Negative Fraction Times A Negative Fraction

Mastering the Mystery: Multiplying Negative Fractions

Multiplying fractions can seem daunting, but understanding the process, especially when negative numbers are involved, unlocks a powerful tool in mathematics. This article will break down the concept of multiplying negative fractions, clarifying the rules and providing practical examples to build your confidence. We'll explore why the result is positive, and equip you with the skills to tackle these calculations with ease.

Understanding the Basics: Multiplying Fractions

Before diving into negative fractions, let's refresh our understanding of basic fraction multiplication. The fundamental rule is simple: multiply the numerators (top numbers) together and multiply the denominators (bottom numbers) together. For example:

1/2 * 3/4 = (13) / (24) = 3/8

This holds true regardless of whether the fractions are positive or negative.

The Rule of Signs: Why Negative Times Negative Equals Positive

The core principle governing the multiplication of negative numbers is that a negative times a negative always results in a positive. Think of it as a "double negative" canceling each other out. This applies to all forms of multiplication, including fractions.

• Negative * Positive = Negative
• Positive * Negative = Negative
• Negative * Negative = Positive

Multiplying Negative Fractions: A Step-by-Step Guide

Let's put it all together. To multiply negative fractions, follow these steps:

1. Ignore the signs: Initially, disregard the negative signs and multiply the fractions as if they were positive. This simplifies the calculation.

2. Multiply numerators: Multiply the numerators together.

3. Multiply denominators: Multiply the denominators together.

4. Determine the sign: Now consider the signs. If you have an even number of negative signs (e.g., two negatives, four negatives), the result is positive. If you have an odd number of negative signs (e.g., one negative, three negatives), the result is negative.

Example 1: (-1/3) * (-2/5)

1. Ignore signs: 1/3 * 2/5 = 2/15

2. Determine the sign: We have two negative signs, an even number, therefore the result is positive.

3. Final answer: (-1/3) * (-2/5) = 2/15

Example 2: (-3/4) * (1/2)

1. Ignore signs: 3/4 * 1/2 = 3/8

2. Determine the sign: We have one negative sign, an odd number, therefore the result is negative.

3. Final answer: (-3/4) * (1/2) = -3/8

Example 3: (-2/7) * (-3/8) * (-1/2)

1. Ignore signs: 2/7 * 3/8 * 1/2 = 6/112 (which simplifies to 3/56)

2. Determine the sign: We have three negative signs, an odd number, resulting in a negative answer.

3. Final answer: (-2/7) * (-3/8) * (-1/2) = -3/56

Simplifying Fractions: A Crucial Step

Remember to always simplify your final answer to its lowest terms. This means finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it. For example, 6/12 simplifies to 1/2 (because the GCD of 6 and 12 is 6).

Mastering negative fraction multiplication is essential for more advanced mathematical concepts. By understanding the rules and practicing with examples, you'll build a solid foundation for future success in algebra and beyond. Remember to take it step-by-step, and don't be afraid to practice!