1. What Is Fraction Multiplication?

Fraction multiplication is a mathematical operation that combines two fractions to produce a new fraction. The numerator of the product is the product of the numerators, and the denominator of the product is the product of the denominators.

2. How Fraction Multiplication Works

The fundamental rule for multiplying fractions:

Where:

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

Key Point: Unlike addition, denominators don't need to be the same for multiplication.

3. Step-by-Step Calculation

Example: Multiply 2/3 by 4/5

1. Multiply numerators: 2 × 4 = 8
2. Multiply denominators: 3 × 5 = 15
3. Combine results: 8/15
4. Simplify if possible (in this case, 8/15 is already simplified)

4. Practical Applications

Fraction multiplication is used in:

• Scaling recipes in cooking
• Calculating probabilities in statistics
• Determining areas of rectangular shapes with fractional dimensions
• Computing success rates in quality control

5. Frequently Asked Questions (FAQ)

Q1: Do I need common denominators to multiply fractions?
A: No, unlike addition/subtraction, you can multiply fractions with different denominators.

Q2: How do I multiply mixed numbers?
A: First convert mixed numbers to improper fractions, then multiply normally.

Q3: What if one of the denominators is zero?
A: Division by zero is undefined, so denominators must never be zero.

Q4: Should I always simplify the result?
A: While not strictly necessary, simplified form is generally preferred.

Q5: Can I cancel terms before multiplying?
A: Yes, cross-canceling can simplify calculations before multiplication.