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Quantitative reasoning involves the ability to use mathematical concepts to solve real-world problems. When working on ratios, we apply quantitative reasoning to understand how two quantities relate to each other. In the given exercise, you are comparing two different lengths: '2 long' and '9 short'. To begin, identify and understand the quantities involved. Knowing the type and magnitude of each quantity is fundamental for accurate comparison and analysis. This step ensures you have a clear understanding of what is being measured and compared, which is crucial for precise mathematical reasoning.

A ratio represents the relationship between two quantities, showing how many times one value contains or is contained within the other. There are several ways to express a ratio:

• Using the colon symbol: e.g., 2:9
• As a fraction: e.g., \(\frac{2}{9}\)
• In words: e.g., '2 long to 9 short'

Understanding the correct format helps in precisely communicating the comparative relationship. In this exercise, you are asked to write '2 long to 9 short' as a ratio. This is done by following a basic format and ensuring both quantities are clearly identified. Thus, the ratio of 2 long to 9 short can be written as \(\frac{2 \text{ long}}{9 \text{ short}}\), or simply '2 to 9'.

Substitution is a fundamental concept in algebra where we replace variables or placeholders with actual values. In the context of this exercise, substitution helps in transforming a verbal description into an algebraic or numerical one. Here, when you are asked to write '2 long to 9 short' as a ratio, you substitute the word quantities 'long' and 'short' with their respective numerical values:

• Identify the quantities: 2 (long) and 9 (short)
• Substitute into the ratio format: \(\frac{2 \text{ long}}{9 \text{ short}}\)

This method ensures that the verbal phrase is accurately translated into a mathematical representation. Substitution makes the manipulation and use of these quantities easier in further calculations or comparisons.