Math Problems Solved: Step-by-Step Calculations
Hey guys! Let's break down these math problems step-by-step. We're going to solve: 1020 ÷ 5, 550 ÷ 10, 320 × 67, 41 × 17, 2630 ÷ 12, and 22 × 15. I'll show you all the calculations, so you can follow along and understand how we get to the answers. Let's dive in!
1. Solving 1020 ÷ 5
When tackling division problems like 1020 ÷ 5, it’s essential to break it down into manageable steps. This approach not only makes the calculation easier but also helps in understanding the process thoroughly. So, let's get started by focusing on the first few digits of the dividend, which is 1020 in this case.
First, we look at the number 10. Can 5 go into 10? Absolutely! It goes in exactly 2 times. So, we write '2' above the 0 in 1020. Next, we multiply 2 by 5, which gives us 10. We subtract this 10 from the original 10, leaving us with 0. This indicates that 5 goes into 10 a clean 2 times with no remainder so far.
Now, we bring down the next digit, which is 2. So, we now have 2. Can 5 go into 2? Nope, 5 is larger than 2. In this case, we write '0' next to the 2 in our quotient (the answer above). This is a crucial step because it holds the place value. If we skip this, our final answer will be off.
Since 5 doesn't go into 2, we bring down the next digit, which is 0. Now, we have 20. How many times does 5 go into 20? Exactly 4 times! We write '4' next to the 0 in our quotient. Now, we multiply 4 by 5, which gives us 20. Subtracting this 20 from the 20 we had leaves us with 0. This means we have no remainder.
So, when we put it all together, we have 204. This tells us that 1020 divided by 5 equals 204. To double-check our work, we can multiply 204 by 5. If we did it correctly, we should get 1020. Let's see: 204 multiplied by 5 is indeed 1020. Great! We've confirmed our answer.
Therefore, the solution to 1020 ÷ 5 is 204. Remember, breaking down division problems into smaller, more manageable steps is key to solving them accurately. It's like building a puzzle – piece by piece, we arrive at the complete picture. And always double-check your answer to ensure accuracy!
2. Solving 550 ÷ 10
Let's tackle the problem of 550 ÷ 10 together! Dividing by 10 is often one of the simpler arithmetic tasks, and I'll walk you through it to ensure you grasp the concept fully. When you're dividing by 10, you're essentially looking at how many groups of 10 can fit into the number 550.
The most straightforward way to handle this division is to recognize a pattern. Whenever you divide a number by 10, you can think of it as simply removing a zero from the end of the number. This works because our number system is based on powers of 10. Each place value (ones, tens, hundreds, etc.) represents a power of 10, and dividing by 10 shifts each digit one place value to the right.
So, if we look at 550, we can remove one zero from the end. This leaves us with 55. That's it! The answer to 550 ÷ 10 is 55. Easy peasy, right?
Now, let's think about why this works. The number 550 can be thought of as 55 tens. When you divide 55 tens by 10, you're asking, "How many whole groups of 10 are in 55 tens?" The answer is simply 55.
To further illustrate, consider this: 10 goes into 550 fifty-five times. If you were to multiply 55 by 10, you would get 550, confirming our solution. This is an excellent way to check your answer and ensure that you've performed the division correctly.
So, to recap, dividing by 10 is a breeze. Just remove the trailing zero, and you have your answer. The solution to 550 ÷ 10 is 55. Remember this trick, and you'll be dividing by 10 in your head in no time!
3. Solving 320 × 67
Okay, let's dive into the multiplication problem 320 × 67. This one might seem a bit more complex, but don't worry, we'll break it down step-by-step. We're going to use the standard multiplication method, where we multiply each digit of the second number (67) by the first number (320), and then add the results together.
First, we start by multiplying 320 by the digit in the ones place of 67, which is 7. So, we calculate 7 times 320. You can think of this as (7 × 0) + (7 × 20) + (7 × 300). Let's do it:
- 7 × 0 = 0
- 7 × 2 = 14, so 7 × 20 = 140
- 7 × 3 = 21, so 7 × 300 = 2100
Adding these together: 0 + 140 + 2100 = 2240. So, 320 multiplied by 7 is 2240. We'll write this down as our first partial product.
Next, we're going to multiply 320 by the digit in the tens place of 67, which is 6. However, since it's in the tens place, we're actually multiplying by 60. To keep things organized, we'll add a zero at the end of our second partial product as a placeholder. Now, let's multiply 6 by 320:
- 6 × 0 = 0
- 6 × 2 = 12, so we write down 2 and carry over 1
- 6 × 3 = 18, plus the 1 we carried over, equals 19
So, 6 × 320 = 1920. But remember, we're actually multiplying by 60, so our partial product is 19200.
Now, we have our two partial products: 2240 and 19200. To get the final answer, we need to add these together:
2240
- 19200
= 21440
So, 320 × 67 equals 21440. It's a big number, but by breaking the multiplication down into smaller steps, we made it manageable. Remember, patience and organization are key when tackling larger multiplication problems.
4. Solving 41 × 17
Alright, let's tackle the multiplication problem 41 × 17. We're going to use the standard multiplication method here as well. This means we'll multiply each digit of 17 by 41, and then add the results together. Breaking it down like this makes the process much simpler.
First, we'll multiply 41 by the digit in the ones place of 17, which is 7. So, we need to calculate 7 times 41. Let's do it:
- 7 × 1 = 7
- 7 × 4 = 28
Putting these together, we get 287. So, 41 multiplied by 7 is 287. This is our first partial product.
Next, we're going to multiply 41 by the digit in the tens place of 17, which is 1. But since it's in the tens place, we're actually multiplying by 10. To keep things organized, we'll add a zero at the end of our second partial product as a placeholder. Now, let's multiply 1 by 41:
- 1 × 41 = 41
Since we're multiplying by 10, our partial product is 410.
Now, we have our two partial products: 287 and 410. To get the final answer, we need to add these together:
287
- 410
= 697
So, 41 × 17 equals 697. See? By breaking it down into these manageable steps, even a seemingly complex multiplication becomes pretty straightforward. Always remember to take your time, stay organized, and you'll nail it every time!
5. Solving 2630 ÷ 12
Now, let's dive into the division problem 2630 ÷ 12. Division problems can sometimes look intimidating, but we'll break this down step-by-step to make it super clear. We're essentially figuring out how many times 12 can fit into 2630.
First, we look at the first two digits of the dividend, which is 26. How many times does 12 go into 26? Well, 12 goes into 26 twice (since 12 × 2 = 24), so we write '2' above the 6 in 2630.
Next, we multiply 2 by 12, which gives us 24. We subtract this 24 from the 26, leaving us with 2. This means that after taking out two groups of 12, we have 2 left over.
Now, we bring down the next digit from 2630, which is 3. So, we now have 23. How many times does 12 go into 23? It goes in once (since 12 × 1 = 12), so we write '1' next to the '2' in our quotient (the answer above).
We multiply 1 by 12, which gives us 12. Subtracting this 12 from 23 leaves us with 11. This means that after taking out one more group of 12, we have 11 left over.
Now, we bring down the last digit from 2630, which is 0. So, we have 110. How many times does 12 go into 110? This might take a bit of thinking, but 12 goes into 110 nine times (since 12 × 9 = 108), so we write '9' next to the '1' in our quotient.
We multiply 9 by 12, which gives us 108. Subtracting this 108 from 110 leaves us with 2. This is our remainder.
So, when we put it all together, we get 219 with a remainder of 2. This means that 2630 divided by 12 equals 219 with 2 left over. We can write this as 2630 ÷ 12 = 219 R 2.
To double-check our work, we can multiply 219 by 12 and then add the remainder 2. If we did it correctly, we should get 2630. Let's see: (219 × 12) + 2 = 2628 + 2 = 2630. Great! We've confirmed our answer.
6. Solving 22 × 15
Let's tackle the final multiplication problem, 22 × 15. We're going to stick with our standard multiplication method, which means we'll multiply each digit of 15 by 22 and then add the results. This step-by-step approach will keep everything nice and clear.
First, we'll multiply 22 by the digit in the ones place of 15, which is 5. So, we need to calculate 5 times 22. Let's break it down:
- 5 × 2 = 10, so we write down 0 and carry over 1
- 5 × 2 = 10, plus the 1 we carried over, equals 11
Putting these together, we get 110. So, 22 multiplied by 5 is 110. This is our first partial product.
Next, we're going to multiply 22 by the digit in the tens place of 15, which is 1. But remember, since it's in the tens place, we're actually multiplying by 10. To keep things organized, we'll add a zero at the end of our second partial product as a placeholder. Now, let's multiply 1 by 22:
- 1 × 22 = 22
Since we're multiplying by 10, our partial product is 220.
Now, we have our two partial products: 110 and 220. To get the final answer, we need to add these together:
110
- 220
= 330
So, 22 × 15 equals 330. We've reached the end of our math problem set! By consistently using our step-by-step method, we were able to solve each multiplication with confidence. Remember, practice makes perfect, so keep at it!
Conclusion
So, guys, we've solved all six math problems: 1020 ÷ 5 = 204, 550 ÷ 10 = 55, 320 × 67 = 21440, 41 × 17 = 697, 2630 ÷ 12 = 219 R 2, and 22 × 15 = 330. I hope breaking each problem down step-by-step helped you understand the process. Remember, math can be fun when you take it one step at a time! Keep practicing, and you'll become a math whiz in no time!