How To Multiply Fractions Using Cancellation Method

How to Multiply Fractions Using the Cancellation Method

Multiplying fractions can seem daunting, but with the right technique, it becomes a breeze! The cancellation method, also known as simplification before multiplication, is a powerful tool that simplifies the process and reduces the risk of dealing with large numbers. This method leverages the fundamental principle of fractions: you can simplify a fraction by dividing both the numerator and denominator by the same number without changing its value. Let's dive in!

Understanding the Basics: What is Fraction Cancellation?

Before we tackle multiplication, let's review the core concept. Fraction cancellation is the process of simplifying a fraction by dividing both the numerator (the top number) and the denominator (the bottom number) by their greatest common divisor (GCD). The GCD is the largest number that divides both the numerator and denominator without leaving a remainder.

For example:

• 6/9 can be simplified by dividing both 6 and 9 by their GCD, which is 3. This simplifies to 2/3.

Multiplying Fractions with Cancellation: A Step-by-Step Guide

The magic of cancellation lies in applying this simplification before you multiply the numerators and denominators. This significantly reduces the size of the numbers you're working with, making the calculation much easier.

Here's the step-by-step process:

1. Identify Common Factors: Look at the numerators and denominators of the fractions you're multiplying. Identify any common factors between a numerator and a denominator in different fractions.

2. Cancel Out Common Factors: Divide both the numerator and denominator by their common factor. This is where the 'cancellation' happens. You essentially cross out the common factor and replace it with the result of the division.

3. Multiply the Simplified Fractions: Once you've cancelled out all common factors, multiply the remaining numerators together and the remaining denominators together.

4. Simplify the Result (if necessary): While you’ve likely simplified as much as possible through cancellation, double-check if the final fraction can be reduced further.

Examples to Illustrate the Method

Let's clarify this with some examples:

Example 1:

Multiply (2/3) * (9/4)

1. Common factors: 2 and 4 share a common factor of 2; 3 and 9 share a common factor of 3.

2. Cancellation:

   • Divide 2 and 4 by 2: (1/3) * (9/2)
   • Divide 3 and 9 by 3: (1/1) * (3/2)

3. Multiplication: (1 * 3) / (1 * 2) = 3/2

Example 2:

Multiply (4/5) * (15/8) * (2/3)

1. Common factors:

   • 4 and 8 share a common factor of 4
   • 5 and 15 share a common factor of 5
   • 2 and 8 share a common factor of 2 (note we can use 8 again, because we have multiple fractions)
   • 3 and 15 share a common factor of 3

2. Cancellation:

   • Divide 4 and 8 by 4: (1/5) * (15/2) * (2/3)
   • Divide 5 and 15 by 5: (1/1) * (3/2) * (2/3)
   • Divide 2 and 2 by 2: (1/1) * (3/1) * (1/3)
   • Divide 3 and 3 by 3: (1/1) * (1/1) * (1/1)

3. Multiplication: 1/1 = 1

Mastering Fraction Multiplication: Practice Makes Perfect

The cancellation method significantly streamlines fraction multiplication. The more you practice, the quicker you’ll become at identifying common factors and simplifying your calculations. So grab a pencil and paper and start practicing! You'll be multiplying fractions like a pro in no time.