How To Multiply All Fractions

Fraction Multiplication Formula:

\[ \frac{a}{b} \times \frac{c}{d} \times \frac{e}{f} = \frac{a \times c \times e}{b \times d \times f} \]

First numerator (a):

First denominator (b):

Second numerator (c):

Second denominator (d):

Third numerator (e):

Third denominator (f):

Result:

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1. What is Fraction Multiplication?

Fraction multiplication is a mathematical operation where two or more fractions are multiplied together to produce a new fraction. Unlike addition, denominators don't need to be the same - you simply multiply numerators together and denominators together.

2. How Does Fraction Multiplication Work?

The general formula for multiplying fractions is:

\[ \frac{a}{b} \times \frac{c}{d} \times \frac{e}{f} = \frac{a \times c \times e}{b \times d \times f} \]

Key points:

Multiply all numerators together
Multiply all denominators together
Simplify the resulting fraction by dividing numerator and denominator by their greatest common divisor (GCD)
Denominators cannot be zero

3. Step-by-Step Calculation

Example: Multiply 1/2 × 3/4 × 5/6

Multiply numerators: 1 × 3 × 5 = 15
Multiply denominators: 2 × 4 × 6 = 48
Result is 15/48
Simplify by GCD of 15 and 48 (which is 3): 5/16

4. Practical Examples

Real-world applications:

Calculating probabilities of independent events
Determining combined ratios in chemistry
Scaling recipes in cooking
Computing success rates in quality control

5. Frequently Asked Questions (FAQ)

Q1: Can I multiply more than three fractions?
A: Yes, the same rule applies - multiply all numerators and all denominators, then simplify.

Q2: What if one denominator is zero?
A: Division by zero is undefined. All denominators must be non-zero.

Q3: Do I need common denominators to multiply?
A: No, unlike addition, you don't need common denominators for multiplication.

Q4: How do I handle mixed numbers?
A: Convert mixed numbers to improper fractions first, then multiply.

Q5: Can I cancel before multiplying?
A: Yes, you can simplify by canceling common factors between any numerator and denominator before multiplying.