Distributive (split) strategy for multiplication
Theory
The distributive (split) strategy is a Year 4 maths strategy to multiply a single-digit number by a two-digit number. You split the two-digit number into tens and ones, multiply each part, then add the two answers. This page explains the strategy with area models, a clear method, worked examples and common pitfalls. Curriculum: VC2M4N06, VC2M4A02 / AC9M4N06, AC9M4A02.
The split strategy makes a hard multiplication easier by breaking a two-digit number into smaller parts. You split the number into its tens and ones, multiply each part on its own, then add the two answers together.
For \(7\times 13\), split \(13\) into \(10 + 3\). Then \(7\times 13 = 7\times 10 + 7\times 3 = 70 + 21 = 91\). The tens part is \(70\) and the ones part is \(21\).
An area model is a picture of this idea. It is a rectangle split into two parts: one part shows the tens and the other shows the ones. Splitting a number into parts does not change the total, so the answer is always the same.
The split strategy always follows the same pattern. Split the two-digit number, multiply each part, then add.
How to multiply with the split strategy
- Split the two-digit number into its tens and ones, using place value. For \(24\), that is \(20 + 4\).
- Multiply each part by the other number on its own. Work out the tens part, then the ones part.
- Add the two answers together. This total is the answer to the original multiplication.
Multiplying tens. Use a times-table fact. \(4 \times 30\) is 4 groups of 3 tens, which is 12 tens, or \(120\). In the same way, \(8 \times 20\) is 16 tens, or \(160\).
| \(8\times 13\) | \(=\) | \(8\times 10 + 8\times 3\) |
| \(\) | \(=\) | \(80 + 24\) |
| \(\) | \(=\) | \(104\) |
So \(8\times 13 = 104\).
| \(6\times 24\) | \(=\) | \(6\times 20 + 6\times 4\) |
| \(\) | \(=\) | \(120 + 24\) |
| \(\) | \(=\) | \(144\) |
So \(6\times 24 = 144\).
| \(4\times 19\) | \(=\) | \(4\times 10 + 4\times 9\) |
| \(\) | \(=\) | \(40 + 36\) |
| \(\) | \(=\) | \(76\) |
There are \(76\) muffins.
| \(3\times 27\) | \(=\) | \(3\times 20 + 3\times 7\) |
| \(\) | \(=\) | \(60 + 21\) |
| \(\) | \(=\) | \(81\) |
So \(3\times 27 = 81\).
Common pitfalls
Frequently asked questions
What is the split strategy for multiplication?
The split strategy breaks a two-digit number into its tens and ones, multiplies each part on its own, then adds. For example, \(7\times 13 = 7\times 10 + 7\times 3 = 70 + 21 = 91\).
How do you multiply using the split strategy?
Split the two-digit number into tens and ones, multiply each part by the other number, then add. For \(8\times 13\), work out \(8\times 10 = 80\) and \(8\times 3 = 24\), then add to get \(104\).
Why does splitting a number not change the answer?
Splitting shares the same amount into two groups, so the parts still add up to the whole. Since \(13 = 10 + 3\), the number \(7\times 13\) is the same as \(7\times 10 + 7\times 3\).
What is an area model in multiplication?
An area model is a rectangle split into two parts. One part shows the tens and one shows the ones. You find each part, then add them. It is a picture of the split strategy.
How do you split a two-digit number into tens and ones?
Use place value. The tens digit tells you the tens and the ones digit tells you the ones. So \(24 = 20 + 4\) and \(27 = 20 + 7\).
Do you have to multiply both parts?
Yes. You must multiply the tens part and the ones part. For \(4\times 17\) you need \(4\times 10 + 4\times 7 = 40 + 28 = 68\). Adding only the ones would be wrong.