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Percentages are a way to express a number as a fraction of 100. The symbol for percent is %. For example, if you have 50%, it means 50 out of 100, or simply half of a whole. One of the key ideas of working with percentages is to understand how they convert into fractions and decimals. For instance, 25% can be written as \( \frac{25}{100} \) or 0.25.

• Percent means 'per hundred'.
• 130% can be expressed as \( \frac{130}{100} \).
• Understanding percentages helps in translating real-life problems into mathematical equations.

When faced with questions involving percentages, your first step should always be to convert the percentage into a fraction or decimal, as it makes further calculations easier. In our example, 130% can be written as \( 1.3 \) in decimal form or \( \frac{130}{100} \) in fraction form.

A proportion is an equation that states two ratios are equal. Ratios are comparisons between two numbers, showing how many times one number contains another. For instance, in a classroom, if there are 2 teachers for every 30 students, the ratio of teachers to students is 2:30, which simplifies to 1:15.

• A proportion is generally written as \( \frac{a}{b} = \frac{c}{d} \).
• It shows the equality of two ratios.
• Proportions are useful in solving for an unknown quantity.

In our given problem, we were asked to translate 130% of 352 into a proportion. We did this by setting the ratio \( \frac{130}{100} \) equal to \( \frac{x}{352} \), where \( x \) stands for the unknown value. This proportion helps us understand that 130% of 352 is directly comparable to how 130 relates to 100.

Mathematical translation involves converting a word problem or real-life situation into a mathematical format, such as an equation or proportion. This makes solving the problem straightforward as the arithmetic operations follow clear and defined rules. To translate word problems into mathematical language:

• Identify the quantities involved.
• Determine the relationships between these quantities.
• Convert these relationships into mathematical expressions like equations or proportions.

In our exercise about finding '130% of 352', the first step was recognizing that '130%' converts to \( \frac{130}{100} \). Then, we set up a proportion where \( \frac{130}{100} \) represents the ratio of the percentage to 100, and \( \frac{x}{352} \) represents 'some number out of 352'. Writing \( \frac{130}{100} = \frac{x}{352} \) translates the word problem directly into a proportion. This not only simplifies the problem but also helps in setting the stage for solving more complex problems.