BAB 2 Bilangan Bentuk Pecahan | Matematika Dasar | Alternatifa

Introduction

This tutorial covers the basics of understanding fractional numbers, specifically focusing on the representation and manipulation of fractions in mathematics. This foundational knowledge is essential for solving problems that involve ratios and proportions in various real-life applications.

Step 1: Understanding the Components of a Fraction

To grasp fractions, start by familiarizing yourself with their components:

• Numerator: The top part of the fraction that indicates how many parts are being considered.
• Denominator: The bottom part that shows how many equal parts the whole is divided into.

Example

For the fraction 3/4:

• The numerator is 3.
• The denominator is 4.

Step 2: Identifying Types of Fractions

Fractions can be categorized into several types:

• Proper Fractions: The numerator is smaller than the denominator (e.g., 2/5).
• Improper Fractions: The numerator is greater than or equal to the denominator (e.g., 5/3).
• Mixed Numbers: A whole number combined with a proper fraction (e.g., 1 1/2).

Practical Tip

Understanding these categories helps in performing operations like addition, subtraction, multiplication, and division with fractions more effectively.

Step 3: Converting Improper Fractions to Mixed Numbers

Improper fractions can be converted to mixed numbers by following these steps:

1. Divide the numerator by the denominator.
2. The result is the whole number part.
3. The remainder becomes the new numerator, while the denominator remains the same.

Example

Convert 9/4 to a mixed number:

• Divide: 9 ÷ 4 = 2 (whole number) with a remainder of 1.
• Result: 2 1/4.

Step 4: Simplifying Fractions

Fractions can often be simplified to their lowest terms. Here’s how to do it:

1. Find the greatest common divisor (GCD) of the numerator and denominator.
2. Divide both the numerator and denominator by the GCD.

Example

Simplify 8/12:

• GCD of 8 and 12 is 4.
• Divide both by 4: 8 ÷ 4 = 2, 12 ÷ 4 = 3.
• Result: 2/3.

Step 5: Performing Operations with Fractions

Addition and Subtraction

1. Ensure the denominators are the same. If not, find a common denominator.
2. Add or subtract the numerators while keeping the denominator the same.

Multiplication

1. Multiply the numerators together.
2. Multiply the denominators together.

Division

1. Invert the second fraction (the divisor).
2. Multiply the first fraction by this inverted fraction.

Example

To add 1/3 and 1/4:

• Common denominator: 12.
• Convert: 1/3 = 4/12 and 1/4 = 3/12.
• Add: 4/12 + 3/12 = 7/12.

Conclusion

Understanding and manipulating fractions is a fundamental skill in mathematics. By mastering the components of fractions, their types, simplification, and operations, you can tackle a variety of math problems more confidently. For further practice, consider working on example problems or using online resources.