Solving for One-Fifth of a Number when Half is Known

In mathematics, solving for a fraction of a number when its half is known is a common problem. This article delves into the steps necessary to find one-fifth of a number given that its half is a specific value.

Problem Statement and Solution

Given that half of a number is 25, we are tasked with finding what one-fifth of that number would be. Let's denote the number as x.

Equation: (frac{1}{2}x  25)

First, we can solve for x by multiplying both sides of the equation by 2:

[x  25 times 2  50]

Calculation Steps

Now that we have determined that the number x is 50, we can find one-fifth of 50. To do this, we use the following equation:

[frac{1}{5} times 50]

Perform the calculation:

[frac{50}{5}  10]

Calculation with Different Methods

Let's explore more ways to arrive at the same result.

Method 1

Let the number be (X). Given that (frac{1}{2}) of (X) is 25, then: [X 25 div frac{1}{2} 50] Hence, one-fifth of 50 is: [frac{1}{5} times 50 frac{50}{5} 10]

Method 2

Let the number be (xx). According to the problem, half of the number is 25, so we can write the equation: [frac{x}{2} 25] By multiplying both sides of the equation by 2, we find: [x 25 times 2 50] To find one-fifth of 50: [frac{1}{5} times 50 frac{50}{5} 10]

Conclusion

In conclusion, using different methods, it is clear that if half of a number is 25, then one-fifth of the number is 10. These calculations are a fundamental concept in solving fraction problems and can be applied in various real-world scenarios such as financial calculations, measurements, and more.

Understanding the steps and logic behind such problems enhances one's mathematical problem-solving skills, making it easier to handle more complex mathematical questions in the future.