Math Problems: Notation And Calculation

by Lumberyard 40 views

Hey guys! Today, we're diving into some cool math problems where we'll learn how to express them using mathematical notation and then calculate the results. It's like translating English into math and then solving it – super fun! So, let’s get started and break down each problem step by step. Get your thinking caps on, and let's make math a blast!

a) The Sum of the Product of 781 and 6, and the Number 12,450

Okay, let's break down this first problem. In this section, we'll translate the verbal expression into a mathematical one and solve it step by step. Understanding the order of operations is crucial here, so let’s get right to it!

First off, we need to understand exactly what the question is asking. Our main goal is to find the sum. But this sum isn't just any sum – it's the sum of two specific parts:

  1. The product of the numbers 781 and 6
  2. The number 12,450

So, before we can add anything, we first need to figure out what the product of 781 and 6 is. Remember, "product" in math means the result of multiplication. Let’s write this part down mathematically:

781 * 6 = ?

Now, let’s do the multiplication. You can grab a calculator or do it manually – whatever floats your boat. If we multiply 781 by 6, we get:

781 * 6 = 4686

Great! We've got the product. Now we know the first part of our sum is 4686. The next part is the number 12,450. This part is straightforward – it’s just a number waiting to be added.

So, our next step is to add these two parts together. We're adding the product we just calculated (4686) to 12,450. Let's write this down:

4686 + 12450 = ?

Now, it’s time to add these numbers. Adding them up, we get:

4686 + 12450 = 17136

And that’s it! We’ve found the sum. The final answer to the first part of our math problem is 17,136.

To summarize, the mathematical expression for this problem is:

(781 * 6) + 12450

And the result of this expression is:

17136

So, by breaking down the problem into smaller, manageable steps, we’ve successfully translated and solved the problem. Remember, math is all about taking it one step at a time and understanding what each word and operation means. You've nailed this first one – awesome job!

b) The Difference Between the Quotient of 23,400 and 6, and the Number 1,659

Alright, let's tackle the second problem! This one's all about differences and quotients, so get ready to divide and subtract. Just like before, we'll break it down piece by piece to make sure we nail it. We’ll start by translating the words into math, and then we’ll crunch those numbers. Ready? Let’s do this!

First, let’s figure out what exactly we're trying to find. The problem asks for the difference, which means we’re going to be subtracting something from something else. But what are we subtracting? Well, it’s the difference between two things:

  1. The quotient of 23,400 and 6
  2. The number 1,659

So, just like in the first problem, we’ve got a little operation to handle before we can get to the main subtraction. We need to find the quotient of 23,400 and 6. Remember, "quotient" means the result of division. So, let’s write this part out:

23400 / 6 = ?

Now it’s time to do the division. You can use a calculator, do long division, or even break it down in your head if you’re feeling like a math wizard. When we divide 23,400 by 6, we get:

23400 / 6 = 3900

Awesome! We’ve found our quotient. Now we know that the first part of our difference is 3900. The second part is the number 1,659, which is just sitting there, ready to be subtracted.

So, our next step is to subtract 1,659 from 3900. Let’s write that down:

3900 - 1659 = ?

Now, it’s subtraction time! Let’s subtract 1,659 from 3900. You might need to borrow some numbers here, so take your time and be careful. The result is:

3900 - 1659 = 2241

Boom! We’ve got it. The difference we were looking for is 2,241.

So, to recap, the mathematical expression for this problem is:

(23400 / 6) - 1659

And the result of this expression is:

2241

You’ve done it again! By carefully breaking down the problem and tackling each operation one at a time, we’ve successfully found the difference. You're becoming math problem-solving pros! Keep up the awesome work, guys!

c) The Product of the Difference Between 4,580 and 3,976, and the Number 40

Alright, let's dive into the third problem! This time, we're mixing things up with differences and products. Don’t worry, though, we’ll tackle it just like before – step by step. We're going to break down the words, turn them into math, and then solve it like total pros. Get ready to subtract and multiply! Let's go!

So, let's start by figuring out what the problem is really asking for. We need to find the product, which means we're going to be multiplying. But what exactly are we multiplying? The problem tells us it's the product of two things:

  1. The difference between the numbers 4,580 and 3,976
  2. The number 40

Okay, this means before we can multiply, we’ve got to handle that difference. We need to find out what we get when we subtract 3,976 from 4,580. Let’s write this part down mathematically:

4580 - 3976 = ?

Time for some subtraction! Let’s subtract 3,976 from 4,580. You might need to borrow here, so take your time and make sure you line up those numbers correctly. The result is:

4580 - 3976 = 604

Nice! We’ve found our difference. Now we know that one part of our product is 604. The other part is the number 40, which is just waiting for us to multiply it.

So, our next step is to multiply 604 by 40. Let’s write this down:

604 * 40 = ?

Time to multiply! You can use a calculator, do it manually, or whatever works best for you. When we multiply 604 by 40, we get:

604 * 40 = 24160

And there we have it! We’ve found the product. The final answer to this problem is 24,160.

To recap, the mathematical expression for this problem is:

(4580 - 3976) * 40

And the result of this expression is:

24160

You guys are crushing it! By breaking down the problem, figuring out the order of operations, and tackling each step one at a time, you’ve nailed this one too. Keep up the fantastic work!

d) The Quotient of 42,300 and the Sum of 13,285 and 715

Last one, guys! Let's tackle this final problem, which involves a quotient and a sum. By now, you're practically pros at this, so let's break it down step by step and finish strong. We’re going to turn those words into math, and then we’ll solve it like the math rockstars you are. Ready to wrap this up? Let’s go!

First things first, let's figure out exactly what we're looking for. The problem asks for the quotient, which means we're going to be dividing. But what are we dividing? It’s the quotient of two things:

  1. The number 42,300
  2. The sum of the numbers 13,285 and 715

Okay, so before we can divide, we've got a little sum to take care of. We need to find out what we get when we add 13,285 and 715. Let’s write this part down mathematically:

13285 + 715 = ?

Time for some addition! Let’s add 13,285 and 715 together. Line up those numbers and add carefully. The result is:

13285 + 715 = 14000

Awesome! We’ve found our sum. Now we know that one part of our division is 14,000. The other part is 42,300, which is waiting for us to divide it by our sum.

So, our next step is to divide 42,300 by 14,000. Let’s write this down:

42300 / 14000 = ?

Time for some division! You can use a calculator or do it manually. When we divide 42,300 by 14,000, we get:

42300 / 14000 = 3.02142857143 (approximately)

Now, since we're dealing with real-world problems, we can round this to a more practical number. Let’s round it to two decimal places:

  1. 02

And there you have it! We’ve found the quotient. The final answer to this problem is approximately 3.02.

To recap, the mathematical expression for this problem is:

42300 / (13285 + 715)

And the result of this expression is:

  1. 02 (approximately)

You guys are absolutely amazing! By carefully breaking down the problem, handling the sum first, and then dividing, you’ve nailed the last problem. You've officially conquered these math challenges!

Conclusion

So, there you have it, guys! We've tackled some awesome math problems today, breaking them down into easy steps and turning words into mathematical expressions. You've learned how to handle sums, products, differences, and quotients like total pros. Remember, the key to solving these problems is to take it one step at a time, understand what each word means, and keep practicing.

Math can be super fun when you approach it with a clear head and a step-by-step strategy. Keep up the great work, and remember to challenge yourself with new problems. You've got this! Keep shining and keep solving! You're all math superstars in the making!