1. What is Cross Multiplication?

Cross multiplication is a method for comparing two fractions by multiplying the numerator of each fraction by the denominator of the other. This technique avoids finding a common denominator and provides a quick way to determine which fraction is larger.

2. How Does Fraction Comparison Work?

The comparison is made using the following method:

Where:

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

Explanation: 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 equal, the fractions are equivalent.

3. Importance of Comparing Fractions

Details: Comparing fractions is fundamental in mathematics, helping with ordering, solving equations, and making real-world comparisons like ratios and proportions.

4. Using the Calculator

Tips: Enter all four values (two numerators and two denominators). Denominators must be positive integers. 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 common denominators?
A: Cross multiplication is often faster and more straightforward for simple comparisons, especially when denominators are large or prime.

Q2: Does this work for mixed numbers?
A: First convert mixed numbers to improper fractions before comparing.

Q3: What about negative fractions?
A: The method works but remember the rules for multiplying negatives. Compare absolute values first, then consider signs.

Q4: Can this method be used for adding fractions?
A: No, cross multiplication is only for comparison. Addition requires a common denominator.

Q5: How does this relate to Desmos calculators?
A: This worksheet demonstrates the mathematical principle that can be visualized using Desmos graphing tools.