Mastering Percentage: Connecting Theory and Practice

Objectives

1. Understand the concept of percentage and its relationship with proportionality.

2. Apply knowledge of percentages to solve practical everyday problems.

3. Develop skills to calculate percentages in different contexts, such as discounts and price increases.

Contextualization

Imagine making a purchase and receiving a 20% discount. Or calculating how much tip to leave at a restaurant. These are everyday situations where we use percentages. Understanding percentages helps us make better financial decisions and understand the world around us more clearly. For example, if a product costs R$ 50.00 and has a 20% discount, you will pay R$ 40.00. Another example is calculating a 10% tip on a bill of R$ 120.00, resulting in R$ 12.00.

Relevance of the Theme

The ability to calculate percentages is essential for daily life and many professions. In the job market, especially in areas such as sales, finance, and marketing, percentages are used to calculate discounts, increases, interest rates, and returns on investments. Additionally, understanding percentages aids personal financial decisions, such as purchases and investments.

Concept of Percentage

Percentage is a way to express a proportion or fraction in relation to one hundred. It is a mathematical tool that facilitates the comparison of relative values, allowing us to better understand the relationship between different quantities.

• Percentage means 'per hundred' and is represented by the symbol '%'.

• It is used to express relative quantities in comparison to a total of 100.

• It facilitates understanding and comparison of values in different contexts, such as finance, statistics, and sales.

Relationship Between Percentage and Proportionality

Percentage is a special case of proportionality, where the relationship is always based on 100 units. This allows calculations and comparisons to be made in a standardized and easily understandable manner.

• Proportionality involves the comparison of two different quantities.

• Percentage is a proportion in relation to 100.

• It allows simple and direct calculations of price increases and reductions.

Calculation of Percentages in Different Contexts

The calculation of percentages can be applied in various everyday contexts, such as discounts on purchases, price increases, bank interest, and tips. Each context may have a specific formula, but all follow the basic principle of multiplying the percentage by the total value.

• Discounts: Percentage reduction of the original price of a product.

• Price Increases: Percentage increase applied to the original price.

• Interest: Percentage applied to the invested or borrowed amount.

Practical Applications

• Calculate the final price of products on sale by applying a percentage discount.
• Determine a salary increase by applying a percentage increase to the current salary.
• Calculate the tip at a restaurant by applying a percentage to the total bill amount.

Key Terms

• Percentage: Proportion or fraction expressed in relation to one hundred.

• Proportionality: Relationship between two quantities that varies in a constant manner.

• Discount: Percentage reduction applied to the original price of a product or service.

• Price Increase: Percentage increment applied to the original value of a product or service.

• Interest: Cost of borrowed money or yield from invested money, expressed as a percentage of the total amount.

Questions

• How can understanding percentages help in making more informed financial decisions?

• In what ways is the ability to calculate percentages useful in the job market?

• What are some everyday situations where you frequently use percentages and how does that impact your decisions?

Conclusion

To Reflect

Throughout this lesson, we explored the concept of percentage and its deep connection with proportionality. Understanding and applying percentages is a crucial skill not only for mathematics but for daily life and the job market. From calculating discounts on purchases to understanding bank interest, percentages are present in various situations we encounter daily. Reflecting on how this skill can help us make more informed financial decisions is fundamental. Continuous practice and application of concepts in real situations will further strengthen your understanding and confidence in using percentages effectively.

Mini Challenge - Family Budget Challenge

Let's apply what we learned about percentages to help a family manage their monthly budget.

• Imagine that a family has a monthly income of R$ 5,000.00.
• They want to allocate the budget as follows: 30% for housing, 20% for food, 15% for transportation, 10% for education, 10% for leisure, and 15% for savings.
• Calculate the amount in reais corresponding to each budget category.
• Record your calculations and check if the sum of the amounts corresponds to the family's total income.