1. What is Fraction Comparison?

Fraction comparison is the process of determining which of two fractions is larger or if they are equal. This calculator uses the cross-multiplication method which is reliable for all positive fractions.

2. How Does the Calculator Work?

The calculator uses cross multiplication:

Where:

• \( a \) — Numerator of first fraction
• \( b \) — Denominator of first fraction
• \( c \) — Numerator of second fraction
• \( d \) — Denominator of second fraction

Rules:

• If \( a \times d > b \times c \), then \( \frac{a}{b} > \frac{c}{d} \)
• If \( a \times d < b \times c \), then \( \frac{a}{b} < \frac{c}{d} \)
• If \( a \times d = b \times c \), then \( \frac{a}{b} = \frac{c}{d} \)

3. Importance of Cross Multiplication

Details: Cross multiplication is the most reliable method for comparing fractions without converting them to decimal form. It works for all positive fractions regardless of their denominators.

4. Using the Calculator

Tips: Enter all four values (two numerators and two denominators). Denominators must be positive numbers. The calculator will show which fraction is larger or if they're equal.

5. Frequently Asked Questions (FAQ)

Q1: Why use cross multiplication instead of decimal conversion?
A: Cross multiplication gives exact results without rounding errors that can occur with decimal conversion.

Q2: Does this work for negative fractions?
A: This calculator is designed for positive fractions only. For negative fractions, additional rules apply.

Q3: What if denominators are equal?
A: With equal denominators, you can simply compare numerators, but cross multiplication works in all cases.

Q4: Can I compare more than two fractions?
A: This calculator compares two fractions at a time. For multiple fractions, you would need to compare them pairwise.

Q5: How precise are the results?
A: Results are mathematically exact when using exact values, though computer floating-point arithmetic has inherent limitations.