How to Cut Ribbons into Equal Lengths: A Mathematical Solution

When working on crafting or decoration projects, one might need to cut ribbons into equal lengths. For example, if you have a roll of ribbon with a length of 69.85 meters and you want to cut it into pieces of 2.5 meters each, how many full pieces can you get? Let’s explore this problem mathematically.

Step-by-Step Solution

The first step in solving this problem is to perform the division. We start with the total length of the ribbon and divide it by the desired length of each piece:

69.85 meters / 2.5 meters  27.94

This result, 27.94, tells us that 27 full lengths of 2.5 meters can be cut from the roll, with a remainder. The decimal part of the result, 0.94, indicates the length of the leftover piece.

Conclusion

Based on the division, we can conclude that we can cut 27 full pieces of ribbon, each 2.5 meters long. However, it is important to note that there will be a small piece of ribbon left over, measuring 0.94 meters, which is not enough to form another full piece of 2.5 meters. Even if you decide to make slight adjustments to the final piece, it will still be too short to be usable for the desired length.

Mathematical Explanation

The step-by-step solution can be broken down into simpler calculations:

First Calculation: 69.85 meters / 2.5 meters 27.94 Second Calculation: 2.5 meters x 0.94 2.35 meters. This value, 2.35 meters, is shorter than 2.5 meters, indicating the leftover length is insufficient for another full piece.

Another way to look at it is to directly calculate the number of full pieces:

69.85 meters / 2.5 meters/piece  27.94 pieces.

Here, we see that 27 full pieces of ribbon can be cut, and there will be a small piece left over. The remaining length is less than 2.5 meters, so it cannot be used to form another full piece of the specified length.

Practical Application

In practical terms, this means if you have a roll of ribbon with a length of 69.85 meters and you need to cut it into 2.5-meter pieces, you will get 27 full pieces. Any effort to cut a tiny bit shorter for 28 pieces would result in a piece that is only slightly shorter, approximately 0.0054 meters, which is only about 1/160 of an inch.

This example demonstrates the importance of precise measurements in crafting and project planning. Ensuring you have enough material for each piece is crucial to avoid frustration and wasted resources.