91Ó°ÊÓ

The initial step in solving a ratio problem is to pinpoint the quantities involved. In this exercise, we are given '9 short' and '2 long'. It is crucial to clearly understand what these quantities represent. Identifying quantities means recognizing the specific numbers or measurements that are being compared.

For instance, if you are given 9 markers and 2 pencils, '9 markers' and '2 pencils' are the quantities you are comparing. Always ensure these quantities are clearly noted before proceeding to the next steps.

It's a good practice to list them out, which helps to avoid confusion. So remember, identifying the quantities correctly sets a solid foundation for writing the ratio accurately.

The next step is to write the ratio. A ratio shows the relative sizes of two or more values by comparing them directly. In our exercise, the phrase '9 short to 2 long' gives us a clear hint on how to structure our ratio.

Let's break it down further:

• The word 'to' in the phrase '9 short to 2 long' tells us we are comparing the first quantity (9 short) with the second quantity (2 long).
• So, we place the first quantity before the colon (:) and the second quantity after the colon. That results in a ratio of 9:2.

We could express this ratio in a few different textual formats too:

• Using a colon: 9:2
• As a fraction: \(\frac{9}{2}\)

Remember, the order in which you write the quantities matters. '9 short to 2 long' is not the same as '2 long to 9 short'. Be attentive to the wording while writing ratios.

The phrase '9 short to 2 long' explicitly outlines the order in which to place the quantities. Maintaining this order is essential, as reversing them changes the ratio's meaning entirely.

To preserve the correct order:

• Identify which quantity comes first in the given phrase.
• Ensure your written ratio honors this order.

In our example, '9 short' comes first, so it should be placed before the colon. Following this, '2 long' comes second, appearing after the colon. This sequence is not arbitrary and reflects the specific relationship between the quantities given.

Misplacing this order could lead to incorrect conclusions in any calculations or comparisons that follow. So always double-check the given phrase and align your ratio accordingly.