Garis dan Sudut (2) - Sexasimal, Penjumlahan Sexasimal, Perkalian Sexasimal - Matematika SMP

Introduction

This tutorial focuses on the concepts of sexasimal (base-6) arithmetic, including addition and multiplication. These topics are essential for understanding advanced mathematics in middle school (SMP). By mastering sexasimal calculations, students can enhance their numerical skills and prepare for more complex mathematical concepts.

Step 1: Understanding Sexasimal System

• The sexasimal system is a base-6 number system, which means it uses six digits: 0, 1, 2, 3, 4, and 5.
• Each digit's place value is a power of 6, similar to how the decimal system uses powers of 10.

Example

The sexasimal number 245 represents

• 2 * 6² + 4 * 6¹ + 5 * 6⁰ = 2 * 36 + 4 * 6 + 5 * 1 = 72 + 24 + 5 = 101 in decimal.

Step 2: Performing Sexasimal Addition

To add two sexasimal numbers

1. Align the numbers vertically.
2. Start adding from the rightmost digit to the left.
3. If the sum of any column is 6 or more, carry over to the next column.

Example of Addition:

• Adding 245 and 134:

      245
    + 134
    ------
  

  • Rightmost column: 5 + 4 = 9 (write down 3, carry over 1)
  • Next column: 4 + 3 + 1 (carried) = 8 (write down 2, carry over 1)
  • Leftmost column: 2 + 1 + 1 (carried) = 4 (write down 4)

  Result: 423

Step 3: Performing Sexasimal Multiplication

To multiply two sexasimal numbers

1. Write the numbers one above the other.
2. Multiply each digit of the bottom number by each digit of the top number.
3. Carry over any sums greater than or equal to 6.
4. Align results according to their place values and add them up.

Example of Multiplication:

• Multiplying 24 and 13:

     24
    x13
    ----
    72   (This is 24 x 3)
   24    (This is 24 x 1, shifted one position to the left)
   ------
  

  Sum the results

  • Rightmost column: 2 + 2 = 4
  • Next column: 7 + 4 = 11 (write down 5, carry over 1)
  • Leftmost column: 1 (carried) = 1

  Result: 145

Step 4: Practical Tips for Sexasimal Operations

• Always check your work by converting to decimal and back.
• Practice with more examples to strengthen your understanding.
• Use visual aids, like base-6 blocks, to grasp concepts better.

Conclusion

Understanding sexasimal calculations is crucial for building a strong foundation in mathematics. Practice addition and multiplication with various examples to become proficient. As you become more comfortable with these operations, explore more complex mathematical topics that build on this knowledge, such as algebra and geometry.