Matematika Kelas 7 Bab 1 Bilangan Bulat - Positif dan Negatif - hal. 12 - 20 Kurikulum Merdeka

Introduction

In this tutorial, we will explore the concepts of positive and negative integers as taught in the 7th-grade mathematics curriculum, specifically from pages 12 to 20 of the Kurikulum Merdeka. Understanding these fundamental concepts is essential for solving various mathematical problems and building a strong foundation for future studies in mathematics.

Step 1: Understanding Integers

• Definition of Integers: Integers include all whole numbers, positive and negative, as well as zero. They can be represented on a number line.
• Positive Integers: These are the numbers greater than zero (1, 2, 3, ...).
• Negative Integers: These are the numbers less than zero (-1, -2, -3, ...).
• Zero: Zero is considered neither positive nor negative.

Practical Tip

Visualize integers on a number line to better understand their positions relative to each other.

Step 2: Identifying Positive and Negative Numbers

Recognize Sign

• Positive numbers are typically written without a sign (e.g., 5).
• Negative numbers have a minus sign (e.g., -5).

Application in Real Life

• Positive integers can represent quantities like money earned, while negative integers can represent debts or temperatures below zero.

Common Pitfall

Confusing the signs of numbers can lead to errors in calculations. Always double-check the signs when performing arithmetic operations.

Step 3: Comparing Integers

Larger and Smaller

• A positive integer is always greater than a negative integer.
• Use a number line to visually compare integers.

Examples

• Compare 3 and -2: 3 is greater than -2.
• Compare -4 and -1: -1 is greater than -4.

Practical Tip

When comparing integers, remember that moving to the right on the number line indicates increasing value.

Step 4: Adding and Subtracting Integers

• Adding Positive and Negative Integers:

  • If you add a positive integer to a negative integer, subtract the smaller absolute value from the larger one and keep the sign of the integer with the larger absolute value.
  • Example: 3 + (-5) = -2 (subtract 3 from 5, keep the negative sign).

• Subtracting Integers:

  • To subtract a negative integer, add its positive counterpart.
  • Example: 4 - (-2) = 4 + 2 = 6.

Common Pitfall

Misapplying the rules for adding and subtracting negative numbers can lead to confusion. Always remember to convert subtraction of a negative into addition.

Step 5: Multiplying and Dividing Integers

• Multiplication Rules:

  • Positive × Positive = Positive
  • Positive × Negative = Negative
  • Negative × Negative = Positive

• Division Rules: The same rules apply as for multiplication.

Example

• 3 × (-2) = -6
• (-4) ÷ (-2) = 2

Conclusion

In this tutorial, we covered the basics of integers, including their definitions, how to identify and compare them, and how to perform arithmetic operations. Understanding these concepts is crucial for advancing in mathematics.

For your next steps, practice identifying integers and performing operations with them in various exercises. Consider using a number line as a visual aid for better comprehension.