7th Grade Math: Solution To Exercise 20, Page 25, Paralela 45

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Solving Exercise 20, Page 25 from Paralela 45 - 7th Grade Math

Hey guys! Let's dive into solving Exercise 20 from page 25 in your "Paralela 45" math textbook for 7th grade, 2025 edition, Part 1. This exercise can seem tricky at first, but I'm going to break it down for you step-by-step so you can understand exactly how to solve it. Remember, math is all about practice, so let's get started!

Understanding the Problem

Before we even think about calculations, let's make sure we really understand what the problem is asking. Read the exercise carefully. What concepts does it involve? Are we dealing with algebraic expressions, geometric figures, or something else entirely? Identifying the core concepts is the first crucial step. For this particular problem, it's Exercise 20 on page 25 of the Paralela 45 textbook, 2025 edition, Part 1 for 7th grade. This usually involves topics covered in the first part of the 7th-grade curriculum. It might include things like:

  • Rational Numbers: Operations with fractions and decimals.
  • Algebraic Expressions: Simplifying expressions, solving equations and inequalities.
  • Geometry Basics: Angles, lines, triangles, and basic geometric shapes.

Understanding the specific concepts involved will help us choose the right approach to solve the problem. Don’t just jump into calculations without a plan! Take a moment to reflect and strategize. What formulas or rules might be relevant here? Think about similar problems you've solved before.

Breaking Down the Exercise

Now that we have a general idea of the topics involved, let's break down Exercise 20 into smaller, more manageable parts. What information are we given? What are we trying to find? Sometimes, the problem statement includes extra information that isn't necessary for the solution. Identifying the key information is essential. Let's assume, for the sake of this explanation, that the problem involves simplifying an algebraic expression. Something like: Simplify: 3(x + 2) - 2(x - 1). If the exercise involves a word problem, try to translate it into mathematical expressions or equations. Draw diagrams or figures if necessary, especially for geometry problems. Visualizing the problem can often make it easier to understand and solve. For example, if it involves angles, draw the angles; if it involves a triangle, sketch the triangle and label the sides and angles. This visual representation helps to clarify the relationships between the different elements of the problem. Also, break the problem into smaller steps. Instead of trying to solve everything at once, tackle one part at a time. This approach will make the overall problem less daunting and easier to manage.

Step-by-Step Solution (Example)

Let’s use the example algebraic expression from before: Simplify: 3(x + 2) - 2(x - 1).

  1. Distribute: Apply the distributive property to remove the parentheses.
    • 3(x + 2) becomes 3 * x + 3 * 2 = 3x + 6
    • -2(x - 1) becomes -2 * x + (-2) * (-1) = -2x + 2
  2. Rewrite: Now we have 3x + 6 - 2x + 2.
  3. Combine Like Terms: Group the terms with 'x' and the constant terms together.
    • (3x - 2x) + (6 + 2)
  4. Simplify: Combine the like terms.
    • x + 8 So, the simplified expression is x + 8. This step-by-step approach makes the process much clearer and reduces the chance of making mistakes. You can apply this method to other types of problems by identifying the key operations and performing them in a logical sequence. Remember to double-check your work at each step to ensure accuracy.

Common Mistakes and How to Avoid Them

Math problems often have common pitfalls. Let's talk about some of them and how to avoid them. One common mistake is forgetting the order of operations (PEMDAS/BODMAS). Remember: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). Always follow this order to ensure you get the correct answer. Another common error is making mistakes with signs, especially when dealing with negative numbers. Be extra careful when distributing negative signs or combining terms with different signs. Double-check your work and pay close attention to the signs. Also, be mindful of fractions and decimals. Ensure you are performing the correct operations (adding, subtracting, multiplying, or dividing) and that you're simplifying your answers appropriately. It's a good idea to practice converting between fractions and decimals to improve your fluency. And guys, don't skip steps! Show your work clearly, even for seemingly simple steps. This helps you track your progress and makes it easier to identify any errors. Rushing through the problem can lead to careless mistakes that could be easily avoided. Writing out each step methodically will help you stay organized and accurate.

Practice Makes Perfect

The best way to get better at math is, you guessed it, practice! The more problems you solve, the more comfortable you'll become with different concepts and techniques. Don't just read the solutions; actually work through the problems yourself. Try solving similar exercises from the textbook or online resources. The more you challenge yourself, the better you'll understand the material. If you're struggling with a particular concept, seek help from your teacher, classmates, or online resources. There are tons of helpful videos and explanations available on the internet. Don't be afraid to ask for clarification or extra guidance. Keep practicing consistently, and you'll see your skills improve over time. Consistent effort is key to success in mathematics. Schedule regular study sessions and stick to your plan. Even short, focused practice sessions can be more effective than long, infrequent ones.

Extra Tips for Success

Here are a few more tips to help you succeed in math:

  • Review the basics: Make sure you have a solid understanding of the fundamental concepts. Math builds on itself, so a strong foundation is essential.
  • Use your resources: Take advantage of your textbook, notes, and online resources. There's a wealth of information available to help you learn.
  • Work with others: Studying with classmates can be a great way to learn and reinforce your understanding. You can discuss concepts, solve problems together, and learn from each other's perspectives.
  • Stay organized: Keep your notes and assignments organized so you can easily find what you need.
  • Believe in yourself: Math can be challenging, but everyone is capable of learning it. Stay positive, keep practicing, and you'll see results.

Solving math problems, like Exercise 20 from page 25, becomes much easier when you break it down, understand the concepts, and practice consistently. Don't get discouraged if you encounter challenges – they're just opportunities to learn and grow. Keep up the hard work, and you'll conquer those math problems in no time!

I hope this explanation helped you guys! If you have any more questions about this exercise or any other math problem, feel free to ask. Keep practicing, and you'll become a math whiz in no time!