Pecahan (2) - Operasi Hitung Pecahan, Penjumlahan Pecahan - Matematika SMP

Introduction

This tutorial will guide you through the process of performing operations on fractions, specifically focusing on addition. Understanding how to work with fractions is essential for students in middle school mathematics, and this guide will break down the concepts into manageable steps.

Step 1: Understanding Fractions

• A fraction consists of two parts: the numerator (top number) and the denominator (bottom number).
• The numerator indicates how many parts you have, while the denominator indicates how many equal parts make up a whole.

Practical Tip

• Always ensure that fractions are in their simplest form to make calculations easier.

Step 2: Finding a Common Denominator

• When adding fractions with different denominators, you must first find a common denominator.
• The common denominator is typically the least common multiple (LCM) of the different denominators.

Steps to Find the LCM

1. List the multiples of each denominator.
2. Identify the smallest multiple that appears in both lists.

Example

For fractions 1/4 and 1/6

• Multiples of 4: 4, 8, 12, 16...
• Multiples of 6: 6, 12, 18...
• LCM is 12.

Step 3: Converting Fractions

• Convert each fraction to have the common denominator.

To convert a fraction

1. Divide the common denominator by the original denominator.
2. Multiply both the numerator and denominator of the fraction by this result.

Example

For 1/4

• Convert to 12: (12/4) = 3 → (1 * 3)/(4 * 3) = 3/12.

For 1/6

• Convert to 12: (12/6) = 2 → (1 * 2)/(6 * 2) = 2/12.

Step 4: Adding the Fractions

• Now that both fractions have the same denominator, you can add them.
• Keep the common denominator and add the numerators.

Example

• 3/12 + 2/12 = (3 + 2)/12 = 5/12.

Step 5: Simplifying the Result

• If possible, simplify the resulting fraction to its lowest terms.
• Check if the numerator and denominator have any common factors and divide them to simplify.

Example

• In the previous case, 5/12 is already in simplest form.

Conclusion

In this tutorial, you learned how to add fractions by finding a common denominator, converting the fractions, and simplifying the result. Practicing these steps will help strengthen your understanding of fractions. For further practice, consider working with different fractions and applying these steps to more complex problems.