#### Revision Notes

##### Non-Calculator) Multiplication – Why so many methods?

You would have no doubt seen various methods, from various teachers, textbooks and websites, etc showing ways to multiply numbers together without a calculator.

There are lots of methods.  Different methods work for different people.  Different methods are better depending on the size of number you are dealing with.

There is no one size fits all.  If you are here as part of your revision programme and are still not sure which method you should use, we recommend the following three depending on the size of number you are dealing with.

(If in doubt all methods will work for all numbers!)

1. LATTICE Method (Best for numbers with two or more digits)

This method allows you to work with digits – so in the number 3 516 you would only need to work with the digits 3, 5, 1 and 6 – so if you can multiply up to 9×9 you can’t go wrong!

So 3516 × 23 = 80 868

2. PARTITION Method (Best when one number has just one digit)
This method keeps the value of the larger number intact – so with 3 516 you would use 3000, 500, 10 and 6. This method is not suitable for two larger numbers as you can end up with a lot of zero digits that are hard to keep track of.

So 3516 × 7 = 24 612

3. REPEATED ADDITION Method (Best for smaller, simple-ish cases)
You may have seen this called ‘chunking’ and is a way of building up to the answer using simple multiplication facts that can be worked out easily.

eg 13 × 23
1 × 23 = 23
2 × 23 = 46
4 × 23 = 92
8 × 23  =184
So 13 × 23 = 1 × 23 + 4 × 23 + 8 × 23 = 23 + 92 + 184 = 299

4. DECIMALS
The methods here can easily be adapted for use with decimal numbers – in fact the methods are no different! You ignore the decimal point whilst multiplying but put it back in the correct place in order to reach a final answer.

eg 1.3 × 2.3

Ignoring the decimals this is 13×23 which from above is 299

There are two decimal places in total in the question, so there will be two decimal places in the answer.

So 1.3 × 2.3 = 2.99

#### Example

1. Multiply 2879 by 36

As you have a 4-digit number multiplied by a 2-digit number then the lattice method (1) is the best choice

Notice the use of listing the 8 times table at the bottom to help with any you may have forgotten

2879 × 36 = 103 644

Note that the method would still work if you had set it up as a 2×4 grid

2. Pencils are sold in boxes. Each box costs £1.25 and each box contains 15 pencils.
Tyler buys 35 boxes of pencils.
(a) Work out how many pencils Tyler has in total.

(b) Work out the total cost for all the boxes Tyler buys.

(a)

This is a roundabout way of asking you to work out 15×35
As this is a simpl-ish case (3) you should use the repeated addition method

1 × 35 = 35
2 × 35 = 70
4 × 35 = 140
8 × 35 = 280
16 × 35 = 560       It doesn’t matter if you go past 15 …

15 × 35 = 16 × 35 – 1 × 35 = 560 – 35
15 × 35 = 525

(b)

This question is 1.25×35 so involves decimals (4)
Ignoring the decimals it becomes 125×35 and so the lattice method is best

125 × 35 = 4375

Now count the decimal places from the question and put the decimal point back in the correct place

£1.25 × 35 = £43.75

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