Swapping Digits: Adding 17 Tens To The New Number

by TextBrain Team 50 views

Hey guys! Let's dive into this fun math problem where we're going to swap some digits and then add some tens. It might sound a bit tricky, but trust me, we'll break it down step by step and make it super easy to understand. We're going to tackle the question: When the units and hundreds digits of the number 593 are swapped, what is the result when 17 tens are added to the new number? So, grab your thinking caps, and let's get started!

Understanding Place Value

Before we jump into swapping digits and adding tens, let's quickly recap place value. Place value is the foundation of understanding how numbers work. It basically tells us the value of each digit in a number based on its position. Think of it like this: each position in a number has its own special weight.

In the number 593, we have three digits: 5, 9, and 3. Each of these digits occupies a different place, and that place determines its value:

  • Hundreds Place: The digit in the hundreds place tells us how many hundreds we have. In 593, the digit 5 is in the hundreds place, so we have 5 hundreds, which is 500.
  • Tens Place: The digit in the tens place tells us how many tens we have. In 593, the digit 9 is in the tens place, so we have 9 tens, which is 90.
  • Units Place (or Ones Place): The digit in the units place tells us how many ones we have. In 593, the digit 3 is in the units place, so we have 3 ones, which is 3.

So, the number 593 is actually 500 + 90 + 3. Knowing this, we can easily manipulate the digits and understand the effect on the number's value.

Swapping the Digits

The problem asks us to swap the units and hundreds digits of the number 593. This means we're going to take the digit in the units place (3) and move it to the hundreds place, and we're going to take the digit in the hundreds place (5) and move it to the units place. The digit in the tens place (9) will stay right where it is.

So, when we swap the units and hundreds digits of 593, we get the new number 395. Let's break this down using our knowledge of place value:

  • The digit 3 is now in the hundreds place, so we have 3 hundreds, which is 300.
  • The digit 9 is still in the tens place, so we have 9 tens, which is 90.
  • The digit 5 is now in the units place, so we have 5 ones, which is 5.

Therefore, 395 is equal to 300 + 90 + 5. Now that we've successfully swapped the digits, let's move on to the next part of the problem: adding 17 tens.

Adding 17 Tens

The next part of our problem involves adding 17 tens to the new number we got after swapping the digits, which was 395. But what does it mean to add 17 tens? Well, remember that 1 ten is equal to 10. So, 17 tens is simply 17 multiplied by 10.

17 tens = 17 * 10 = 170

Now we know that we need to add 170 to our new number, 395. This is a straightforward addition problem:

395 + 170 = ?

We can solve this by lining up the numbers vertically and adding each place value column:

  395
+ 170
------
  565
  • Units Place: 5 + 0 = 5
  • Tens Place: 9 + 7 = 16. We write down 6 and carry over 1 to the hundreds place.
  • Hundreds Place: 3 + 1 + 1 (carried over) = 5

So, 395 + 170 = 565. Therefore, when we add 17 tens to the new number (395), we get 565.

Putting It All Together

Okay, let's recap what we've done so far. We started with the number 593 and swapped the units and hundreds digits, resulting in the new number 395. Then, we added 17 tens (which is equal to 170) to 395. This gave us our final answer:

395 + 170 = 565

So, the answer to the question, "When the units and hundreds digits of the number 593 are swapped, what is the result when 17 tens are added to the new number?" is 565. Awesome job, guys! We tackled this problem by understanding place value, swapping digits, and then adding tens. These are fundamental concepts in math, and mastering them will help you solve all sorts of problems.

Why This Matters

Understanding place value and how numbers work is not just about solving math problems in school. It's a crucial skill for everyday life. Think about it – we use numbers constantly, whether we're calculating grocery bills, managing our finances, or even just telling time. A strong grasp of place value helps us make sense of these numbers and make informed decisions.

For example, if you're buying something that costs $5.93 and you pay with a $10 bill, you need to understand place value to calculate how much change you should receive. Similarly, if you're saving up for something, understanding how many tens, hundreds, and thousands you need will help you set realistic goals and track your progress.

Practice Makes Perfect

Now that we've solved this problem together, it's time to put your skills to the test! Try practicing similar problems with different numbers. You can even make up your own problems and challenge your friends or family. The more you practice, the more comfortable and confident you'll become with these concepts.

Here are a few ideas to get you started:

  1. Swap the tens and units digits of the number 724 and add 25 tens to the new number.
  2. Swap the hundreds and tens digits of the number 916 and subtract 12 tens from the new number.
  3. What happens if you swap all the digits of the number 482 in a cyclical manner (hundreds to tens, tens to units, units to hundreds)?

By working through these kinds of problems, you'll solidify your understanding of place value and digit manipulation, and you'll be well on your way to becoming a math whiz!

Wrapping Up

So, guys, we've successfully navigated a digit-swapping, ten-adding math problem! Remember, the key is to break down the problem into smaller, manageable steps. We first understood the concept of place value, then we swapped the digits as instructed, and finally, we added the required number of tens. And just like that, we arrived at our answer: 565.

I hope this explanation has been helpful and has made the concept a little clearer for you. Keep practicing, keep exploring, and most importantly, keep having fun with math! Math isn't just about numbers and formulas; it's about problem-solving, critical thinking, and seeing the world in a logical way. So, embrace the challenge, and you'll be amazed at what you can achieve. Keep shining, mathletes!