply by 11?
Yes! For single-digit numbers, you can just repeat the digit. For example, 11 × 8 = 88. It's a quick way to solve these problems.
What if I forget the pattern?
You can always add 11 repeatedly or use arrays to help you find the answer. For example, 11 × 6 = 6 + 6 + 6 + 6 + 6 + 6 = 36, or 11 × 6 = 60 + 6 = 66.
Is this pattern in the 11 times table?
Yes, it’s a special pattern that appears in the 11 times table for 1 through 9. It’s one of the easiest patterns to remember.