1. What is Cross Multiplication?

Cross multiplication is a mathematical technique used to solve proportions by multiplying the numerator of one fraction by the denominator of the other fraction, and vice versa. This method helps determine if two fractions are equivalent or to find missing values in proportions.

2. How Does Cross Multiplication Work?

The cross multiplication formula:

Where:

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

Explanation: If the product of the means (a × c) equals the product of the extremes (b × d), then the two fractions are proportional.

3. Applications of Cross Multiplication

Details: Cross multiplication is commonly used in solving ratio problems, scaling recipes, calculating percentages, solving for unknown variables in proportions, and verifying if two fractions are equivalent.

4. Using the Calculator

Tips: Enter the four values (a, d, b, c) from your proportion. The calculator will verify if the cross products are equal and determine if the fractions form a valid proportion.

5. Frequently Asked Questions (FAQ)

Q1: What if one of the denominators is zero?
A: Division by zero is undefined. The calculator requires all denominators to be non-zero values.

Q2: Can cross multiplication be used with decimals?
A: Yes, cross multiplication works with both fractions and decimal numbers.

Q3: How accurate is the calculation?
A: The calculator uses floating-point arithmetic with precision to 4 decimal places for accurate results.

Q4: What if the cross products are almost equal but not exactly?
A: The calculator uses a small tolerance (0.0001) to account for floating-point precision issues.

Q5: Can I use this to solve for an unknown variable?
A: Yes, if you have three known values and one unknown, you can rearrange the equation to solve for the missing variable.