Understanding Ratios through a Length Problem

Understanding ratios is a crucial skill in solving a wide range of mathematical problems, such as the one where the ratio of two pieces of ribbon is given as 2:7. This article will walk you through the step-by-step process of solving a specific problem, where one of the pieces of ribbon is 12 meters long. By the end of this article, you will have a clear understanding of how to approach ratio problems and solve similar questions effectively.

Problem Statement

The ratio of two pieces of ribbon is 2:7. The shorter piece of the ribbon is 12 meters long. What is the total length of the two pieces of ribbon?

Step-by-Step Solution

Method 1: Dividing the Shorter Piece into Shares

To solve the problem, we can divide the shorter piece of ribbon into its respective shares according to the given ratio.

The shorter piece (2 shares) is 12 meters long. Therefore, each share is equal to 12 meters ÷ 2 6 meters. The longer piece (7 shares) is equal to 6 meters × 7 42 meters. To find the total length of the two pieces of ribbon, we add the lengths of the shorter and the longer pieces: 12 meters 42 meters 54 meters.

Method 2: Directly Using the Ratio

Alternatively, we can use the total shares directly to find the total length of the ribbon.

2 7 9 shares

Since 2 shares (the shorter piece) equal 12 meters, we can determine the length of 1 share by dividing 12 meters by 2:

12 meters ÷ 2 6 meters

The length of the longer piece, which is 7 shares, is then calculated as:

7 × 6 meters 42 meters

The total length of the two pieces of ribbon is:

42 meters 12 meters 54 meters

Using Ratios in Real-World Contexts

Ratios are not just an abstract concept; they have practical applications in various fields. For instance, in construction, mixing concrete or paint often requires following a specific ratio. In finance, ratios such as debt-to-equity or price-to-earnings can help investors evaluate a company's financial health.

Conclusion

In this article, we explored how to solve a ratio problem involving the length of two pieces of ribbon. By breaking down the problem into smaller, manageable steps, we were able to arrive at the correct solution of 54 meters. Remember, understanding ratios is crucial for solving a wide variety of mathematical and practical problems. If you're still struggling with the concept, don't hesitate to look up more resources and practice similar problems.

Additional Resources

For more information on ratios, length calculations, and problem solving techniques, consider exploring these resources:

Math Is Fun: Ratios Khan Academy: Ratios and Proportions Math-Only-Math: Ratios and Proportions