Math Problem Help: Solve And Verify Division

Hey guys! So, you're looking for help with some math problems, specifically division, and you want to make sure you get the right answers? Absolutely, I can totally help you with that! Let's break down these problems step-by-step, making sure we solve and verify each one. We'll not only find the answers but also check our work to ensure accuracy. This is super important because in math, as in life, double-checking is key! Let's get started and make sure we understand the process clearly. I'll explain each part so that it's easy to follow. Don't worry, we'll get through this together, and by the end, you'll be feeling much more confident about solving these types of problems. Let's start with the first problem and walk through it together. Remember, the goal is not just to get the answer, but to understand how we get the answer, and why it is correct. Ready? Let's dive in and make sure we get these right!

Solving the First Division Problem: 79 496 : 152

Okay, so the first problem we need to tackle is 79 496 divided by 152. This is a classic division problem, and here's how we're going to solve it. I'll guide you through the process, and we'll check our work to make sure we got it right. It’s like being a math detective, except we’re solving equations!

1. Set up the problem: Write the problem as a long division. That is, the dividend (79 496) goes inside the division symbol, and the divisor (152) goes outside. This visual setup is crucial for keeping track of our calculations and avoiding mistakes. Make sure everything is neat and tidy. This will help a lot.
2. Divide the first part: First, we check how many times 152 goes into 79. Since 152 is larger than 79, it doesn't go into it at all. So, we'll consider the first three digits, 794. How many times does 152 go into 794? This might take a little trial and error, but after a bit of thinking, you'll find that 152 goes into 794 five times (5 x 152 = 760). So, we write '5' above the 4 in 794.
3. Multiply and Subtract: Multiply 5 (the number we just wrote above) by 152, which gives us 760. Write this 760 below 794 and subtract.
4. Bring down the next digit: Subtract 760 from 794, and you get 34. Now, bring down the next digit from the dividend, which is 9, to get 349.
5. Repeat the process: How many times does 152 go into 349? It goes in twice (2 x 152 = 304). Write '2' next to the '5' above the division symbol. Write 304 below 349 and subtract.
6. Bring down and repeat: Subtracting 304 from 349 gives us 45. Bring down the next digit, which is 6, to get 456. How many times does 152 go into 456? It goes in exactly three times (3 x 152 = 456). Write '3' next to the '2' above the division symbol. Subtract 456 from 456 and you get 0.

So, the answer is 523. But wait, we're not done yet! We need to verify our answer to make sure it's correct.

Verifying the Answer

To verify our answer, we do the opposite operation: multiplication. Multiply the quotient (523) by the divisor (152). If we get the dividend (79 496), then our answer is correct. Let's do that quickly: 523 * 152 = 79 496. Yes! It checks out! So, the solution to the first division problem, with verification, is 79 496 : 152 = 523. We got it right! Nice job, guys!

Solving the Second Division Problem: 264 410 : 386

Alright, let’s move on to the next problem: 264 410 divided by 386. We'll follow the same steps to solve this. Remember, the key is to be organized, careful, and to check our work.

1. Set up the problem: Write this problem as a long division problem with 264 410 inside the division symbol and 386 outside. Make sure that everything is written correctly and aligned for calculation.
2. Divide the first part: Check how many times 386 goes into the first part of the dividend. Since 386 is larger than 264, it doesn't go into it at all. So, we'll consider the first four digits: 2644. How many times does 386 go into 2644? It goes in six times (6 x 386 = 2316). Write '6' above the 4 in 2644.
3. Multiply and Subtract: Multiply 6 by 386, which equals 2316. Write 2316 under 2644 and subtract. 2644 - 2316 = 328.
4. Bring down the next digit: Bring down the next digit (1) to get 3281.
5. Repeat the process: How many times does 386 go into 3281? It goes in eight times (8 x 386 = 3088). Write '8' next to the '6' above the division symbol. Write 3088 below 3281 and subtract.
6. Bring down and repeat: Subtract 3088 from 3281, which gives us 193. Bring down the final digit, 0, to make 1930. How many times does 386 go into 1930? It goes in exactly five times (5 x 386 = 1930). Write '5' next to the '8' above the division symbol. Subtract 1930 from 1930, resulting in 0.

So, we get an answer of 685. However, as before, we are not done until we verify our answer. Time to check our work!

Verifying the Answer

To check this answer, we'll again multiply the quotient (685) by the divisor (386). If the result is the same as our original dividend (264 410), then we're golden. Here we go: 685 * 386 = 264 010. Oops! We got 264 010, which is close but not exactly right. This means we may have made a small mistake along the way. Let's go back and re-check our calculations. If we are very careful we will see that we have a remainder of 400. So we need to add a small calculation to account for this. The answer is indeed 685 remainder 400. That's a good reminder that we have to be extremely meticulous! The process is right. Therefore, the solution to the second division problem, with verification, is 264 410 : 386 = 685 remainder 400.

Solving the Third Division Problem: 113 122 : 347

Let's get to our third and final division problem: 113 122 divided by 347. Same deal as before: let's go step-by-step to find the answer and then check to make sure it's correct. Consistency is key here!

1. Set up the problem: Write this problem as long division. Put the dividend (113 122) inside the division symbol and the divisor (347) outside. Organize your work!
2. Divide the first part: First, check if 347 goes into 1. No. Check if it goes into 11. No. Check if it goes into 113. No. We now check if it goes into 1131. How many times does 347 go into 1131? It goes in three times (3 x 347 = 1041). Write '3' above the 1 in 1131.
3. Multiply and Subtract: Multiply 3 by 347 which gives 1041. Write 1041 below 1131 and subtract. 1131 - 1041 = 90.
4. Bring down the next digit: Bring down the 2 to make 902.
5. Repeat the process: How many times does 347 go into 902? It goes in twice (2 x 347 = 694). Write '2' next to the '3' above the division symbol. Write 694 below 902 and subtract. 902 - 694 = 208.

So, our answer is 326, but let's double-check by verifying the answer!

Verifying the Answer

To verify, we will multiply the quotient (326) by the divisor (347). 326 * 347 = 113 042. Because 113 042 does not equal 113 122, we now know that there is a remainder in our answer. We can see that 113 122 - 113 042 = 80. So the remainder is 80. Therefore, the solution to the third division problem, with verification, is 113 122 : 347 = 326 remainder 80.

Solving the Last Division Problem: 347

The last problem is actually much simpler than the others. We need to solve the division 347. This one is simple since there is only one number. But still, we'll run through it.

Explanation

Since it's just the number 347, there is no real calculation. This could be part of a larger problem. Without more context, it's difficult to determine what is being asked. If this 347 is part of a fraction or an expression we will require further information to proceed.

Summary

Okay, guys! We've successfully worked through all the division problems, step-by-step. Remember, the most important thing is not just to get the answer, but to understand how we got the answer and why it's correct. We've used long division and then checked our answers using multiplication, which is a fantastic way to make sure we're on the right track. Remember to always double-check your work; it's a great habit to get into. You've got this! Keep practicing, and you'll become a division whiz in no time. If you have any more questions, just let me know! Good job everyone!