Dreisatz - einfach erklärt (Prozentwert berechnen) | Lehrerschmidt

Lehrerschmidt

17 Mar 202009:01

Summary

TLDRIn 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.

Outlines

00:00

📊 Introduction to Percent Calculations

In this segment, the instructor introduces the concept of the 'rule of three' as a fundamental step towards understanding percentage calculations. The video starts with a basic problem: finding 8% of 500 euros. Key terms such as 'Grundwert' (base value), 'Prozentwert' (percentage value), and 'Prozentsatz' (percentage rate) are explained. The base value is defined as the whole amount (in this case, 500 euros), the percentage rate is identified as 8%, and the percentage value is the result obtained by applying the percentage to the base value. The instructor emphasizes the importance of understanding these terms to solve percentage problems effectively.

05:05

🧮 Step-by-Step Calculation: Examples with 7% and 15%

This section provides step-by-step examples of calculating percentage values using the rule of three. The instructor first demonstrates how to find 7% of 300 euros, breaking down the process into manageable steps. This includes calculating 1% of the base value and then multiplying it by 7 to get the desired percentage. The second example deals with 15% of 600 euros, following the same method but with slightly more complex multiplication. The instructor shows how breaking down these steps makes it easier to tackle more challenging percentage problems. Each example concludes with the correct percentage value, reinforcing the method.

Mindmap

Keywords

💡Proportional Calculation

Proportional calculation is the process of determining what fraction or percentage of a number is. In the video, it is the main theme, focusing on how to calculate percentages of a given amount, such as finding 8% of 500 euros. The script uses this concept to teach viewers how to break down the problem into steps using the 'three-step method' or 'dreisatz' in German.

💡Percentage

A percentage is a way of expressing a number as a fraction of 100. It is a key concept in the video, where the teacher explains how to calculate different percentages of a total amount. For example, calculating 'eight percent of 500 euros' is a task that involves understanding the meaning and calculation of percentages.

💡Base Value

The base value, often abbreviated as 'GV' in German, is the original total amount that the percentage is calculated from. In the script, the base value is consistently the amount of money (e.g., 500 euros) that the percentage calculation is based upon.

💡Result

In the context of the video, the result or 'Ergebnis' is the final value obtained after performing the proportional calculation. It is represented by the percentage value, such as determining that 8% of 500 euros equals 40 euros.

💡Percentage Value

The percentage value, often denoted by 'W' or 'P' in the script, is the amount that corresponds to a specific percentage of the base value. It is a crucial part of the proportional calculation process demonstrated in the video.

💡Three-Step Method

The three-step method, or 'dreisatz' in German, is the process outlined in the video for calculating percentages. It involves breaking down the calculation into three logical steps: starting with the base value, determining the value of 1%, and then scaling that to find the desired percentage.

💡Hundred Percent

Hundred percent represents the whole or the base value in percentage calculations. In the video, the teacher starts each calculation by equating 100% to the base value, such as stating that '100% corresponds to 500 euros' before breaking it down further.

💡One Percent

One percent is used as a reference point in the three-step method to find the value of a smaller percentage of the base value. For instance, if 100% is 500 euros, then 1% is 5 euros, as shown in the script.

💡Scaling

Scaling in the context of the video refers to the process of multiplying the value of one percent by the desired percentage to find the percentage value. For example, if 1% is 5 euros, then 8% would be 40 euros, which is calculated by multiplying 5 by 8.

💡Exercise

The script includes exercises to help viewers practice the three-step method. These exercises involve calculating different percentages of various base values, such as finding 7% of 300 euros or 15% of 600 euros, to reinforce learning.

💡Conceptual Understanding

Throughout the video, the teacher emphasizes the importance of understanding the concepts of base value, percentage value, and percentage rate. This understanding is essential for correctly applying the three-step method and solving proportional calculation problems.

Highlights

Introduction to the three-part formula for percentage calculation.

Explanation of the terms 'base value', 'percentage value', and 'percentage rate'.

The base value is the whole amount, represented by 'G' or 'GEH'.

The percentage value is denoted by 'W' or 'P' and represents the result.

The percentage rate is the simplest, indicated by the percent sign or 'P'.

Understanding the concepts of base value, percentage value, and percentage rate.

Demonstration of calculating 8% of 500 euros using the three-part formula.

Step-by-step calculation of 8% of 500 euros resulting in 40 euros.

Recommendation to practice the calculation steps for better understanding.

Calculation of 7% of 300 euros as a practice example.

Explanation of breaking down 100% to 1% to find the value of 1%.

Final calculation of 7% of 300 euros resulting in 21 euros.

Introduction of a more challenging problem: calculating 15% of 600 euros.

Detailed calculation of 15% of 600 euros resulting in 90 euros.

Another practice problem: calculating 70% of 500 euros.

Final calculation of 70% of 500 euros resulting in 350 euros.

Emphasis on the importance of practicing the calculation steps for the three-part formula.

Conclusion and预告 of the next video continuing the topic.