A percentage is a way of expressing a part of a whole as a fraction of 100. It is a unit used to represent a proportional relationship or rate of change between two values.
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Percentages are commonly used to express part-to-whole relationships, such as sales figures, tax rates, and population statistics.
The symbol for percentage is the '%' sign, which means 'per hundred' or 'out of 100'.
Percentages can be used to compare values, calculate increases or decreases, and analyze trends over time.
Converting between percentages, decimals, and fractions is a key skill in understanding and applying percentages.
Percentages are often used in problem-solving strategies, such as finding the unknown value in a proportion or calculating a discounted price.
Review Questions
Explain how percentages can be used in a problem-solving strategy.
Percentages are a valuable tool in problem-solving strategies because they allow you to express and manipulate part-to-whole relationships. For example, if you know the total value and the percentage of that value represented by a specific part, you can use this information to calculate the value of the part. Percentages can also be used to find the unknown value in a proportion, such as determining the original price of an item given the discounted price and the percentage discount.
Describe how percentages can be used to analyze trends over time.
Percentages are often used to track changes and trends over time, such as in sales figures, market share, or population growth. By expressing the change as a percentage, you can easily compare the relative magnitude of the change, regardless of the original values. For example, if a company's sales increased from $100,000 to $120,000, the percentage increase would be 20%. This allows you to understand the significance of the change and make informed decisions or predictions based on the trend.
Evaluate the importance of being able to convert between percentages, decimals, and fractions when working with percentages.
The ability to convert between percentages, decimals, and fractions is crucial when working with percentages, as it allows you to easily translate between different representations of the same value. This is important for a variety of applications, such as calculating discounts, interest rates, or tax rates. Being able to move fluidly between these forms also helps you better understand the underlying relationships and proportions involved, which is essential for solving problems and making informed decisions. Mastering these conversions is a key skill in effectively applying percentages in a problem-solving strategy.