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:

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.

Example 3: 124 x 26

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 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.

(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)

Read more

• What Is A Square Number
• Lowest Common Multiple
• Highest Common Factor
• What is a Multiple
• Factors
• What Is A Cube Number

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