6th Grade Math Kazakhstan: Solutions For Exercises 489-490

Nov 6, 2025 by Admin 59 views

Hey guys! Let's dive into the solutions for exercises 489 and 490 from the first part of the sixth-grade math textbook in Kazakhstan. Math can sometimes feel like a puzzle, but with a little bit of understanding and practice, we can solve anything. This article aims to break down these problems step by step, making it super easy for you to grasp the concepts and nail those answers. We'll explore the key concepts involved, walk through the solutions, and provide some extra tips to help you master similar problems. So, grab your textbooks, and let's get started!

Understanding the Core Concepts

Before we jump straight into solving exercises 489 and 490, it’s crucial to understand the underlying mathematical principles. These exercises likely touch on several key areas, such as fractions, decimals, percentages, and basic algebraic equations. Having a solid foundation in these concepts will make tackling the problems much easier.

Fractions: Fractions represent parts of a whole. Understanding how to add, subtract, multiply, and divide fractions is essential. We'll likely encounter problems that require us to simplify fractions, find common denominators, and convert between mixed numbers and improper fractions. Remember, fractions are your friends – they help us break down complex problems into manageable parts!
Decimals: Decimals are another way to represent parts of a whole, and they are closely related to fractions. Converting between decimals and fractions is a handy skill. Operations with decimals, such as addition, subtraction, multiplication, and division, will also be important. Think of decimals as fractions in disguise – understanding this connection can make calculations much smoother.
Percentages: Percentages are used to express a number as a fraction of 100. Calculating percentages, finding the percentage of a number, and converting between percentages, fractions, and decimals are skills we might need. Percentages are everywhere in real life, from sales discounts to interest rates, so mastering them is a big win!
Basic Algebraic Equations: These involve variables and require us to solve for unknown values. We might need to apply the principles of balancing equations, isolating variables, and using inverse operations. Don't let the variables scare you – they're just placeholders for numbers we need to find!

By reinforcing these core concepts, we'll be well-prepared to tackle the specific challenges presented in exercises 489 and 490. Let's get ready to put our knowledge to the test!

Exercise 489: A Detailed Solution

Okay, let's dive into Exercise 489! To provide a thorough solution, we need to make some assumptions about what the exercise actually entails since we don't have the textbook in front of us. However, we can create a realistic example based on typical sixth-grade math problems in Kazakhstan. Let’s assume Exercise 489 involves a word problem dealing with fractions and requires us to calculate a specific quantity.

Example Problem:

A farmer has a field that is 5/8 planted with wheat and 1/4 planted with barley. If the total area of the field is 48 hectares, how many hectares are planted with wheat?

Step-by-Step Solution:

Identify the knowns: We know the field is 5/8 planted with wheat, and the total area is 48 hectares.
Determine the goal: We need to find the area planted with wheat.
Set up the equation: To find the area planted with wheat, we need to calculate 5/8 of the total area, which is 48 hectares. This can be written as:

Area of wheat = (5/8) * 48 hectares
Perform the calculation: To multiply a fraction by a whole number, we can think of the whole number as a fraction with a denominator of 1. So, we have:

(5/8) * (48/1)

Multiply the numerators (5 * 48) and the denominators (8 * 1):

(5 * 48) / (8 * 1) = 240 / 8
Simplify the fraction: Now, we need to simplify 240/8. We can divide both the numerator and the denominator by their greatest common divisor, which is 8:

240 ÷ 8 = 30

8 ÷ 8 = 1

So, 240/8 simplifies to 30/1, which is just 30.
State the answer: The area planted with wheat is 30 hectares.

Key Takeaways

Always identify the knowns and the goal in word problems. This helps you focus on what you need to find.
Break down complex problems into smaller, manageable steps.
Double-check your calculations to avoid simple errors.

By working through this example, you've seen how to tackle a problem involving fractions and area calculation. Remember, the key is to understand the underlying principles and apply them step by step. Let's move on to Exercise 490!

Exercise 490: A Detailed Solution

Now, let's tackle Exercise 490! Again, without the exact problem, we’ll create a representative example that aligns with the sixth-grade math curriculum in Kazakhstan. Let’s assume Exercise 490 involves solving a basic algebraic equation. These types of problems are crucial for developing problem-solving skills. Understanding how to manipulate equations is a fundamental skill that you'll use throughout your math journey.

Example Problem:

Solve for x: 3x + 7 = 22

Step-by-Step Solution:

Identify the goal: We need to find the value of x that makes the equation true.
Isolate the term with x: To do this, we need to get rid of the +7 on the left side of the equation. We can do this by subtracting 7 from both sides of the equation. Remember, whatever we do to one side of the equation, we must do to the other to keep it balanced!

3x + 7 - 7 = 22 - 7

This simplifies to:

3x = 15
Solve for x: Now, we have 3x = 15. To isolate x, we need to divide both sides of the equation by 3:

(3x) / 3 = 15 / 3

This simplifies to:

x = 5
Check your solution: It’s always a good idea to check your answer to make sure it’s correct. Substitute x = 5 back into the original equation:

3(5) + 7 = 22

15 + 7 = 22

22 = 22

Since the equation holds true, our solution is correct.
State the answer: The value of x is 5.

Key Takeaways

Always remember to perform the same operation on both sides of the equation to keep it balanced.
Use inverse operations (addition/subtraction, multiplication/division) to isolate the variable.
Checking your solution helps prevent errors and builds confidence.

By working through this example, you've seen how to solve a basic algebraic equation. Practice is key, so try solving similar problems to strengthen your skills. Let's move on to some general tips for tackling math problems!

General Tips for Mastering Math

Math can be challenging, but with the right approach, it can also be incredibly rewarding. Here are some general tips to help you master math, boost your confidence, and ace those exams:

Practice Regularly: Math is like a sport – the more you practice, the better you become. Set aside some time each day to work on math problems. Consistent practice reinforces concepts and improves problem-solving skills. Even just 30 minutes a day can make a big difference. Think of it as exercising your brain!
Understand the Concepts: Don't just memorize formulas and procedures. Take the time to understand why they work. This will help you apply them in different situations and remember them better. When you understand the "why" behind the math, it becomes much more intuitive.
Work Through Examples: Start by working through example problems in your textbook or online. Pay attention to each step and try to understand the reasoning behind it. Once you understand the example, try solving similar problems on your own. Examples are like training wheels – they help you build confidence before you go solo.
Break Down Problems: Complex problems can seem overwhelming. Break them down into smaller, more manageable steps. This makes the problem less intimidating and easier to solve. It's like eating an elephant – one bite at a time!
Seek Help When Needed: Don't be afraid to ask for help if you're struggling. Talk to your teacher, classmates, or a tutor. Explaining your difficulties can help you understand the concepts better. Remember, there's no shame in asking for help – it's a sign of strength!
Review and Revise: Regularly review your notes and practice problems. This will help you retain the information and identify areas where you need more practice. Revision is key to long-term retention. It's like revisiting a familiar place – you'll notice new details each time!
Stay Positive: Math can be frustrating at times, but it's important to stay positive. Believe in yourself and your ability to learn. Celebrate your successes, no matter how small. A positive mindset can make a huge difference in your learning journey.
Use Visual Aids: Visual aids like diagrams, charts, and graphs can help you understand math concepts better. They provide a visual representation of the problem, making it easier to grasp. Visualizing math can make it more concrete and less abstract.
Apply Math to Real Life: Look for opportunities to apply math in real-life situations. This will help you understand its relevance and make it more interesting. Math is everywhere – from calculating grocery bills to measuring ingredients for a recipe!

By following these tips, you'll be well on your way to mastering math and achieving your academic goals. Remember, math is a journey, not a destination. Enjoy the process and celebrate your progress along the way!

Conclusion

So, guys, we've walked through potential solutions for Exercises 489 and 490 from your sixth-grade math textbook in Kazakhstan. We covered fractions, decimals, percentages, and basic algebraic equations, along with some general tips for mastering math. Remember, the key is to understand the core concepts, practice regularly, and stay positive. Math might seem tough sometimes, but with a bit of effort and the right approach, you can conquer it! Keep up the great work, and don't hesitate to ask for help when you need it. You've got this!