Mastering the Multiplication of Negative Numbers with Fractions- A Step-by-Step Guide

How to Multiply a Negative Number by a Fraction

Multiplying a negative number by a fraction can seem like a daunting task at first, but with a clear understanding of the rules and a step-by-step approach, it becomes a straightforward process. In this article, we will explore how to multiply a negative number by a fraction, and provide you with the necessary knowledge to solve such problems with ease.

Understanding the Basics

Before diving into the multiplication process, it is essential to understand the basic rules of multiplying negative numbers and fractions. A negative number is any number that is less than zero, and a fraction represents a part of a whole. When multiplying a negative number by a fraction, you need to remember that the product will always be negative unless the fraction is an even integer.

Step-by-Step Guide

1. Identify the Negative Number and Fraction: First, identify the negative number and the fraction you need to multiply. For example, let’s consider the problem (-3) × (2/3).

2. Multiply the Numerators: Multiply the numerators of the fraction. In our example, the numerators are 3 and 2. Multiplying them gives us 3 × 2 = 6.

3. Multiply the Denominators: Next, multiply the denominators of the fraction. In our example, the denominators are 1 and 3. Multiplying them gives us 1 × 3 = 3.

4. Combine the Results: Combine the results from steps 2 and 3 to form the product. In our example, the product is 6/3.

5. Simplify the Fraction: Simplify the fraction, if possible. In our example, 6/3 simplifies to 2.

6. Determine the Sign of the Product: Finally, determine the sign of the product. Since we have a negative number multiplied by a fraction, the product will be negative. Therefore, the final answer is -2.

Examples

To further illustrate the process, let’s consider a few more examples:

– (-4) × (3/5) = -12/5
– (-2) × (4/7) = -8/7
– (-5) × (2/3) = -10/3

In each of these examples, we followed the same steps to multiply the negative number by the fraction and arrived at the correct product.

Conclusion

Multiplying a negative number by a fraction is a fundamental math skill that can be easily mastered with practice and understanding. By following the step-by-step guide and applying the basic rules, you can solve these types of problems with confidence. Remember to always pay attention to the signs of the numbers involved and simplify the fraction, if possible, to arrive at the final answer.