Dreisatz - einfach erklärt (Prozentwert berechnen) | Lehrerschmidt

Summary

In this educational video, Lehrer Schmidt introduces the concept of percentage calculation using the 'three-part formula'. The formula involves the base value (denoted by 'G' for 'Geh'), the percentage value (denoted by 'W' or 'P'), and the percentage rate (indicated by the percent sign). The video demonstrates how to calculate percentages of amounts, such as finding 8% of 500 euros, by breaking down the process into steps. It starts with equating 100% to the base value, then calculating 1% of it, and finally determining the desired percentage by multiplying the 1% value by the percentage rate. The video includes several examples to practice this method, emphasizing the importance of understanding the roles of each part of the formula.

Takeaways

• 📊 The video is a math tutorial on using the rule of three (Dreisatz) as preparation for percentage calculations.
• 🧮 The tutorial covers key terms: Grundwert (base value), Prozentsatz (percentage rate), and Prozentwert (percentage value).
• 🔢 Grundwert is the total amount or the whole, for example, 500 euros in the scenario of calculating 8% of 500 euros.
• 📉 Prozentsatz is identified by the percentage symbol and represents the percentage, like 8% in the example.
• 💰 Prozentwert is the calculated value, which is the result of applying the Prozentsatz to the Grundwert.
• ➗ The rule of three involves breaking down 100% of the Grundwert to 1% and then multiplying it by the desired percentage.
• ✅ The example provided calculates 8% of 500 euros, leading to a result of 40 euros.
• ✏️ The steps involve calculating 1% first (500 euros ÷ 100 = 5 euros) and then multiplying by 8 to get the final percentage value (5 euros × 8 = 40 euros).
• 📏 Further examples are given, including calculations of 7% of 300 euros, 15% of 600 euros, and 70% of 500 euros, following the same method.
• 🎯 The video emphasizes practicing the calculation steps to master the rule of three in percentage calculations.

Q & A

What is the purpose of the video?

The purpose of the video is to teach viewers about the rule of three, which is a fundamental concept in mathematics used to calculate percentages.

What are the three key terms explained in the video?

The three key terms explained are the base value (Grundwert), the percentage (Prozentsatz), and the percentage value (Prozentwert).

How is the base value (Grundwert) defined?

The base value (Grundwert) is defined as the whole or total value from which a percentage is calculated. In the example provided, it is 500 euros.

What is the percentage (Prozentsatz) in the example provided?

The percentage (Prozentsatz) in the example provided is 8%.

How do you calculate the percentage value (Prozentwert) using the rule of three?

To calculate the percentage value (Prozentwert) using the rule of three, you first determine 1% by dividing the base value by 100, then multiply the result by the percentage (Prozentsatz).

What is the result of calculating 8% of 500 euros?

The result of calculating 8% of 500 euros is 40 euros.

Why is it helpful to start with 100% in percentage calculations?

Starting with 100% is helpful because it represents the total value, making it easier to scale down to 1% and then multiply to find the desired percentage.

How would you calculate 7% of 300 euros using the rule of three?

To calculate 7% of 300 euros, you first find 1% by dividing 300 euros by 100, which equals 3 euros, and then multiply 3 euros by 7, resulting in 21 euros.

What is the significance of performing the same operation on both sides of the equation in the rule of three?

Performing the same operation on both sides of the equation ensures that the proportional relationship is maintained, allowing for accurate percentage calculations.

What is the result of calculating 70% of 500 euros?

The result of calculating 70% of 500 euros is 350 euros.