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multiplication

Long multiplication step by step

Teach the standard written method with place-value understanding.

Quick answer

Long multiplication is a method for multiplying larger numbers by writing them in columns and multiplying each digit separately. You multiply each digit of the bottom number by each digit of the top number, then add the results together to get your final answer.

Learning outcome

By the end of this page, you will be able to multiply two larger numbers together using the long multiplication method, understanding how place value works in each step. Success signs:
  • You can write two numbers in columns with the bigger number on top
  • You can multiply each digit of the bottom number by each digit of the top number
  • You can add the partial products correctly
  • You can check your answer by estimating or using a calculator

Why this matters

Long multiplication helps you solve problems with bigger numbers that are too hard to do in your head. You’ll use it in school when solving word problems, and in real life when calculating things like:
  • How much money you’ll spend buying 24 packets of stickers that cost £1.75 each
  • How many tiles you need to cover a floor that is 12 metres long and 8 metres wide
  • How many pages you can read in 15 days if you read 24 pages each day
It also builds a strong understanding of how numbers work, which helps with more advanced maths later.

How it works

Long multiplication is like a step-by-step recipe. You:
  1. Write the bigger number on top and the smaller one underneath
  2. Multiply each digit of the bottom number by each digit of the top number
  3. Write each answer in the correct place under the line
  4. Add all the answers together to get your final product
Let’s go through each step carefully.

Examples you can see

Let’s multiply 24 by 13 using long multiplication. Step 1: Write the numbers in columns. 
   24
× 13
-----
Step 2: Multiply 3 by each digit of 24.
  • 3 × 4 = 12 (write 2, carry 1)
  • 3 × 2 = 6, plus 1 = 7
So we write: 
   24
× 13
-----
   72
Step 3: Multiply 1 by each digit of 24.
  • 1 × 4 = 4
  • 1 × 2 = 2
We write this below the first answer, but we shift it one space to the left because 1 is in the tens place: 
   24
× 13
-----
   72
  240
Step 4: Add the two answers. 
   24
× 13
-----
   72
  240
-----
  312
So 24 × 13 = 312.

Try it as a mini adventure

Adventure: The Bakery Challenge You are a young baker helping your grandpa in the shop. He wants you to calculate how many cupcakes he can make with 37 bags of flour if each bag makes 15 cupcakes. How to solve:
  1. Write 37 on top and 15 underneath
  2. Multiply 5 by 37
  3. Multiply 1 by 37
  4. Add the results
Try this challenge:
  • Step 1: 5 × 7 = ?
  • Step 2: 5 × 3 = ?
  • Step 3: 1 × 7 = ?
  • Step 4: 1 × 3 = ?
  • Step 5: Add your two answers

Common mistakes

  • Mistake: Forgetting to shift the second row when multiplying by the tens digit. Why: The tens digit is worth ten times more, so it needs to be in the tens column. Fix: Always leave a space before writing the second row.
  • Mistake: Not carrying numbers properly. Why: When multiplying gives a two-digit number, you must carry the tens digit. Fix: Write the units digit under the line and carry the tens digit above the next column.
  • Mistake: Adding the partial products wrong. Why: Misaligning the numbers makes addition messy. Fix: Line up the columns carefully and check your addition.

Parent and carer guide

Long multiplication can be tricky, but you can help your child by:
  • Practising place value with money or base-10 blocks
  • Using visual aids like grids or arrays to show what multiplication means
  • Letting them explain their steps out loud
  • Encouraging them to check their work with estimation or a calculator
  • Being patient and celebrating small wins
What to say:
  • "Let’s break this down into smaller steps."
  • "What happens when you multiply 6 by 7?"
  • "Can you check your answer by adding it up?"
What not to do:
  • Don’t rush them or say “hurry up”
  • Don’t call it “too hard” or “not important”
  • Don’t skip the practice of checking their work

Practice questions

  1. What is 34 × 12?
  2. Calculate 56 × 23
  3. Find the product of 78 × 45
  4. Multiply 19 × 37
  5. What is 62 × 18?
Answers:
  1. 34 × 12 = 408
  2. 56 × 23 = 1,288
  3. 78 × 45 = 3,510
  4. 19 × 37 = 703
  5. 62 × 18 = 1,116

FAQ

What is long multiplication?

Long multiplication is a way to multiply large numbers by writing them in columns and multiplying each digit separately.

Why do we use long multiplication?

It helps us solve problems with bigger numbers that are hard to do in our heads. It also builds a strong understanding of how numbers work.

How do I know where to put the digits when multiplying?

Each digit in the bottom number is multiplied by each digit in the top number. The answers must be lined up correctly so that the place values match when you add them.

What if I make a mistake in carrying?

If you forget to carry or carry wrong, your final answer will be wrong. Always double-check your carrying, and use estimation to see if your answer makes sense.

Can I use a calculator for long multiplication?

Yes, calculators are great for checking your work, but learning the method helps you understand maths better and builds confidence.