Base 5 Calculation

Table of Contents

PREFACE iii

1. Introduction 1

2. What is base 5 number 1

3. How to read a Multiplication TABLE 2

4. How to read an Addition TABLE 3

5. Process of multiplying two base 5 number 3

APPENDIX A: LIST OF FIGURES 6

APPENDIX B: REFERENCE PAGE 6

ii

PREFACE

Thanks the help of my professor Nancy Acemian and the students who contribute their ideas when I write this instruction.

Wenjun zhu

February 2008

iii

1. Introduction

In reality, people use base 10 numbers quite often in different fields, such as shopping, calculation. However, a few people hear about base 5 number which is quite similar to base 10 number in the calculation. This set of instruction is to explain what is base 5 number and how to multiply a 3-digit positive base 5 number by a 2-digit positive base 5 number.

1

2

2. What is base 5 number

Base 5 numbers are the representation of quantity with symbols which are written using only 0, 1, 2, 3, 4 digits.

3. How to read a Multiplication Table

Let’s understand how to read the Base 5 multiplication TABLE. This table is quite similar to the regular decimals multiplication table. Grey shade cells of the first row and first column are operands .The blue shade cell is the operation. In this case, the operation is multiplication. White shade cells are results which store the answer of two operands. Light red shade cell is the sample. Please see in Figure 3-1.

x 0 1 2 3 4

0 0 0 0 0 0

1 0 1 2 3 4

2 0 2 4 11 13

3 0 3 11 14 22

4 0 4 13 22 31

Figure 3-1 Multiplication Table

For example:

2 Ð"-- 4 = 13

Here you look at 2 and go across the row, then look at four and go down the column. Where they intersect, that is the answer.

3

4. How to read an Addition Table

+ 0 1 2 3 4

0 0 1 2 3 4

1 1 2 3 4 10

2 2 3 4 10 11

3 3 4 10 11 12

4 4 10 11 12 13

Figure 4-1 Addition Table

The rule to read figure 4-1 is the same as to read the figure 3-1.

For example:

2 + 4 = 11.

Here you look at 2 and go across the row, then look at 4 and go down the column. Where they intersect, that is the answer.

5. Process of multiplying two base 5 numbers

Now, let’s learn multiply a 3-digit base 5 number by a 2-digit base 5 number following these steps with the help of the Addition and Multiplication Table.

Step 1: write the 43 under the 342 aligning vertically for each digit, and draw a horizontal line under them.

3 4 2

Ð"-- 4 3

---------

Step 2: Start with the ones-column, the multiplicand is 342 and ones-multiplier is 3.Perform the multiplication under the line. At this point, use the multiplication TABLE to do the operation.3 Ð"-- 2 = 11.Eleven has two digits. Write its last digit,1, in the ones-column under the line, and write the “carry digit” which is 1 above the top digit of the next column: in this case the next column is the tens-column.

4

1

3 4 2

Ð"-- 4 3

---------

1

Step 3: Perform 3Ð"--4 = 22.Suppose to write down the 2 under the line in the tens-column. However, there is still one carry digit,1, which added to 2 is equals to 3.So write down the 3 under the line in the tens-column, write the “carry digit” which is 2 on top of the hundreds-column.

2 1

3 4 2

Ð"-- 4 3

---------

3 1

Step 4: Perform 3 Ð"-- 3 =14. Note this is a special situation. Since 14 is a two digits number, write down the 1 in the thousands-column under the line temporarily. Add 4 with the previous carry digit,2, which equals to 11 with the help of the Addition Table. Write down 1 in the hundreds-column under the line, and write down the carry digit,1, on top of the thousands-column. Next,