Digit Value Problem: Find The Missing Number!

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Digit Value Problem: Find the Missing Number!

Hey guys! Ever get those math problems that seem a bit like puzzles? Today, we're diving into one that mixes digit values and a little bit of subtraction. It’s like a mini-detective game with numbers! So, let’s break down this problem step by step and figure out the answer together. Get ready to put on your thinking caps!

Breaking Down the Problem

Our main goal here is to figure out a missing digit. We've got the number 86_, and we know that all the digits added together should equal 23. Then, we need to find out what that missing digit's place value is and subtract 300 from it. Sounds like a plan? Let's jump in!

Understanding the Question

The question we're tackling is: In the number 86_, the sum of the digits is 23. What is the value of the digit that should be written in the blank, minus 300?

This might seem a little complicated at first, but let’s break it down. We have a number that looks like 86_ , where the blank represents a missing digit. We know that if we add up all the digits in this number, we should get 23. The goal is to find the missing digit and then subtract 300 from its place value. Place value basically means how much a digit is worth depending on its position in the number (ones, tens, hundreds, etc.).

To solve this, we'll follow a few simple steps:

  1. Find the missing digit: We'll use the information about the sum of the digits to figure out what number goes in the blank.
  2. Determine the place value: We'll identify whether the missing digit is in the ones, tens, or hundreds place.
  3. Subtract 300: Finally, we'll subtract 300 from the place value of the missing digit to get our final answer.

So, let's get started and solve this numeric puzzle together!

Solving for the Missing Digit

Okay, team, let's roll up our sleeves and start solving for that mystery digit! Remember, we have the number 86_ , and all the digits need to add up to 23. So, the first thing we've got to do is figure out what that missing number actually is. Ready to do some math magic?

Setting up the Equation

To kick things off, let’s set up a simple equation. We know the digits 8 and 6 are part of our number, and we need to find the missing digit, which we can call "x". So, our equation looks like this:

8 + 6 + x = 23

This equation is just a fancy way of saying that when we add 8, 6, and our mystery number together, we should get 23. Now, let’s simplify this a bit.

Simplifying and Solving

First, let’s add the numbers we already know. What's 8 plus 6? That’s right, it's 14. So, we can rewrite our equation like this:

14 + x = 23

Now, we need to figure out what number we can add to 14 to get 23. Think of it like this: If you have 14 cookies, how many more do you need to have 23 cookies? To find that out, we can subtract 14 from 23.

So, let’s do that subtraction:

23 - 14 = ?

If you do the math, you'll find that 23 minus 14 is 9. That means our missing digit, x, is 9!

Verifying the Solution

Just to be super sure, let's check our answer. We said the missing digit is 9, so let’s plug that back into our original equation:

8 + 6 + 9 = ?

When we add 8, 6, and 9, we get:

8 + 6 = 14 14 + 9 = 23

Woo-hoo! It works! Our digits add up to 23, just like the problem said. So, we’ve successfully found our missing digit. The number we're working with is actually 869. Great job, team! We’re one step closer to cracking this numerical puzzle.

Determining the Place Value

Alright, mathletes, now that we've uncovered the missing digit, it's time to figure out its place value! Place value is super important because it tells us how much a digit is actually worth based on where it sits in the number. Think of it like each spot in a number has its own special power. So, let’s figure out what power our digit has in the number 869.

Understanding Place Value

First off, let’s quickly review what place value means. In a number, each position has a value that's a multiple of 10. Starting from the right, we have the ones place, then the tens place, then the hundreds place, and so on. Here’s a quick breakdown:

  • Ones Place: The rightmost digit represents ones (1, 2, 3, etc.).
  • Tens Place: The digit to the left of the ones place represents tens (10, 20, 30, etc.).
  • Hundreds Place: The digit to the left of the tens place represents hundreds (100, 200, 300, etc.).

And it keeps going like that for thousands, ten-thousands, and beyond! But for our problem, we just need to focus on these first three places.

Identifying the Place Value of 9

Now, let’s zoom in on our number: 869. We found out that the missing digit was 9, and it’s sitting right there in the ones place. So, what does that mean for its value?

Since 9 is in the ones place, it simply represents 9 ones. There’s no extra power-up from being in the tens or hundreds place. It’s just good old 9.

So, we know the digit is 9, and its place value is 9. We’re making excellent progress! Now we're ready for the final step: subtracting 300 from the place value.

Subtracting 300 from the Place Value

Okay, folks, we’re in the home stretch! We've found our missing digit (9), figured out its place value (also 9), and now we just have one final calculation to make. The question asks us to subtract 300 from the place value of the digit. So, let’s put on our subtraction hats and get this done!

Setting up the Subtraction

Remember, the place value of our missing digit 9 is just 9 because it’s in the ones place. Now, we need to subtract 300 from this value. So, our subtraction problem looks like this:

9 - 300 = ?

This might look a little tricky at first, because we're subtracting a much bigger number from a smaller one. But don’t worry, we can handle it!

Performing the Subtraction

When we subtract a larger number from a smaller one, we’re going to end up with a negative number. Think of it like this: if you have 9 cookies and someone asks you to give them 300, you’d be short! You’d owe them cookies. In math terms, that means we'll have a negative amount.

So, let’s do the subtraction. To make it easier, we can think of it as finding the difference between 300 and 9, and then making sure our answer is negative. The difference between 300 and 9 is:

300 - 9 = 291

But since we’re subtracting 300 from 9, our answer will be negative. So, we get:

9 - 300 = -291

Final Answer

And there we have it! The value of the digit that should be written in the blank, minus 300, is -291. Great job, everyone! We’ve successfully navigated through this number puzzle and come out with the correct answer. High fives all around!

Conclusion

Awesome work, math detectives! We’ve officially cracked the case of the missing digit and the subtraction challenge. Let’s take a quick victory lap and recap what we’ve accomplished.

Recap of the Solution

We started with a number that had a missing digit: 86_. Our mission was to figure out what that digit was, knowing that the sum of all the digits had to be 23. We then needed to find the place value of that digit and subtract 300 from it.

Here’s a quick rundown of the steps we took:

  1. Found the Missing Digit: We set up an equation (8 + 6 + x = 23) and solved for x, finding that the missing digit was 9.
  2. Determined the Place Value: We identified that the digit 9 was in the ones place, so its place value was simply 9.
  3. Subtracted 300: Finally, we subtracted 300 from the place value (9 - 300), which gave us -291.

So, the final answer to our problem is -291.

Why This Matters

You might be thinking, “Okay, cool, we solved a math problem. But why does this matter?” Well, problems like these help us sharpen our problem-solving skills, which are super useful in all sorts of situations. We used basic arithmetic, a little bit of algebra, and some logical thinking to get to our answer.

Understanding place value is crucial because it’s the foundation for working with larger numbers and more complex math. Being able to manipulate numbers and solve equations is a skill that comes in handy not just in math class, but also in everyday life, from managing your budget to figuring out how much pizza to order for a party!

So, keep practicing, keep puzzling, and remember that every math problem is just another opportunity to flex those brain muscles. You guys nailed it today!