Matemática Zero 2.0 - Aula 7 - Divisão - (parte 1 de 2)

Introduction

This tutorial will guide you through the fundamentals of division in mathematics, specifically focusing on the algorithm for dividing real numbers. Whether you're preparing for exams or just looking to strengthen your math skills, understanding these concepts will help you tackle division problems with confidence.

Step 1: Understanding Division Basics

Before diving into the algorithm, it's essential to grasp the foundational concepts of division:

• Definition of Division: Division is the process of determining how many times one number (the divisor) can fit into another number (the dividend).
• Terminology:
  • Dividend: The number being divided.
  • Divisor: The number by which the dividend is divided.
  • Quotient: The result of the division.

Practical Tip

Always remember that division by zero is undefined, so ensure your divisor is never zero.

Step 2: The Division Algorithm for Real Numbers

The division algorithm allows you to perform division systematically. Here’s how to apply it step by step:

1. Identify the Numbers:

   • Determine your dividend and divisor.
   • Example: For 12 ÷ 3, 12 is the dividend, and 3 is the divisor.

2. Set Up the Division:

   • Write the division in long form: place the dividend inside the division bracket and the divisor outside.
   • Example:

       _____
     3 | 12
     

3. Divide:

   • Look at how many times the divisor can fit into the dividend.
   • For 12 ÷ 3, think of how many times 3 can fit into 12. The answer is 4.

4. Multiply:

   • Multiply the divisor by the quotient obtained in the previous step.
   • Example: 3 * 4 = 12.

5. Subtract:

   • Subtract the result from the dividend.
   • Example: 12 - 12 = 0.

6. Repeat if Necessary:

   • If there is a remainder, repeat the process using the remainder as the new dividend.

Common Pitfalls to Avoid

• Forgetting to subtract properly, which can lead to incorrect answers.
• Not checking if the divisor can fit into the dividend at each step.

Step 3: Working with Decimal Numbers

When dividing decimal numbers, the process is similar but requires additional attention to the decimal point:

1. Align Decimal Places:

   • If the dividend is a decimal, make sure it aligns with the divisor.
   • Example: Dividing 5.4 by 1.2.

2. Convert to Whole Numbers:

   • If necessary, multiply both the dividend and divisor by 10, 100, etc., to eliminate the decimal.
   • Example: 5.4 ÷ 1.2 becomes 54 ÷ 12.

3. Follow the Division Steps:

   • Proceed with the division as outlined in Step 2.

Practical Application

Understanding decimal division is crucial in real-world situations like calculating prices, measurements, and ratios.

Conclusion

Mastering the division algorithm for real numbers is a vital skill in mathematics. By following these steps, you'll be able to solve division problems confidently. As you continue practicing, try varying the numbers and incorporating decimals to enhance your understanding. For further learning, consider exploring additional resources or practice problems related to division.