1. What is Cross Multiplication?

Cross multiplication is a method to check the equality of two fractions or to solve for an unknown variable in a proportion. It's based on the principle that if two fractions are equal, the product of the numerator of the first and the denominator of the second equals the product of the denominator of the first and the numerator of the second.

2. How Does Cross Multiplication Work?

The cross multiplication principle:

Explanation: This method works because multiplying both sides of the equation by the product of the denominators (b × d) eliminates the fractions and leaves the cross products equal.

3. Applications of Cross Multiplication

Details: Cross multiplication is used for:

• Checking if two fractions are equivalent
• Solving proportions in algebra
• Comparing ratios in real-world problems
• Solving for unknown variables in fractional equations

4. Using the Calculator

Instructions: Enter the four integer values (a, b, c, d) representing the two fractions a/b and c/d. The calculator will perform the cross multiplication and determine if the fractions are equal.

5. Frequently Asked Questions (FAQ)

Q1: Why does cross multiplication work?
A: It's derived from the mathematical principle that two fractions are equal if and only if their cross products are equal.

Q2: Can I use this for fractions with variables?
A: Yes, cross multiplication works with variables as long as denominators aren't zero.

Q3: What if one denominator is zero?
A: The fraction becomes undefined. Our calculator checks for this condition.

Q4: How is this different from finding common denominators?
A: Cross multiplication is generally quicker for checking equality, while common denominators are better for adding/subtracting fractions.

Q5: Can this be used to solve for x in proportions?
A: Yes! For example, in a/b = x/d, cross multiplication gives x = (a×d)/b.