Long Division: 210 ÷ 35 Solution

by SLV Team 33 views

Hey guys! Ever get tangled up trying to divide numbers? Don't sweat it! Long division might seem tricky, but once you get the hang of it, you'll be breezing through those problems. Today, we're going to break down a classic: 210 divided by 35. We'll go through each step slowly, so you totally get it. Let's dive in!

Understanding the Basics of Long Division

Before we jump into the problem, let's quickly refresh what long division is all about. Long division is a method we use to divide large numbers into smaller, manageable parts. It helps us find out how many times one number (the divisor) fits into another number (the dividend). In our case, 210 is the dividend, and 35 is the divisor. The answer we're looking for is called the quotient.

The basic setup looks like this:

      ________
35 ) 210

We're trying to figure out what number goes on top (the quotient) that, when multiplied by 35, gives us 210.

Step-by-Step Solution: 210 ÷ 35

Step 1: Setting Up the Problem

First, write the problem in the long division format:

      ________
35 ) 210

This setup helps us keep track of each step as we work through the division.

Step 2: Estimating the Quotient

Now, we need to figure out how many times 35 goes into 210. This might seem tough at first, but let’s make an educated guess. Think about it: 35 is close to 40, and 210 is close to 200. How many times does 40 go into 200? Well, 40 x 5 = 200. So, let's try 5 as our estimated quotient.

Step 3: Multiplying the Divisor by the Estimated Quotient

Multiply the divisor (35) by our estimated quotient (5):

35 x 5 = 175

Step 4: Subtracting and Bringing Down

Subtract the result (175) from the dividend (210):

  210
- 175
------
   35

We get 35 as the remainder. Since there are no more digits to bring down from the dividend, we move to the next step.

Step 5: Checking Our Work

Notice that our remainder (35) is the same as our divisor (35). This means that 35 actually goes into 210 more than just 5 times. We need to adjust our quotient. Instead of 5, let's try 6.

Step 6: Adjusting the Quotient

Multiply the divisor (35) by the new estimated quotient (6):

35 x 6 = 210

Step 7: Final Subtraction

Subtract the result (210) from the dividend (210):

  210
- 210
------
   0

We get 0 as the remainder. This means that 35 goes into 210 exactly 6 times.

Step 8: Writing the Quotient

Write the quotient (6) above the division symbol:

      6
35 ) 210

So, 210 divided by 35 is 6. No remainders, nice and clean!

Why This Works: The Math Behind It

Long division works because we're essentially breaking down the dividend into smaller, more manageable chunks. We're figuring out how many groups of the divisor can be found within the dividend. Each step helps us refine our estimate until we find the exact quotient or reach a remainder that's smaller than the divisor.

In this case, we found that 35 fits into 210 exactly 6 times. This means that if you had 210 apples and wanted to divide them equally among 35 friends, each friend would get 6 apples.

Tips for Mastering Long Division

  • Practice Makes Perfect: The more you practice, the easier long division becomes. Try different problems with varying numbers.
  • Estimate First: Before diving in, take a moment to estimate the quotient. This will give you a starting point and help you avoid big mistakes.
  • Check Your Work: Always double-check your multiplication and subtraction. Small errors can lead to incorrect answers.
  • Break It Down: If you're struggling with a large number, break it down into smaller parts. This can make the problem less intimidating.
  • Use Resources: There are tons of online resources and videos that can help you visualize and understand long division better.

Real-World Applications of Division

Division isn't just something you learn in school; it's used every day in real life. Here are a few examples:

  • Sharing Costs: Splitting a dinner bill with friends.
  • Calculating Unit Prices: Figuring out the price per item when buying in bulk.
  • Measuring Ingredients: Dividing a recipe in half or doubling it.
  • Planning Trips: Calculating how long it will take to drive a certain distance.

Common Mistakes to Avoid

  • Misaligning Numbers: Make sure to keep your numbers lined up correctly, especially when subtracting.
  • Forgetting to Bring Down: Don't forget to bring down the next digit from the dividend when needed.
  • Incorrect Multiplication: Double-check your multiplication to avoid errors.
  • Not Estimating: Skipping the estimation step can lead to wild guesses and incorrect answers.

Practice Problems

Want to put your new skills to the test? Try these practice problems:

  1. 144 ÷ 12
  2. 256 ÷ 8
  3. 315 ÷ 9
  4. 448 ÷ 16

Work through each problem step-by-step, and remember to check your work. You got this!

Conclusion

So there you have it! Dividing 210 by 35 using long division is a straightforward process once you understand the steps. Remember to estimate, multiply, subtract, and bring down. With a little practice, you'll become a long division pro in no time. Keep practicing, and don't be afraid to ask for help if you get stuck. You're on your way to mastering this essential math skill! Happy dividing! And always remember, math can be fun!

I hope this guide was helpful! If you have any questions or want to see more examples, let me know in the comments below. Keep practicing and you'll be a long division master in no time! Good luck, and happy dividing!