Understanding 150 cm in the Ratio 4:1: A Comprehensive Guide

The problem of understanding 150 cm in the ratio 4:1 is a common scenario in mathematics where proportional distribution is a fundamental concept. This article aims to explain this concept clearly, providing a step-by-step guide to solving similar problems and offering examples to ensure clarity.

The Ratio 4:1 Explained

The ratio 4:1 means one part is four times the size of the other. When dealing with a total of 150 cm, it is crucial to understand how to split this measurement accordingly.

Method 1: Sum of Parts

First, sum the parts of the ratio: 4 1 5. This means the 150 cm is divided into 5 equal parts.

The length of one part is calculated by dividing the total length by the sum:

1 part 150 cm / 5 30 cm

Using this, we can find the longer and shorter segments:

Longer length (4 parts) 4 × 30 cm 120 cm

Shorter length (1 part) 1 × 30 cm 30 cm

Method 2: Direct Calculation

A more direct approach is to solve for x directly in the equation:

4x x 150 cm

Combine like terms:

5x 150 cm

Solve for x:

x 150 cm / 5 30 cm

Using x, find the longer and shorter segments:

Longer length 4x 4 × 30 cm 120 cm

Shorter length x 30 cm

Therefore, the two segments are 120 cm and 30 cm.

Conclusion

Understanding the ratio 4:1 is essential for various applications, including scaling, measurements, and proportional reasoning. Whether you use the sum of parts method or a direct calculation, the key is to recognize the relationship between the parts and the whole.

Additional Examples

For additional clarity, consider these examples:

1. If 150 cm is the sum of two parts in the ratio 4:1, the segments are 120 cm and 30 cm.

2. If 150 cm is the larger part, the smaller part is 150/4 37.5 cm.

3. If 150 cm is the smaller part, the larger part is 150 × 4 600 cm.

By breaking down the problem this way, you can easily and accurately solve similar problems involving ratios and proportions.