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Understanding how to calculate percentages is a vital skill in mathematics. To convert a part of a whole into a percentage, you use the formula: \( \text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100 \). We start with identifying the part and the whole. For example, in the problem \(\text{\textdollar}24\ \text{ is what percent of } \text{\textdollar}96\),\ \text{\textdollar}24 is the part, and \text{\textdollar}96 is the whole. Plug these into the formula to get: \( \text{Percentage} = \frac{24}{96} \times 100 \). Calculating, we find that the percentage is 25%. Getting comfortable with percentage calculations will help you in many areas, like finance, statistics, and daily life measurements.

Proportions are all about comparing ratios. A ratio shows the relative sizes of two or more values. When we say 'set up the proportion,' we're looking to equate two ratios to find one missing part. A proportion can be written as: \( \frac{a}{b} = \frac{c}{d} \). For the original problem, we know the part (24) and the whole (96) but not the percentage (x). We set this up as: \( \frac{24}{96} = \frac{x}{100} \). This tells us that 24 is to 96 as x is to 100. Setting up proportions correctly is key to solving various mathematical problems efficiently. It ensures you have a clear pathway to find the unknown value.

When dealing with unknown values in equations, identifying the unknown and isolating it is essential. This process requires setting up an equation based on known values and solving for the unknown. In our example, 24 is what percent of 96, we set up the equation: \( \frac{24}{96} = \frac{x}{100} \). Here, x is the unknown percentage. Cross-multiplication helps to solve for x: \[ 24 \times 100 = 96 \times x \] Simplifying, you get: \[ 2400 = 96x \rightarrow x = \frac{2400}{96} \rightarrow x = 25 \]. Thus, x equals 25%, which means 24 is 25% of 96. Understanding how to handle unknown values in equations bridges the gap between recognizing a problem and solving it, a crucial skill in math and real-world applications.