Key points
Napier’s method of multiplication is a method used to multiply large numbers when you do not have a calculator.
The advantage of Napier's method is that it only uses multiplication factsThe word 'fact’ is related to the instant recall of knowledge about a number. A multiplication fact for 20 could be 4 x 5. A division fact for 20 could be 20 ÷ 5 = 4 up to 9 x 9 and addition.
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How to use Napier’s method of long multiplication
Multiplication using Napier's method uses a grid to multiply numbers.
The grid layout depends on the calculation, eg 64 x 77 would need a 2 x 2 grid. For the calculation 321 x 36, either a 3 x 2 grid or a 2 x 3 grid could be used because multiplication is commutativeAn operation is commutative if the order does not matter. Multiplication and addition are commutative, eg 4 × 3 = 3 × 4 and 4 + 3 = 3 + 4 .
A diagonal line is drawn to separate the tens (T) and the units (U) in each box in the grid.
Each cell in the grid represents a two-digit answer to a multiplication productThe result of multiplying one number by another, eg the product of 4 and 5 is 20 since 4 × 5 = 20 made of a tens digit, and a units digit.
Example: calculate 37 x 91
1 of 10
Example: calculate 653 x 72
1 of 9
Practise Napier’s method
Question: spot the mistake
The answer to this calculation is incorrect.Try to find the mistakes in the working. You might need a pen and paper.
The mistake is that the third diagonal from the right should include a carried digit.
23 is the total of the second diagonal but only the 3 digit should be written there. The 2 is carried to the next diagonal.
7 is the total of the third diagonal (4 + 2 + 1) but there should be a 2 carried and added as well to give a total of 9.
Practise: Napier’s method quiz
Practise long multiplication using Napier's method with this quiz. A pen and paper might be useful to help with your workings out.
Real-world maths
When you do not have a calculator, Napier’s method for long multiplication is one way of calculating your answer.
Multiplication is used to determine areas, quantities for batch production, materials needed for construction projects and much more.
It is a skill used by professionals in catering, engineering, construction and across many businesses. It can be an invaluable skill for the world of work.
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