Multiplication Using Napier's Method - Year 7 PDF Download

Introduction

• Napier's method of multiplication is a technique utilized for multiplying large numbers without the aid of a calculator.
• The primary advantage of Napier's method lies in its reliance on multiplication facts. These facts involve the immediate recall of number-related knowledge. For instance, a multiplication fact for 20 could be 4 x 5, while a division fact for 20 could be 20 ÷ 5 = 4, extending up to 9 x 9 and addition operations.
• An engaging way to reinforce multiplication skills is by playing the educational game "Guardians: Defenders of Mathematica" to practice times-tables.

How to Use Napier's Method of Long Multiplication

• Multiplication using Napier's method involves utilizing a grid to perform the multiplication of numbers.
• The layout of the grid is determined by the specific calculation. For instance, a multiplication such as 64 x 77 would necessitate a 2 x 2 grid. In the case of a calculation like 321 x 36, either a 3 x 2 grid or a 2 x 3 grid could be employed due to the commutative property of multiplication.
• An operation is considered commutative when the order of operands does not affect the result. Both multiplication and addition exhibit commutative properties. For example, 4 x 3 is equal to 3 x 4, and 4 + 3 equals 3 + 4.
• Within the grid, a diagonal line is drawn to segregate the tens (T) and the units (U) in each box.
• Each cell in the grid corresponds to a two-digit answer resulting from a multiplication operation, comprising a tens digit and a units digit.

Example

Calculate 37 x 91

Here are the steps to calculate 37 x 91 using a Napier grid:

• Draw a 2 by 2 grid to multiply a 2-digit number by another 2-digit number. Label the grid with figures at the top and the right-hand side.
  
• Draw the diagonals for each cell in the grid from top right to bottom left and extend outside the grid.
  
• Each cell in the grid represents a two-digit answer to a multiplication (product) made of a tens digit and a units digit.
  
• This cell shows the result of 3 x 9. When 3 is multiplied by 9, the answer is 27, which consists of 2 tens and 7 units.
  
• This cell illustrates the product of 7 x 9. The result of multiplying 7 by 9 is 63, comprising of 6 tens and 3 units.
  
• This cell displays the outcome of 3 x 1. When 3 is multiplied by 1, the result is 3, with 0 tens and 3 units.
  
• This cell showcases the product of 7 x 1. When 7 is multiplied by 1, the answer is 7, with 0 tens and 7 units.
  
• The grid now contains all the products. The sum of each diagonal contributes to the final answer. The first diagonal from right to left represents the units, the second diagonal denotes the tens, the third diagonal signifies the hundreds, and the fourth diagonal symbolizes the thousands.
  
• Add up each diagonal. Remember to carry when you get a two-digit answer.
  
• Follow the arrows to write the calculation with the answer: 37 x 91 = 3367

Real-world Maths

• When you lack a calculator, Napier's method for long multiplication offers a way to calculate your answer.
• Multiplication is crucial for determining areas, batch production quantities, construction project materials, and more.
• Professionals in catering, engineering, construction, and various businesses utilize multiplication, making it a valuable skill in the workplace.