Multiply By 10 & 100: Math Problem Solved!

Hey guys! Let's dive into a cool math problem today where we'll be multiplying numbers by 10 and 100. It sounds simple, right? But it’s super important for understanding how numbers work and building a strong foundation in math. We're going to break down each part of the question step by step, making sure everyone understands the process. So, grab your pencils, and let's get started!

Understanding Multiplication by Powers of 10

Before we jump into the specific numbers, let's quickly chat about what happens when we multiply by 10, 100, or any power of 10. This is key to solving these types of problems super fast! When you multiply a number by 10, you're essentially shifting all the digits one place to the left. What was in the ones place moves to the tens place, what was in the tens place moves to the hundreds place, and so on. Think of it like adding a zero to the end of the number. And guess what? Multiplying by 100 is just as easy – you're shifting the digits two places to the left, which is like adding two zeros to the end of the number.

Why does this happen? Well, our number system is based on powers of 10 (ones, tens, hundreds, thousands, etc.). So, when we multiply by 10, we're scaling everything up by a factor of 10. It's a fundamental concept in math, and mastering it will make your life a whole lot easier, especially when you're dealing with larger numbers or decimals. This isn't just some random trick; it's rooted in the way our number system is structured. Understanding the 'why' behind the 'how' is what truly makes you a math whiz! So, let’s keep this in mind as we tackle the actual calculations. Remember, understanding the concept is more important than just memorizing a rule.

Part A: Multiplying by 10

Okay, let's tackle the first part of our problem. We need to find the numbers that are 10 times greater than 86, 129, 500, and 486. Remember our little trick? When we multiply by 10, we just add a zero to the end of the number. Let's take it one by one:

• 86 multiplied by 10: This one's pretty straightforward. Just add a zero to 86, and you get 860. See? Super simple!
• 129 multiplied by 10: Add a zero to 129, and you get 1290. We're on a roll!
• 500 multiplied by 10: Add a zero to 500, and you get 5000. Notice how the zeros just pile up? That's how the magic of multiplying by 10 works.
• 486 multiplied by 10: Last one in this set! Add a zero to 486, and you get 4860. Awesome job, guys!

So, the numbers that are 10 times greater than 86, 129, 500, and 486 are 860, 1290, 5000, and 4860, respectively. Wasn't that easy? Now, let’s think about why this works. When we say '10 times greater', we mean that we are taking the original number and scaling it up ten times. Each digit shifts one place value higher – the ones become tens, the tens become hundreds, and so on. This fundamental principle makes multiplying by 10 a piece of cake. Keep practicing, and you'll become a pro at this in no time! Remember, consistency is key to mastering any skill, and math is no exception.

Part B: Multiplying by 100

Now, let's move on to the second part of our problem. This time, we need to find the numbers that are 100 times greater than 7, 74, 18, and 99. Remember what we learned about multiplying by 10? Well, multiplying by 100 is similar, but even cooler! Instead of adding one zero, we add two zeros to the end of the number. Think of it as multiplying by 10 twice! Let’s break it down:

• 7 multiplied by 100: Add two zeros to 7, and you get 700. Boom! Simple as that.
• 74 multiplied by 100: Add two zeros to 74, and you get 7400. We're crushing this!
• 18 multiplied by 100: Add two zeros to 18, and you get 1800. Feeling like math superstars yet?
• 99 multiplied by 100: Last one for this set! Add two zeros to 99, and you get 9900. High fives all around!

So, the numbers that are 100 times greater than 7, 74, 18, and 99 are 700, 7400, 1800, and 9900, respectively. See how easy it is once you know the trick? But just like before, let's not just memorize the trick; let's understand why it works. When we multiply by 100, we're scaling the number up by a factor of one hundred. This means each digit shifts two place values higher – the ones become hundreds, the tens become thousands, and so on. This is why we add two zeros – it represents that double shift in place value. Understanding this concept makes these calculations much more intuitive and less like rote memorization. Keep up the amazing work, guys! Practice makes perfect, and you're well on your way to becoming multiplication masters!

Putting It All Together

Alright, guys, we've tackled both parts of the problem, and you’ve done an awesome job! We've learned how to multiply numbers by 10 and 100, and more importantly, we've understood why these tricks work. Remember, when you multiply by 10, you add one zero to the end of the number, and when you multiply by 100, you add two zeros. This is because we're shifting the digits one or two places to the left, respectively.

But the real magic isn't just in knowing the trick; it's in understanding the concept behind it. Knowing that we're scaling the number up by a factor of 10 or 100 helps us make sense of the results and apply this knowledge to other math problems. This is the key to becoming a confident and capable mathematician. So, don't just memorize; understand!

Let's quickly recap our answers:

• Numbers 10 times greater than 86, 129, 500, and 486 are: 860, 1290, 5000, and 4860.
• Numbers 100 times greater than 7, 74, 18, and 99 are: 700, 7400, 1800, and 9900.

You’ve nailed it! You’ve successfully solved the problem, and you've deepened your understanding of multiplication by powers of 10. Give yourselves a pat on the back – you’ve earned it! Keep practicing, keep exploring, and keep asking questions. That’s how you truly learn and grow in math. You guys are doing great, and I'm excited to see what math challenges you'll conquer next! Remember, math is a journey, not a destination, so enjoy the ride!