Question

Here is the Fraction class:

public class Fraction
{
private int numer
private int denom;
}

Here in main we create a Fraction:

Fraction f1 = new Fraction();


This will:

Answer 1

Instantiating a new Fraction object in Java sets up a basic structure. To work with fractions effectively, methods for arithmetic operations and simplification must be added to the class, ensuring correct mathematical functioning according to fraction rules.

Step-by-step explanation:

Creating a Fraction object in the given Java code will instantiate a new instance of the Fraction class. However, this code snippet only shows the construction of the object without initializing its state. To truly work with fractions, the class needs to define methods for adding, subtracting, multiplying, and dividing fractions. The Fraction class should also be capable of handling common denominators, simplifying fractions, and following the rules for fraction arithmetic.

For example, the fraction ¹⁄₂₅ could be interpreted as cutting an entity into 25 parts and considering just one of those, or mathematically as having a numerator of 1 and a denominator of 25. Similarly, when multiplying two fractions, such as ¹⁄₃ × ⁵⁄₆, it involves multiplying both numerators and denominators respectively, simplifying if needed.

It's essential for the Fraction class to have mechanisms to simplify fractions and find common denominators when performing operations like addition or subtraction. For instance, adding ¹⁄₄ to ¹⁄₂ requires a common denominator, resulting in ¹⁄₄+²⁄₄ which simplifies to ¹¹⁄₂₄, not the incorrect ²⁄₆. It is this understanding of fraction rules that allows one to perform the correct arithmetic operations and maintain the integrity of mathematical expressions.