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. If the products are equal, the fractions are equivalent.

2. How Does Cross Multiplication Work?

The cross multiplication formula:

Where:

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

Explanation: The method works because multiplying both sides of the equation \( \frac{a}{b} = \frac{c}{d} \) by \( b \times d \) simplifies to \( a \times d = b \times c \).

3. Importance of Cross Multiplication

Details: Cross multiplication is essential for solving proportions, comparing fractions, and finding unknown values in equations involving fractions.

4. Using the Calculator

Tips: Enter all four values (a, b, c, d) as integers. The calculator will verify if the cross products are equal and show the calculation steps.

5. Frequently Asked Questions (FAQ)

Q1: Can cross multiplication be used to solve for an unknown?
A: Yes, if one value is unknown (e.g., x), you can set up the equation \( a \times d = b \times c \) and solve for the unknown.

Q2: Does cross multiplication work for inequalities?
A: Yes, but you must consider the sign of the denominators to determine whether to flip the inequality sign.

Q3: What if one denominator is zero?
A: The fraction would be undefined. The calculator requires non-zero denominators.

Q4: Can this be used for complex fractions?
A: The basic cross multiplication works for simple fractions. Complex fractions may require additional simplification first.

Q5: How is this different from multiplying fractions?
A: Cross multiplication compares two fractions, while fraction multiplication combines them (\( \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d} \)).