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Understanding how to convert percentages can make solving proportion problems much easier. A percentage represents a fraction out of 100, so converting a percentage to a decimal is straightforward. For instance, if you have 25%, you divide 25 by 100 to get 0.25. Here’s how this works:

\[ 25\text{\textpercent} = \frac{25}{100} = 0.25 \]

To practice, try converting other percentages to decimals. For example:

• 50% = 0.50
• 75% = 0.75
• 10% = 0.10

This skill is foundational and will help you solve many kinds of mathematical problems.

Setting up equations correctly is crucial for solving proportion problems. To turn a word problem into a mathematical equation, you need to identify the components and organize them.

Take the original problem: '\text{\(18 is 25\text{\textpercent} of what?\)}'. You already know how to convert 25% to a decimal (0.25). Now, you need to form an equation. In this case, it’s helpful to think of ‘is’ as an equality symbol (=) and ‘of what’ as your variable (\(x\)).

Consequently, you translate the statement into:

\[ 18 = 0.25x \]

This method works for other similar problems too. For example:

• \(7 is 10% of what?\) becomes \(7 = 0.10x\)
• \(50 is 75% of what?\) becomes \(50 = 0.75x\)

Practicing this conversion helps in setting up accurate equations.

Proportion problems often involve finding an unknown value based on the relationship between numbers. In the original exercise, you are asked to find out what number 18 is 25% of.

A proportion generally states that two ratios are equal. Here is how the concept works: If two ratios \(\frac{a}{b}\) and \(\frac{c}{d}\) are proportionate, then \(\frac{a}{b} = \frac{c}{d}\).

In our example, you have the proportion:

\[ \frac{18}{x} = 0.25 \]

This can be rearranged into an equation to solve for \(x\) in further steps. Solving proportion problems often involves cross-multiplication, making it easier to find the unknown value.

Practicing different types of proportion problems can further enhance your understanding. For instance:

• If 4 pencils cost $8, how much do 10 pencils cost? (\(\frac{4}{8} = \frac{10}{y}\))
• A recipe calls for 2 cups of flour for 5 servings. How many cups are needed for 20 servings? (\(\frac{2}{5} = \frac{y}{20}\))

Understanding how to work with these relationships can vastly improve your problem-solving skills.