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What Is Long Multiplication: Explained For Primary School Parents And Kids

Long multiplication is multiplying a number with two or more digits by a two-digit number, e.g. 34 x 27, 851 x 82 or 4,274 x 93. This article explains the process for doing long multiplication following the column multiplication method used in primary schools at KS2.

This article is part of our series designed for teachers to inform their mathematical subject knowledge, and for parents to help support children with home learning. More free home learning resources are also available.

What is long multiplication?

Long multiplication is a method of multiplying larger numbers together. In the primary curriculum long multiplication is taught for multiplying two, three and four digit numbers by two digit numbers.

Long multiplication methods

The mathematics appendix in the National Curriculum demonstrates the formal method of long multiplication:

Long multiplication in primary school

The first and third multiplication demonstrate the most common long multiplication methods.

Example 1: 24 x 16

26 is partitioned to become 20 and 6. 124 is multiplied by 6 first, which equals 744; 126 is then multiplied by 20 to become 2480; 2480 and 744 are added together to make 3224.

In order to succeed at long multiplication, it is essential that children are fluent in their times tables and if your child is struggling to learn them, then we recommend trying out these times tables games as a great next step.

FREE KS2 Long Multiplication Worksheets

FREE KS2 Long Multiplication Worksheets

A series of ready-to-use worksheets to help pupils practice their long multiplication skills.

Example 3: 124 x 26
long multiplication method steps example

Here, you have the steps to do long multiplication for the third example:

  1. Set the question in the formal method
  2. Remember to start the process of multiplication with the ones
  3. Multiply 6 by 4
  4. Write the answer down correctly – including any regrouping
  5. Multiply 6 by 2
  6. Add anything that you have carried from the previous multiplication.
  7. Multiply 6 by 2
  8. Write the answer down correctly
  9. Drop a zero as we are now multiplying with 10s
  10. Multiply 2 by 4
  11. Write the answer correctly
  12. Multiply 2 by 2
  13. Write the answer down
  14. Multiply 2 by 1
  15. Write the answer correctly
  16. Add the two answers up together correctly

Now, all you need to do is follow these steps for any other similar long multiplication question.

When will my child learn about long multiplication in primary school?

Children first learn about the long multiplication method in Year 5, where they are expected to multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers. This is continued in Year 6.

  • In year 5 the national curriculum objectives for multiplication and division include ‘pupils should be taught to multiply numbers up to 4 digits by a one- or two-digit number using a formal written  method, including long multiplication for two-digit numbers.’
  • In year 6 the national curriculum objectives for multiplication and division include ‘pupils should be multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication.’

Third Space Learning’s online one-to-one tutoring is personalised to the needs of each individual student, helping to fill in learning gaps, bringing them up to Year group level, as well as giving students more confidence in maths.

Long multiplication lesson slide
Example of a Third Space Learning online lesson slide on long multiplication

Long multiplication questions

1. 746 x 23 =

(Answer: 17,158)

2. A box contains trays of melons. There are 15 melons in a tray. There are 3 trays in a box. A supermarket sells 40 boxes of melons. How many melons does the supermarket sell?

(Answer: 15 x 3 x 40 = 1,800)

3. Write the two missing digits to make this long multiplication correct.

Long multiplication questions

(Answer: 41 x 26)

4. A toy shop orders 11 boxes of marbles. Each box contains 6 bags of marbles. Each bag contains 45 marbles. How many marbles does the shop order in total?

(Answer: 11 x 6 x 45 = 2,970)

5. A shop sells sheets of sticky labels. On each sheet there are 36 rows and 18 columns of labels. How many labels are there altogether on 45 sheets?

(Answer: 36 x 18 x 45 = 29,160)

What is the meaning of long multiplication?

Long multiplication, also called column multiplication, is a method of multiplication, usually used for 3-digit and larger numbers.

What is the difference between long and short multiplication?

Short multiplication is the method recommended when multiplying a 3-digit or larger number with a 1-digit number. Long multiplication is more often used when multiplying numbers that are both at least 2-digit.

What year do children learn long multiplication?

Long multiplication is most often introduced in Year 5.

Read more

Do you have pupils who need extra support in maths?
Every week Third Space Learning’s maths specialist tutors support thousands of pupils across hundreds of schools with weekly online 1-to-1 lessons and maths interventions designed to plug gaps and boost progress.

Since 2013 we’ve helped over 130,000 primary and secondary school pupils become more confident, able mathematicians. Learn more or request a personalised quote for your school to speak to us about your school’s needs and how we can help.

Primary school tuition targeted to the needs of each child and closely following the National Curriculum.

Sophie Bartlett
Sophie Bartlett
Year 6 Teacher
Sophie teaches mixed age classes at a small school in central England. She is a self confessed grammar pedant and number nerd so we've welcomed her as a regular author and editor for Third Space Learning.
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FREE KS2 Long Multiplication Worksheets

FREE KS2 Long Multiplication Worksheets

A series of ready-to-use worksheets to help pupils practice their long multiplication skills.

Download Free Now!

FREE KS2 Long Multiplication Worksheets

Downloadable resource

A series of ready-to-use worksheets to help pupils practice their long multiplication skills.

Download Free Now!
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FREE KS2 maths SATs practice papers

Get ready for SATs with this set of 6 maths SATs practice papers designed to help your Year 6 pupils improve test skills and build confidence.

Includes:
- 2 arithmetic and 4 reasoning papers that follow the National Curriculum Assessments.
- Mark schemes to diagnose and assess where your pupils need extra support.

Download free