Age 10 guide to long multiplication

Quick answer

Long multiplication is when you multiply a multi-digit number by a two-digit number. You split the calculation into smaller parts, multiply each part, and then add the results together.

Learning outcome

By the end of this page, you will be able to multiply a 2-digit number by a 2-digit number using the long multiplication method.

• You can split a multiplication into smaller parts
• You can multiply using the column method
• You can add partial products to get the final answer
• You can check your answer with a calculator or by estimating

Why this matters

Long multiplication helps you solve bigger problems that are too hard to do in your head. You use this skill when you're shopping, planning a party, or working out how much time you need for a big project. It's also the foundation for more advanced maths you'll learn later, like algebra and working with decimals.

How it works

Long multiplication is a step-by-step process. Here’s how it works:

1. Write the two numbers one on top of the other, aligning the digits
2. Multiply the bottom number’s units digit by each digit of the top number
3. Write the result below, aligning the digits
4. Multiply the bottom number’s tens digit by each digit of the top number
5. Write the result below, but shift it one place to the left
6. Add the two partial products together

Examples you can see

Let’s try an example: 24 × 13.

First, we write the numbers:

Next, we multiply by the tens digit (1):

Now we add the two results:

So, 24 × 13 = 312.

Try it as a mini adventure

You are planning a school fair and need to buy 24 bags of sweets. Each bag costs £13. How much will you spend in total?

Let’s go on a maths adventure to find out!

1. First, you need to multiply 24 × 13
2. Write it out like this:
3. 24
4. × 13
5. Then multiply 3 by each digit in 24:
6. 3 × 4 = 12
7. 3 × 2 = 6
8. Write 12 and 6, but remember to add a zero in the units place for the tens:
9. 12 + 60 = 72
10. Now multiply 10 by each digit in 24:
11. 10 × 4 = 40
12. 10 × 2 = 20
13. Write 200 and 40:
14. 200 + 40 = 240
15. Add the two answers:
16. 72 + 240 = 312
17. You spend £312 on sweets!

Common mistakes

• Mistake: Forgetting to shift the second row one place to the left when multiplying by the tens digit.
• Why it happens: The child might not understand that 10 × 24 is not the same as 1 × 24.
• Fix: Always add a zero in the units place when multiplying by the tens digit.
• Mistake: Adding the partial products incorrectly.
• Why it happens: The child might misalign the numbers or forget to carry over.
• Fix: Line up the numbers carefully and double-check your addition.
• Mistake: Confusing the order of multiplication.
• Why it happens: The child might not understand that 24 × 13 is the same as 13 × 24.
• Fix: Remind them that multiplication is commutative, but the method still works the same way.

Parent and carer guide

Here’s how you can help your child with long multiplication:

• Start by using visual aids like counters or blocks to show how multiplication works
• Practice with smaller numbers first, like 12 × 14
• Encourage your child to check their work with a calculator
• Use real-life examples like shopping or cooking to show why this skill is useful
• Don’t rush – let them make mistakes and learn from them
• Ask your child to explain their steps to you – this helps them learn better

Remember, it's okay if your child finds long multiplication tricky at first. With practice and patience, they will get better!

Practice questions

1. What is 15 × 12?
2. Calculate 23 × 14
3. Find the answer to 31 × 16
4. What is 27 × 18?
5. Try 42 × 23

Answers:

1. 15 × 12 = 180
2. 23 × 14 = 322
3. 31 × 16 = 496
4. 27 × 18 = 486
5. 42 × 23 = 966

FAQ

What is long multiplication?

Long multiplication is a method used to multiply large numbers by breaking the problem into smaller parts and then adding the results.

Why do we use long multiplication?

We use long multiplication when we need to multiply numbers that are too big to do in our heads. It helps us get accurate answers.

How do I know if my answer is correct?

You can check your answer by estimating, using a calculator, or doing the calculation again using a different method.

Can I use long multiplication for decimals?

Yes, but you need to be careful about where you place the decimal point. We don’t cover that here, but it's a skill you'll learn later.

What should I do if I get confused?

Take your time, write everything down, and ask for help. It's normal to find long multiplication tricky at first!