🧠 Number Systems and Basic Operations

Before mathematics can help with land measurement, seed rate, or economics, it begins with a simpler question: what kinds of numbers do we use, and how do we operate on them correctly? This lesson builds that foundation.

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Classification of Numbers

Number systems are organized from simpler sets to broader ones.

Number Set	Meaning	Example
Natural numbers	Counting numbers	1, 2, 3
Whole numbers	Natural numbers including zero	0, 1, 2, 3
Integers	Positive, negative, and zero	-2, -1, 0, 1
Rational numbers	Can be written as p/q	1/2, -3/4, 0.75
Irrational numbers	Cannot be written as simple fraction	sqrt(2), pi
Real numbers	All rational and irrational numbers	Most measurable values

In agriculture, most measured quantities such as area, yield, price, and temperature are treated as real numbers.

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Basic Arithmetic Operations

The four fundamental operations are:

• addition
• subtraction
• multiplication
• division

Some important properties are:

• commutative property for addition and multiplication
• associative property for grouping
• distributive property of multiplication over addition

These properties make calculations easier and help simplify expressions.

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BODMAS Rule

When an expression contains several operations, the order matters. The standard rule is BODMAS:

1. Brackets
2. Orders
3. Division
4. Multiplication
5. Addition
6. Subtraction

Example

For 12 + 4 x (6 - 2)^2 / 8:

1. (6 - 2) = 4
2. 4^2 = 16
3. 4 x 16 = 64
4. 64 / 8 = 8
5. 12 + 8 = 20

So the correct answer is 20.

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Why This Matters in Agriculture

Basic arithmetic is used constantly in tasks such as:

• calculating seed requirement
• mixing solutions
• estimating yield
• finding gross return or net return

Example:

If 80 kg seed is required per hectare and a farmer has 5.5 hectares, total seed required is:

80 x 5.5 = 440 kg

So number systems and arithmetic are not abstract preliminaries; they are daily agricultural tools.

Summary Cheat Sheet

Topic	Key Point
Natural numbers	Counting numbers starting from 1
Integers	Include negatives, positives, and zero
Rational numbers	Can be written as a fraction
Real numbers	Include rational and irrational numbers
BODMAS	Standard order of operations
Main exam trap	Doing multiplication or addition before brackets gives wrong results