Solving (110+45×2) 4=90+200:4: A Math Puzzle!

by SLV Team 46 views

Alright guys, let's dive into this interesting math problem! We've got the equation (110+45×2) 4=90+200:4, and our mission is to break it down and solve it. Math can be a bit like a puzzle, and I'm here to guide you through each step. So, grab your calculators (or your mental math muscles) and let's get started!

Understanding the Equation

Before we start crunching numbers, let’s understand what the equation is telling us. The equation is (110+45×2) 4=90+200:4. This looks like it is trying to compare two expressions. The key here is to follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). This order ensures that we solve the equation correctly.

Breaking Down the Left Side of the Equation

The left side of the equation is (110+45×2) 4. According to PEMDAS, we need to deal with the parentheses first. Inside the parentheses, we have 110+45×2. Multiplication comes before addition, so we multiply 45 by 2 first:

45 × 2 = 90

Now we add this result to 110:

110 + 90 = 200

So, the expression inside the parentheses simplifies to 200. Now we multiply this by 4:

200 × 4 = 800

Therefore, the left side of the equation simplifies to 800.

Analyzing the Right Side of the Equation

The right side of the equation is 90+200:4. Here, we have both addition and division. According to PEMDAS, division comes before addition. So we divide 200 by 4 first:

200 ÷ 4 = 50

Now we add this result to 90:

90 + 50 = 140

Thus, the right side of the equation simplifies to 140.

Comparing Both Sides

Now that we've simplified both sides of the equation, let's compare them:

Left side: (110+45×2) 4 = 800 Right side: 90+200:4 = 140

Clearly, 800 is not equal to 140. So, the equation (110+45×2) 4=90+200:4 is not true.

Step-by-Step Solution

Let’s recap the step-by-step solution to make sure we’re all on the same page:

  1. Left Side: (110+45×2) 4
    • Multiply within parentheses: 45 × 2 = 90
    • Add within parentheses: 110 + 90 = 200
    • Multiply by 4: 200 × 4 = 800
  2. Right Side: 90+200:4
    • Divide: 200 ÷ 4 = 50
    • Add: 90 + 50 = 140
  3. Comparison: 800 ≠ 140

Common Mistakes to Avoid

When tackling equations like this, it’s easy to make a few common mistakes. Here are some pitfalls to watch out for:

  • Forgetting PEMDAS: Always remember the order of operations. Multiply and divide before you add or subtract. Parentheses are your best friends – solve everything inside them first!
  • Incorrectly Distributing: In this particular problem, distribution isn't an issue, but in other equations, be careful when distributing numbers across parentheses. Make sure you multiply each term inside the parentheses by the number outside.
  • Arithmetic Errors: Simple calculation mistakes can throw off your entire solution. Double-check your work, especially during multiplication and division.

Why This Matters

You might be wondering, "Why do I need to know this stuff?" Understanding the order of operations isn't just about solving math problems; it’s about developing logical thinking and problem-solving skills. These skills are super useful in many areas of life, from managing your finances to making strategic decisions at work. Plus, math is the foundation for many fields like engineering, computer science, and even art and music!

Practice Makes Perfect

To really nail these concepts, practice is key. Try solving similar equations, and don’t be afraid to make mistakes. Each mistake is a learning opportunity! Here are a few practice problems you can try:

  1. (50 + 25 × 3) ÷ 5 = ?
  2. 120 – 60 ÷ 2 + 10 = ?
  3. (30 × 2 – 15) × 4 = ?

Work through these problems, and check your answers with a calculator or a friend. The more you practice, the more confident you’ll become in your math skills.

Real-World Applications

Math isn't just something you learn in school; it's all around us. Here are a few real-world examples where understanding the order of operations can come in handy:

  • Cooking: When you’re scaling a recipe, you need to adjust the ingredients proportionally. Understanding multiplication and division is essential to getting the right amounts.
  • Budgeting: Managing your finances involves calculating income, expenses, and savings. You need to be able to add, subtract, multiply, and divide to keep track of your money.
  • Home Improvement: Whether you’re painting a room or building a shelf, you need to measure materials and calculate costs. Math helps you plan your projects and avoid costly mistakes.

Conclusion

So, guys, we've taken a deep dive into the equation (110+45×2) 4=90+200:4 and found that it’s not true. By following the order of operations (PEMDAS) and breaking down each side of the equation, we were able to solve it step by step. Remember to avoid common mistakes and practice regularly to improve your math skills. Math is a powerful tool that can help you in many areas of life, so keep learning and exploring!

Keep practicing, stay curious, and you'll become a math whiz in no time! Whether it's balancing your checkbook, calculating the tip at a restaurant, or figuring out how much paint you need for your living room, math is your friend. Keep honing those skills, and you'll be surprised at how often they come in handy. Until next time, happy calculating!