Original: Thomas Schilb - FracPi[n]s.txt
Based On: Bihar STET TGT (Maths) Unofficial Paper 1.0.1
Held On: 19.08.2025

Pi1 [Machine, I/O]

The expression frac(pi/1) represents a fraction, specifically pi divided by one.
Since any number divided by one is itself, this expression simplifies to just pi (π).
Pi (π) is a mathematical constant, approximately equal to 3.14159, and is known
for being irrational. Therefore, the answer is a real number, irrational number,
and an algebraic number. 

Pi2 [She, Sie]

The number π/2 is an irrational number. It's the result of dividing the mathematical
constant π (pi) by 2. Irrational numbers cannot be expressed as a simple fraction,
and their decimal expansions neither terminate nor repeat. 04.01.2024

Pi3 [He, Er]

The expression frac(pi/3) represents a fraction, specifically a fraction where the
numerator is π (pi) and the denominator is 3. Since π is an irrational number,
this fraction represents an irrational number as well. Any number that can be
expressed in the form of a fraction (where both numerator and denominator are
integers and the denominator is not zero) is considered a rational number.
However, because pi is irrational, the fraction pi/3 cannot be simplified
to a simple fraction of integers, making it an irrational number.

Pi4 [Time, Zeit]

Fractions represent parts of a whole and are fundamentally rational numbers.
They can be categorized into several types based on their structure and
relationship between the numerator and denominator: 

1. Proper Fractions:
In proper fractions, the numerator (top number) is smaller than the denominator (bottom number).
Examples: 1/2, 3/4, 7/10 

2. Improper Fractions:
In improper fractions, the numerator is greater than or equal to the denominator.
Examples: 5/2, 11/8, 6/6 

3. Mixed Fractions:
A mixed fraction combines a whole number and a proper fraction.
Examples: 2 1/2, 3 1/4, 1 5/8 

4. Decimal Fractions:
These are fractions where the denominator is a power of 10 (e.g., 10, 100, 1000) and are expressed as decimals.
Examples: 0.5 (which is equivalent to 1/2), 0.25 (which is equivalent to 1/4) 

5. Unit Fractions:
A unit fraction has a numerator of 1.
Examples: 1/3, 1/5, 1/12 

6. Like Fractions:
These are fractions that have the same denominator.
Examples: 2/7, 5/7, 6/7 

7. Unlike Fractions:
These are fractions that have different denominators.
Examples: 2/5, 3/8, 7/11

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