What is the Result of Dividing 500 by 1/2 and Adding 100?

Math problems like this one can often seem confusing at first glance. But by breaking the problem down step-by-step, you'll find it's not as complex as it looks. Let's explore how to solve the expression 500 ÷ 1/2 100 and understand the underlying mathematical principles.

Understanding the Problem

The question can be written as: 500 ÷ 1/2 100 ?. To solve this, we need to perform the division first, followed by the addition. Here's a detailed breakdown of the solution:

Step 1: Division

When we divide 500 by 1/2, it's essentially the same as multiplying 500 by the reciprocal of 1/2. The reciprocal of 1/2 is 2. So, we can rewrite the expression as:

500 ÷ 1/2 500 × 2 1000

Step 2: Addition

After performing the division, we add 100 to the result:

1000 100 1100

Mathematical Explanation

The division by a fraction can be understood as multiplying the numerator by the inverse of the denominator. This is a key concept that applies to all fractions. Here's how it works:

When you divide a number by a fraction, you multiply that number by the fraction's reciprocal. For example, in the expression 500 ÷ 1/2, 1/2 is the same as 0.5. The reciprocal of 0.5 is 2, so:

500 ÷ 1/2 500 ÷ 0.5 500 × 2 1000

Following the next step, we add 100 to the result of the division:

1000 100 1100

Alternative Representations

Let's consider two alternative representations of the problem:

1. Multiplication with Fractional Notation

Another way to represent the problem is using fractions directly:

500 × 1/2 100 250 100 350

This interpretation is incorrect and leads to a different result, so it's important to follow the original expression:

500 ÷ 1/2 100 1100

2. Division with Decimal Notation

To further clarify, let's write the problem using decimal notation:

500 ÷ 0.5 100 500 × 2 100 1000 100 1100

This confirms our previous solution using the reciprocal method.

Conclusion

When solving the expression 500 ÷ 1/2 100, follow these steps:

Divide 500 by 1/2, which is equivalent to multiplying 500 by 2. Perform the addition:

This yields the final result of 1100. Understanding the concepts of division by a fraction and addition is crucial for solving similar problems in mathematics.

To deepen your understanding of these concepts, explore more problems involving division and multiplication of fractions, and their application in real-world scenarios.

Happy learning!