Determining the Length of Rope Pieces Based on Given Ratios

Imagine you have a rope that is 1.5 meters long and you need to cut it into two pieces in the ratio of 2:3. How can you determine the length of the shorter piece of rope using the information provided?

Mathematical Approach

Let's break down the problem step by step. The rope is divided into 5 equal parts because the ratio of 2:3 sums up to 5.

First, we need to find the length of each part. Since the total length is 1.5 meters, we divide 1.5 by 5. This gives us the length of one part:

1.5m / 5 0.3m

The shorter piece of the rope is represented by 2 parts, so we multiply the length of one part by 2:

0.3m times; 2 0.6m

The longer piece of the rope is represented by 3 parts, so we multiply the length of one part by 3:

0.3m times; 3 0.9m

Alternative Method

Another approach is to use the given ratio directly:

Determine the total parts in the ratio:

2 3 5

Divide the total length of the rope by the total number of parts to find the length of each part:

1.5m / 5 0.3m

Multiply the length of each part by the number of parts for the shorter piece:

0.3m times; 2 0.6m

Similarly, multiply by the number of parts for the longer piece:

0.3m times; 3 0.9m

Conclusion

By using these methods, we can easily determine that the shorter piece of the rope is 0.6 meters in length. This problem is a great example of how ratios and proportional reasoning can be applied to real-world scenarios, such as cutting materials or dividing resources.

Additional Context

Understanding ratios is crucial in various fields, including engineering, construction, and even in everyday life. Whether you need to proportion a recipe, allocate resources, or visualize proportions in art, the ability to work with ratios can be very useful.

If you find this topic interesting and want to learn more, consider exploring the following resources:

The basics of ratios and proportions in mathematics Practical applications of ratios in different industries Problem-solving techniques for ratio-based questions