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Converting a percentage to a fraction is a fundamental skill in solving word problems. A percentage is essentially a fraction with a denominator of 100. To convert a percentage to a fraction, follow these steps:

• Write down the given percentage.
• Replace the percent symbol (%) with the fraction's denominator of 100.
• Reduce the fraction to its simplest form, if needed.

Let's apply this to the given problem. The percentage given is 66%. Write it as a fraction: \( \frac{66}{100} \). This fraction can be simplified further, but for proportion problems, you can often use it as is. We now have the fraction representation of the percentage.

A proportion is an equation that states two ratios are equal. Proportions are useful in solving word problems involving percentages, parts, and wholes. To set up a proportion, follow these steps:

• Identify the two ratios you need to compare.
• Set them up as fractions.
• Use an equal sign to connect the two fractions.

In our exercise, we need to find an unknown value given the percentage of a whole. We have the fraction from the percentage (\( \frac{66}{100} \)), and we know the whole is 74. The unknown value (let's call it x) is the part of the whole. Setting up the proportion involves placing these values into the proportion equation: \( \frac{66}{100} = \frac{x}{74} \). This equation states that the fraction of the part over the whole (\( \frac{x}{74} \)) is equal to the percentage fraction (\( \frac{66}{100} \)).

Identifying components in word problems is crucial to setting up and solving them correctly. The core components often include:

• The percentage
• The whole
• The unknown part

When analyzing a word problem, look for these components:

• Percentage: This is often given directly with a % symbol or implied in the problem.
• The Whole: This is the total amount or quantity. In many cases, it's the number that the percentage is taken from.
• The Unknown Part: This is what you’re trying to find. Often represented by a variable, like x.

In the exercise, the percentage is 66%, the whole is 74, and the unknown part is what we need to find. By clearly identifying these components, we can accurately set up the proportion: \( \frac{66}{100} = \frac{x}{74} \).