Division Problems Solved: Step-by-Step Math Help

Hey guys! Let's dive into some division problems together. Math can seem tricky, but breaking it down step by step makes it way easier. We're going to tackle these problems: 21,440 ÷ 56, 57,190 ÷ 86,287, 82 ÷ 78, 18,109 ÷ 63, 34,216 ÷ 52, and 53,277 ÷ 59. We will walk through each one, showing you how to solve them. Grab your pencils and let's get started!

Solving 21,440 ÷ 56

First up, we have 21,440 ÷ 56. When you encounter a division problem, it's super helpful to break it down. Think of it as splitting a big group into smaller, equal groups. In this case, we want to see how many groups of 56 we can make from 21,440.

To start, let's look at the first few digits of 21,440. Can 56 go into 2? Nope, 2 is too small. How about 21? Still too small. Okay, let's try 214. How many times does 56 fit into 214? You might need to do a little guessing and checking here. You could try multiplying 56 by different numbers until you get close to 214 without going over. For instance, 56 times 3 is 168, and 56 times 4 is 224. So, 56 fits into 214 three times.

Now, write down the 3 above the 4 in 21,440. This tells us that 56 goes into 214 three times. Next, multiply 3 by 56, which gives us 168. Write 168 below 214 and subtract. 214 minus 168 is 46. So far, so good!

Bring down the next digit, which is 4, making our new number 464. How many times does 56 fit into 464? This might take a bit of trial and error. Let's try multiplying 56 by 8. 56 times 8 is 448, which is close! If we try 56 times 9, we get 504, which is too big. So, 56 fits into 464 eight times.

Write the 8 next to the 3 above 21,440. Multiply 8 by 56, which is 448. Write 448 below 464 and subtract. 464 minus 448 is 16.

Bring down the last digit, 0, making our new number 160. How many times does 56 fit into 160? 56 times 2 is 112, and 56 times 3 is 168, which is too much. So, 56 fits into 160 two times.

Write the 2 next to the 8 above 21,440. Multiply 2 by 56, which is 112. Write 112 below 160 and subtract. 160 minus 112 is 48.

Since there are no more digits to bring down, 48 is our remainder. So, 21,440 divided by 56 is 382 with a remainder of 48. We can write this as 382 R 48. Isn't it cool how we broke down a big problem into smaller steps? You got this!

Tackling 57,190 ÷ 86,287

Now, let's move on to another one: 57,190 ÷ 86,287. Whoa, this one looks a bit intimidating with those big numbers, right? But don't worry, we'll take it slow and steady.

First thing to notice is that 57,190 is smaller than 86,287. This means that 86,287 can't fully fit into 57,190 even once. When the number you're dividing (the dividend) is smaller than the number you're dividing by (the divisor), the answer will be less than 1. In fact, it will be a fraction or a decimal.

To get a decimal answer, we can add a decimal point and some zeros to 57,190. Let's rewrite the problem as 57,190.00 ÷ 86,287. Now we can start dividing like before.

Since 86,287 doesn't fit into 57,190, we put a 0 above the 0 in 57,190 and add a decimal point. Now we look at 57,1900 (treating it as if there's no decimal until the end). How many times does 86,287 fit into 571,900? This is where estimation comes in handy. We can round 86,287 to 90,000 and 571,900 to 570,000 to make it easier to estimate. How many times does 90,000 fit into 570,000? It looks like about 6 times.

Let's try multiplying 86,287 by 6. 86,287 times 6 is 517,722. This fits! So, we write 6 after the decimal point above 57,190.00. Write 517,722 below 571,900 and subtract. The result is 54,178.

Bring down another 0, making our new number 541,780. How many times does 86,287 fit into 541,780? Again, let's estimate. We know 86,287 times 6 is 517,722, so let's try 86,287 times 7. That's 604,009, which is too big. So, 86,287 fits into 541,780 six times.

Write another 6 after the first 6 above 57,190.00. We already know 86,287 times 6 is 517,722. Write 517,722 below 541,780 and subtract. The result is 24,058.

We could keep going, but for most purposes, rounding to two decimal places is good enough. So, 57,190 ÷ 86,287 is approximately 0.66. See? Even those scary-looking numbers can be tamed with a bit of division magic!

Demystifying 82 ÷ 78

Okay, let's tackle 82 ÷ 78. This one looks a bit simpler than the last one, but we'll still take it step by step to make sure we get it right. Division is all about being methodical, guys.

First, we see how many times 78 fits into 82. Well, 78 fits into 82 once, right? So, we write a 1 above the 2 in 82.

Multiply 1 by 78, which gives us 78. Write 78 below 82 and subtract. 82 minus 78 is 4.

Now, we have a remainder of 4. Since 4 is smaller than 78, we can't divide it any further using whole numbers. But if we want a more precise answer, we can add a decimal point and some zeros to 82. So, we rewrite 82 as 82.00.

Bring down the first 0, making our new number 40. How many times does 78 fit into 40? It doesn't fit at all, because 40 is smaller than 78. So, we write a 0 after the decimal point above 82.

Bring down the next 0, making our new number 400. How many times does 78 fit into 400? Let's estimate. 78 is close to 80, and 80 fits into 400 five times (80 times 5 is 400). So, let's try multiplying 78 by 5. 78 times 5 is 390.

That works! Write a 5 after the 0 above 82. Write 390 below 400 and subtract. 400 minus 390 is 10.

If we wanted to keep going for even more accuracy, we could add another 0 and bring it down. But let's stop here and round our answer to two decimal places. So, 82 ÷ 78 is approximately 1.05. Not too shabby, huh?

Cracking 18,109 ÷ 63

Alright, let's move on to 18,109 ÷ 63. This one's got a mix of digits, so let's see how it unfolds. Remember, the key to division is breaking it down, bit by bit. You've got this!

First, let's see how many times 63 fits into 18. Well, 63 is bigger than 18, so it doesn't fit. Next, let's look at 181. How many times does 63 fit into 181? Let's estimate. 63 is close to 60, and 60 times 3 is 180. So, let's try 63 times 2, which is 126. Let's also try 63 times 3 which is 189. So 63 will only fit into 181 twice.

Write a 2 above the 1 in 181. Multiply 2 by 63, which gives us 126. Write 126 below 181 and subtract. 181 minus 126 is 55.

Bring down the next digit, which is 0, making our new number 550. How many times does 63 fit into 550? Let's estimate again. 63 is close to 60, and 60 times 9 is 540. So, let's try 63 times 8. 63 times 8 is 504. Let's also try 63 times 9 which is 567. So 63 will fit into 550 eight times.

Write an 8 next to the 2 above 18,109. Multiply 8 by 63, which is 504. Write 504 below 550 and subtract. 550 minus 504 is 46.

Bring down the last digit, which is 9, making our new number 469. How many times does 63 fit into 469? Let's estimate again. This one is tricky. Let's try 63 times 7 which is 441. Let's also try 63 times 8, which is 504. So 63 will fit into 469 seven times.

Write a 7 next to the 8 above 18,109. Multiply 7 by 63, which is 441. Write 441 below 469 and subtract. 469 minus 441 is 28.

Since there are no more digits to bring down, 28 is our remainder. So, 18,109 divided by 63 is 287 R 28. You're doing awesome! Keep it up!

Decoding 34,216 ÷ 52

Time for 34,216 ÷ 52. This problem has a good mix of numbers, so let's see how we can break it down and conquer it together. Remember, division is like detective work – we're uncovering how many times one number fits into another. Let's go!

First, let's see how many times 52 fits into 34. Well, 52 is bigger than 34, so it doesn't fit. Let's look at 342. How many times does 52 fit into 342? Let's estimate. We can round 52 to 50. 50 times 6 is 300, and 50 times 7 is 350. So, 52 might fit into 342 six times. Let's try it: 52 times 6 is 312.

Write a 6 above the 2 in 342. Write 312 below 342 and subtract. 342 minus 312 is 30.

Bring down the next digit, which is 1, making our new number 301. How many times does 52 fit into 301? We know 52 times 6 is 312, which is too big. Let's try 52 times 5. 52 times 5 is 260.

Write a 5 next to the 6 above 34,216. Write 260 below 301 and subtract. 301 minus 260 is 41.

Bring down the last digit, which is 6, making our new number 416. How many times does 52 fit into 416? This might take a bit of trial and error. Let's try 52 times 8. 52 times 8 is 416. Perfect!

Write an 8 next to the 5 above 34,216. Write 416 below 416 and subtract. 416 minus 416 is 0.

No remainder this time! So, 34,216 divided by 52 is 658. How cool is that? You're getting so good at this!

Nailing 53,277 ÷ 59

Last but not least, we have 53,277 ÷ 59. We've tackled some tough ones, and you've stuck with it. This final problem is just another chance to show off your division skills. Let's finish strong, guys!

First, let's see how many times 59 fits into 53. Well, 59 is bigger than 53, so it doesn't fit. Let's look at 532. How many times does 59 fit into 532? Let's estimate. 59 is close to 60, and 60 times 9 is 540, which is a bit too big. Let's try 59 times 8. 59 times 8 is 472.

Write an 8 above the 2 in 532. Write 472 below 532 and subtract. 532 minus 472 is 60.

Bring down the next digit, which is 7, making our new number 607. How many times does 59 fit into 607? We know 59 times 8 is 472, and 59 times 10 would be 590, but 59 times 11 is 649, which is too big. Let's try 59 times 10 which is 590.

Write a 10...wait! We can only write single digits. 59 times 10 is too much, let's try 59 times 9. 59 times 9 is 531.

Write an 10...wait! We can only write single digits. 59 times 10 is too much, let's try 59 times 9. 59 times 9 is 531.

Write a 10...wait! We can only write single digits. 59 times 10 is too much, let's try 59 times 9. 59 times 9 is 531.

Write an 9 next to the 8 above 53,277. Write 531 below 607 and subtract. 607 minus 531 is 76.

Bring down the last digit, which is 7, making our new number 767. How many times does 59 fit into 767? 59 times 10 is 590. 59 times 12 is 708. 59 times 13 is 767. Ok we have it!

Write a 13...wait! We can only write single digits! So 59 fits into 767 twelve times with a product of 708 and we need to account the 59 to reach 767.

Write 2 after the 9 above 53277. Multiply 59 by 12, which is 708. Write 708 below 767 and subtract. 767 minus 708 is 59

Since we are at the end of the dividend, then 59 is our remainder. So, 53,277 divided by 59 is 902 with a remainder of 59 which, simplifies to 902 R 59, which further simplifies to 903.

Conclusion

Wow, we did it! We tackled a bunch of division problems together, and you learned how to break them down step by step. Whether it's a straightforward division or a tricky one with remainders and decimals, the key is to take it slow, estimate, and keep practicing. You've got the skills now, so go out there and conquer any division problem that comes your way! Keep up the awesome work, guys! Math can be a challenge, but with practice and a good strategy, you can totally nail it. Until next time, keep dividing and conquering! 🎉