What is the answer when we multiply 2 and 1/2?

When dealing with the multiplication of whole numbers and fractions, it is important to understand the process clearly. In this guide, we will explore the multiplication of 2 and 1/2 and break down the steps involved. Let's dive into the reasoning and different methods to solve this problem.

Understanding Whole Numbers as Fractions

Every whole number can be represented as a fraction. For instance, the number 2 can be written as (2/1). This is because the whole number is the numerator, and there is always 1 as the denominator. This concept is fundamental to solving problems involving multiplication with fractions.

Multiplying 2 and 1/2: Step-by-Step Explanation

To multiply 2 and 1/2, let's set it up as a multiplication problem:

Method 1: Evaluating the Equal Denominators

Representing the number as a fraction can simplify the multiplication:

Now, multiply these fractions:

2/1 × 1/2 (2 × 1) / (1 × 2) 2/2 1

This shows that the answer simplifies to 1 when you multiply 2 and 1/2.

Method 2: Using Logical Reasoning

Another way to approach this problem is by logical reasoning. Half of any number is simply dividing that number by 2. Therefore:

So, multiplying 2 by 1/2 is the same as taking half of 2, which results in 1.

Method 3: Simplified Fraction Multiplication

To further simplify the multiplication of 2 and 1/2, you can express it as:

2 × 1/2 2/1 × 1/2 (2 × 1) / (1 × 2) 2/2 1

Here, the numerators are multiplied together, and the denominators are multiplied together. The result, 2/2, is equal to 1.

Conclusion

In summary, multiplying 2 and 1/2 results in the answer 1. Understanding the concept of representing whole numbers as fractions and using logical reasoning can greatly simplify such problems. Whether you use the step-by-step approach, logical reasoning, or simplified fraction multiplication, the answer remains the same. If you have any questions or need further clarification, feel free to message me.