1. What is Fraction Multiplication?

Fraction multiplication is a mathematical operation that combines two fractions to produce a new fraction. The product of two fractions is obtained by multiplying their numerators together and their denominators together.

2. How Does the Calculator Work?

The calculator uses the fraction 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 calculator multiplies the numerators (a × c) to get the new numerator, and the denominators (b × d) to get the new denominator. It then simplifies the resulting fraction by dividing both numerator and denominator by their greatest common divisor (GCD).

3. Importance of Fraction Multiplication

Details: Fraction multiplication is fundamental in mathematics, used in scaling recipes, calculating probabilities, solving algebraic equations, and many real-world applications involving ratios and proportions.

4. Using the Calculator

Tips: Enter all four values (two numerators and two denominators). Denominators cannot be zero. The calculator will show both the direct product and simplified form (if different).

5. Frequently Asked Questions (FAQ)

Q1: Can I multiply fractions with different denominators?
A: Yes! Unlike addition, fraction multiplication works directly with different denominators.

Q2: What if one fraction is a whole number?
A: Whole numbers can be written as fractions with denominator 1 (e.g., 5 = 5/1).

Q3: How do I simplify fractions?
A: Find the greatest common divisor (GCD) of numerator and denominator, then divide both by it.

Q4: What about mixed numbers?
A: Convert mixed numbers to improper fractions before multiplying.

Q5: Can denominators be negative?
A: Yes, but typically the negative sign is placed with the numerator or the whole fraction.