1. What is Whole Number Times Fraction?

This calculator demonstrates the mathematical equivalence between multiplying a whole number by a fraction (left form) and multiplying the whole number by the numerator then dividing by the denominator (right form).

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( c \) — Whole number (unitless)
• \( a \) — Numerator of fraction (unitless)
• \( b \) — Denominator of fraction (unitless, must be > 0)

Explanation: This demonstrates the distributive property of multiplication over division.

3. Mathematical Principle

Details: The equation shows that multiplying a whole number by a fraction is equivalent to multiplying the whole number by the numerator and then dividing by the denominator. This is fundamental to fraction arithmetic.

4. Using the Calculator

Tips: Enter whole number for c, numerator for a, and denominator for b (must be positive). The calculator will show both forms of the calculation.

5. Frequently Asked Questions (FAQ)

Q1: Why does this equivalence work?
A: It's based on the associative property of multiplication and the definition of fractions as division operations.

Q2: What if the denominator is zero?
A: The calculator prevents this as division by zero is undefined in mathematics.

Q3: Does this work with negative numbers?
A: The calculator uses non-negative numbers, but the principle holds for negatives too.

Q4: Can this be used for mixed numbers?
A: Yes, but you'd need to convert the mixed number to an improper fraction first.

Q5: Why show both forms?
A: To demonstrate the mathematical equivalence and help understand fraction multiplication.