Introduction to Rational Numbers:

Rational numbers are a subset of real numbers that can be expressed as a fraction, where the numerator and denominator are both integers. In other words, a rational number can be written in the form of p/q, where p and q are integers and q is not equal to zero.

Examples of Rational Numbers:
- 1/2
- 4/5
- -3/7
- 2 (which can be written as 2/1)

Properties of Rational Numbers:
- Rational numbers can be positive, negative, or zero.
- Rational numbers can be expressed in both fraction and decimal forms.
- Rational numbers can be added, subtracted, multiplied, and divided.
- The sum, difference, product, and quotient of two rational numbers are also rational numbers.
- Rational numbers can be ordered on the number line and can be compared using inequality symbols.

Finding Six Rational Numbers between Three and Four:
To find six rational numbers between three and four, we can use the concept of decimal representation of rational numbers.

1. Convert three and four to decimals:
- Three = 3.000...
- Four = 4.000...

2. Divide the interval between three and four into equal parts:
- 3.000... to 4.000... can be divided into 10 equal parts.

3. Add 0.1 to each part:
- The six rational numbers between three and four are:
- 3.1
- 3.2
- 3.3
- 3.4
- 3.5
- 3.6

Summary:
Rational numbers are a subset of real numbers that can be expressed as a fraction. They have properties such as being positive, negative, or zero, being expressible in both fraction and decimal forms, and being closed under addition, subtraction, multiplication, and division. To find rational numbers between given values, we can use the concept of decimal representation and divide the interval into equal parts. In this case, we found six rational numbers between three and four by dividing the interval into 10 equal parts and adding 0.1 to each part.