Dividing Made Easy: Step-by-Step Solutions

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Hey guys! Let's break down some division problems and make them super easy to understand. We're going to tackle 845 ÷ 20 and 153 ÷ 12 step by step. Division can seem tricky, but with the right approach, it's totally manageable. So, grab your pencils, and let's dive in!

Solving 845 ÷ 20

When we're looking at 845 ÷ 20, we're essentially asking, "How many times does 20 fit into 845?" To solve this, we'll use the long division method. This might sound intimidating, but trust me, it's just a series of smaller, easier steps.

First off, let's set up our long division problem. We write 845 inside the division bracket and 20 outside. Now, we need to figure out how many times 20 goes into 8. Well, 20 doesn't fit into 8, so we move on to the next digit. How many times does 20 fit into 84? This is where some mental math or a quick guess comes in handy. We know that 20 times 4 is 80, which is close to 84. So, let’s try 4.

Write the 4 above the 4 in 845. Now, multiply 4 by 20, which gives us 80. Write 80 below 84 and subtract. 84 minus 80 is 4. Next, we bring down the 5 from 845, placing it next to the 4, making it 45. Now, our new question is: How many times does 20 fit into 45?

We know that 20 times 2 is 40, which is less than 45, and 20 times 3 is 60, which is too big. So, 20 goes into 45 two times. Write the 2 next to the 4 on top of the division bracket. Multiply 2 by 20, which gives us 40. Write 40 below 45 and subtract. 45 minus 40 is 5.

Now, we have a remainder of 5. To express this as a decimal, we add a decimal point to 845 and a 0 after the 5, making it 50. How many times does 20 fit into 50? It goes in 2 times (20 times 2 is 40). Write 2 after the decimal point on top. Subtract 40 from 50, leaving us with 10. Add another 0, making it 100. How many times does 20 fit into 100? Exactly 5 times. So, 20 times 5 is 100. Subtract 100 from 100, and we get 0. No more remainder!

So, 845 ÷ 20 equals 42.25. We’ve successfully divided 845 by 20 using long division. It's all about breaking it down into manageable steps, guys!

Key Steps for Dividing 845 by 20

  • Set up the long division problem correctly.
  • Estimate how many times the divisor (20) goes into the dividend (845).
  • Multiply and subtract to find the remainder.
  • Bring down the next digit.
  • Add a decimal to continue dividing past the whole number.
  • Keep going until you get a remainder of 0 or a desired decimal place.

Tackling 153 ÷ 12

Now, let’s move on to the next problem: 153 ÷ 12. Again, we're asking ourselves, "How many times does 12 fit into 153?" We’ll use the same long division method to solve this.

Set up the long division with 153 inside the bracket and 12 outside. First, we look at how many times 12 goes into 1. It doesn't, so we look at 15. How many times does 12 fit into 15? It goes in once. Write 1 above the 5 in 153. Multiply 1 by 12, which gives us 12. Write 12 below 15 and subtract. 15 minus 12 is 3.

Bring down the 3 from 153 next to the 3, making it 33. Now, how many times does 12 fit into 33? We know that 12 times 2 is 24, and 12 times 3 is 36, which is too big. So, 12 goes into 33 two times. Write 2 next to the 1 on top of the division bracket. Multiply 2 by 12, which gives us 24. Write 24 below 33 and subtract. 33 minus 24 is 9.

We have a remainder of 9. To express this as a decimal, we add a decimal point to 153 and a 0 after the 9, making it 90. How many times does 12 fit into 90? This might require a bit of thinking. We know 12 times 7 is 84, which is close to 90. So, let's try 7. Write 7 after the decimal point on top. Multiply 7 by 12, which gives us 84. Subtract 84 from 90, leaving us with 6.

Add another 0, making it 60. How many times does 12 fit into 60? Exactly 5 times! 12 times 5 is 60. Subtract 60 from 60, and we get 0. No more remainder!

So, 153 ÷ 12 equals 12.75. We’ve successfully divided 153 by 12. You're getting the hang of it, aren't you?

Steps to Divide 153 by 12

  • Set up the long division correctly.
  • Estimate how many times 12 goes into the first part of 153.
  • Multiply and subtract to find the remainder.
  • Bring down the next digit.
  • Add a decimal to continue dividing past the whole number.
  • Keep going until you get a remainder of 0 or a desired decimal place.

Understanding the Division Process

Division, at its core, is about breaking a number into equal groups. When we divide 845 by 20, we're figuring out how many groups of 20 we can make from 845. The same goes for 153 ÷ 12. By understanding this concept, the long division method becomes less of a mechanical process and more of a logical one.

Why Long Division Matters

Long division is a fundamental skill in mathematics. It's not just about getting the right answer; it’s about understanding how numbers work and building problem-solving skills. This method helps in various real-life situations, from splitting a bill among friends to figuring out ingredient ratios in a recipe.

Tips for Mastering Division

  1. Practice Makes Perfect: The more you practice, the more comfortable you’ll become with the process. Try different problems with varying numbers.
  2. Estimate First: Before you start dividing, make an estimate of the answer. This will help you check if your final answer is reasonable.
  3. Know Your Multiplication Tables: Being familiar with multiplication tables makes division much easier.
  4. Break It Down: Divide the problem into smaller steps. Focus on one digit at a time.
  5. Check Your Work: After you’ve found your answer, multiply it by the divisor to make sure it equals the dividend.

Common Mistakes to Avoid

  • Misplacing Digits: Ensure you’re writing digits in the correct columns.
  • Skipping Steps: Don’t rush through the process. Each step is important.
  • Incorrect Subtraction: Double-check your subtraction to avoid errors.
  • Forgetting the Remainder: If there’s a remainder, make sure to address it appropriately, either as a fraction or by adding a decimal.

Real-World Applications of Division

Division isn't just something we do in math class. It's used every day in various situations. For example:

  • Cooking: Dividing a recipe in half or doubling it requires division.
  • Finance: Splitting bills, calculating unit prices, and figuring out loan payments involve division.
  • Travel: Calculating travel time and distance often requires division.
  • Construction: Measuring and cutting materials to specific lengths uses division.

By understanding the basics of division, you're not just improving your math skills; you're also preparing yourself for many real-world scenarios.

Conclusion: You've Got This!

So there you have it, guys! We've walked through how to solve 845 ÷ 20 and 153 ÷ 12 using long division. Remember, the key to mastering division is practice and breaking down the problem into smaller, manageable steps. Don’t be afraid to make mistakes – they’re part of the learning process. Keep practicing, and you’ll become a division pro in no time! Whether it's for a math assignment or a real-life situation, you've now got the tools to tackle those division problems with confidence. Keep up the great work!