Kurikulum Merdeka Matematika Kelas 7 Bab 3 Rasio

Introduction

This tutorial aims to provide a comprehensive guide on the topic of ratios as discussed in the seventh-grade mathematics curriculum under the Kurikulum Merdeka framework. Understanding ratios is essential in mathematics as they are used to compare quantities and are foundational for more advanced concepts.

Step 1: Understanding Ratios

• Definition of Ratios: A ratio is a comparison between two quantities, showing how many times one value contains or is contained within the other.
• Notation: Ratios can be expressed in different forms such as:
  • Fraction: a/b
  • Colon: a:b
  • Words: "a to b"
• Real-World Application: Ratios are used in recipes, scaling models, and financial analysis, making them practical for everyday situations.

Step 2: Writing Ratios

• Identify the Quantities: Determine the two quantities you want to compare.
• Express in Simplest Form: Reduce ratios by dividing both parts by their greatest common divisor (GCD).
  • Example: The ratio of 8 to 12 can be simplified to 2 to 3 by dividing both by 4.

Step 3: Types of Ratios

• Part-to-Part Ratios: Compare different parts of a whole.

  • Example: In a fruit basket with 4 apples and 6 bananas, the part-to-part ratio of apples to bananas is 4:6, which simplifies to 2:3.

• Part-to-Whole Ratios: Compare one part to the whole.

  • Example: In the same basket, the ratio of apples to the total number of fruits (10) is 4:10, simplifying to 2:5.

Step 4: Solving Ratio Problems

• Setting Up the Problem: Translate word problems into ratios.

  • Example: “If there are 3 cats for every 2 dogs, what is the ratio of dogs to cats?”

• Cross-Multiplication Method: For problems involving proportions, use cross-multiplication to solve.

  • Example: If x/y = 3/2, then cross-multiply to get 2x = 3y.

Step 5: Practice with Ratios

• Work on Sample Problems: Apply what you’ve learned by solving different ratio problems.

  • Example Problems:
    1. Simplify the ratio 16:24.
    2. If a recipe calls for 2 cups of sugar to 5 cups of flour, what is the ratio of flour to sugar?

• Check Your Answers: Always verify your answers by simplifying and ensuring the ratio is in the correct form.

Conclusion

Understanding ratios is a foundational skill in mathematics that has practical applications in various fields, from cooking to finance. By mastering how to write, simplify, and solve ratio problems, you’ll enhance your mathematical abilities and prepare yourself for more complex topics in the future. To further your learning, consider tackling additional practice problems or exploring related mathematical concepts such as proportions and percentages.