How to Solve a Fractional Length Problem Using Decimal and Metric Conversions

The metric system, being decimal-based, does not typically use common fractions. However, understanding how to convert and manipulate fractional values in the metric system is crucial for solving practical problems. This article will guide you through a step-by-step solution to a fractional length problem, demonstrating the importance of converting between fractions and decimals for accuracy.

Understanding the Problem

The problem statement presents a stick of 24 1/5 cm length that is broken into two pieces. We are given that one of the pieces is 15 1/5 cm long and are asked to determine the length of the other piece. The metric system, while decimal-based, often requires converting between fractional and decimal values to ensure accuracy.

Step-by-Step Solution

First, let’s break down the problem into its component parts:

Convert the mixed fractions into improper fractions for easier calculation. Subtract the length of the known piece from the total length. Convert the result back into a mixed fraction if necessary.

Let's go through each step in detail.

Step 1: Convert Mixed Fractions

The total length of the stick is 24 1/5 cm. The length of one piece is 15 1/5 cm. We can convert these mixed fractions to improper fractions for easier calculation:

24 1/5 (24*5 1)/5 121/5 15 1/5 (15*5 1)/5 76/5

Step 2: Subtraction

To find the length of the other piece, we subtract the length of the known piece from the total length:

121/5 - 76/5 (121 - 76)/5 45/5 9

The result is 9 cm. However, to align with the original mixed fraction scheme, we can express 9 cm as 9 0/5, which is equivalent to 9 cm.

Step 3: Verification

To verify, let’s perform the calculation using the original mixed fractions directly:

24 1/5 - 15 1/5 (24 - 15) (1/5 - 1/5) 9 0 9 cm

This confirms that the length of the other piece is indeed 9 cm.

Practical Applications

Understanding how to convert fractional lengths into decimals and vice versa is essential in several practical applications. Whether you are a student, a professional, or just someone dealing with measurements in the metric system, this knowledge can be incredibly helpful. For instance, engineers, carpenters, and other professionals who work with precise measurements need to be adept at these conversions.

Conclusion

In conclusion, solving fractional length problems using decimal and metric conversions is a valuable skill. Understanding how to manipulate fractional values for accuracy in the metric system is crucial. By converting between mixed fractions and improper fractions, and performing the necessary arithmetic, you can accurately determine the length of the other piece of the stick.