1. What is Integer Multiplication and Division?

Integer multiplication and division are fundamental arithmetic operations. Multiplication is repeated addition, while division is the inverse operation of multiplication, representing equal distribution or partitioning.

2. How Does the Calculator Work?

The calculator performs basic integer operations:

Where:

• \( a \) — First integer (dividend in division)
• \( b \) — Second integer (divisor in division)
• Product — Result of multiplication
• Quotient — Result of division (integer if divisible, decimal otherwise)

3. Mathematical Principles

Multiplication Properties:

• Commutative: \( a \times b = b \times a \)
• Associative: \( (a \times b) \times c = a \times (b \times c) \)
• Distributive: \( a \times (b + c) = (a \times b) + (a \times c) \)

Division Notes:

• Division by zero is undefined
• If \( a \div b \) is integer, we say b divides a

4. Using the Calculator

Steps:

1. Enter two integers in the input fields
2. Select the operation (multiplication or division)
3. Click "Calculate" to see the result

5. Frequently Asked Questions (FAQ)

Q1: What happens if I divide by zero?
A: The calculator will show "Undefined (division by zero)" as division by zero is mathematically undefined.

Q2: Does this calculator handle decimal numbers?
A: No, it's designed for integers only. Decimal inputs will be truncated to integers.

Q3: How are negative numbers handled?
A: Standard rules apply: negative × negative = positive, negative ÷ positive = negative, etc.

Q4: What's the maximum number size?
A: Limited by PHP's integer size (typically ±2,147,483,647 on 32-bit systems).

Q5: Why might division results show decimals?
A: If the numbers don't divide evenly, the calculator shows a decimal result rounded to 4 places.