Mastering Division A Step-by-Step Guide To Finding Quotients

In the realm of mathematics, division stands as a fundamental operation, essential for partitioning quantities and understanding relationships between numbers. This comprehensive guide delves into the process of finding quotients for a series of division problems, providing a step-by-step approach to mastering this crucial skill. We'll explore a variety of scenarios, from simple divisions to more complex problems, ensuring a thorough understanding of the underlying principles. So, let's embark on this mathematical journey and unlock the secrets of division!

Problem 1 27)1,296

Our initial challenge involves dividing 1,296 by 27. To conquer this, we'll employ the long division method, a systematic approach that breaks down the problem into manageable steps. First, we assess how many times 27 fits into the initial digits of 1,296. Since 27 doesn't go into 1 or 12, we consider the first three digits, 129. We estimate that 27 goes into 129 approximately 4 times (27 x 4 = 108). We write the 4 above the 9 in 1,296 and subtract 108 from 129, resulting in 21. Next, we bring down the 6 from 1,296, forming 216. We then determine how many times 27 goes into 216. Through estimation or multiplication, we find that 27 goes into 216 exactly 8 times (27 x 8 = 216). We write the 8 above the 6 in 1,296 and subtract 216 from 216, leaving us with 0. This signifies that the division is complete, and the quotient is 48. Therefore, 1,296 divided by 27 equals 48.

Problem 2 14)2,856

Moving on to the second problem, we aim to divide 2,856 by 14. Once again, we turn to the reliable long division method. We begin by examining how many times 14 fits into the initial digits of 2,856. 14 doesn't go into 2, so we consider the first two digits, 28. We observe that 14 goes into 28 exactly 2 times (14 x 2 = 28). We write the 2 above the 8 in 2,856 and subtract 28 from 28, resulting in 0. We then bring down the 5 from 2,856. However, 14 doesn't go into 5, so we write a 0 above the 5 in 2,856 and bring down the next digit, 6, forming 56. Now, we determine how many times 14 goes into 56. We find that 14 goes into 56 exactly 4 times (14 x 4 = 56). We write the 4 above the 6 in 2,856 and subtract 56 from 56, leaving us with 0. This indicates that the division is complete, and the quotient is 204. Thus, 2,856 divided by 14 equals 204.

Problem 3 22)1,056

For the third problem, we seek to divide 1,056 by 22. Employing long division once more, we start by assessing how many times 22 fits into the initial digits of 1,056. 22 doesn't go into 1 or 10, so we consider the first three digits, 105. We estimate that 22 goes into 105 approximately 4 times (22 x 4 = 88). We write the 4 above the 5 in 1,056 and subtract 88 from 105, resulting in 17. We then bring down the 6 from 1,056, forming 176. Next, we determine how many times 22 goes into 176. Through estimation or multiplication, we find that 22 goes into 176 exactly 8 times (22 x 8 = 176). We write the 8 above the 6 in 1,056 and subtract 176 from 176, leaving us with 0. This signifies that the division is complete, and the quotient is 48. Hence, 1,056 divided by 22 equals 48.

Problem 4 25)2,125

In this problem, we aim to divide 2,125 by 25. We'll utilize long division again, starting by determining how many times 25 fits into the initial digits of 2,125. 25 doesn't go into 2 or 21, so we consider the first three digits, 212. We estimate that 25 goes into 212 approximately 8 times (25 x 8 = 200). We write the 8 above the 2 in 2,125 and subtract 200 from 212, resulting in 12. We then bring down the 5 from 2,125, forming 125. Next, we determine how many times 25 goes into 125. We find that 25 goes into 125 exactly 5 times (25 x 5 = 125). We write the 5 above the 5 in 2,125 and subtract 125 from 125, leaving us with 0. This indicates that the division is complete, and the quotient is 85. Therefore, 2,125 divided by 25 equals 85.

Problem 5 30)1,440

Now, let's tackle the division of 1,440 by 30. Employing long division, we start by assessing how many times 30 fits into the initial digits of 1,440. 30 doesn't go into 1 or 14, so we consider the first three digits, 144. We estimate that 30 goes into 144 approximately 4 times (30 x 4 = 120). We write the 4 above the 4 in 1,440 and subtract 120 from 144, resulting in 24. We then bring down the 0 from 1,440, forming 240. Next, we determine how many times 30 goes into 240. We find that 30 goes into 240 exactly 8 times (30 x 8 = 240). We write the 8 above the 0 in 1,440 and subtract 240 from 240, leaving us with 0. This signifies that the division is complete, and the quotient is 48. Thus, 1,440 divided by 30 equals 48.

Problem 6 19)8,208

For the sixth problem, we aim to divide 8,208 by 19. We will use the long division method. Start by determining how many times 19 goes into 82. We estimate 19 goes into 82 four times (19 * 4 = 76). Write 4 above the 2 in 8,208. Subtract 76 from 82, which leaves 6. Bring down the 0 to form 60. Now, determine how many times 19 goes into 60. We estimate 19 goes into 60 three times (19 * 3 = 57). Write 3 above the 0 in 8,208. Subtract 57 from 60, which leaves 3. Bring down the 8 to form 38. Determine how many times 19 goes into 38. We find 19 goes into 38 exactly two times (19 * 2 = 38). Write 2 above the 8 in 8,208. Subtract 38 from 38, which leaves 0. The division is complete, and the quotient is 432. Therefore, 8,208 divided by 19 equals 432.

Problem 7 42)8,610

In this case, we are dividing 8,610 by 42. Using long division, we first assess how many times 42 goes into 86. We estimate that 42 goes into 86 two times (42 * 2 = 84). Write 2 above the 6 in 8,610. Subtract 84 from 86, which leaves 2. Bring down the 1 to form 21. Since 42 does not go into 21, write 0 above the 1 in 8,610. Bring down the 0 to form 210. Now, we determine how many times 42 goes into 210. We find that 42 goes into 210 exactly 5 times (42 * 5 = 210). Write 5 above the 0 in 8,610. Subtract 210 from 210, which leaves 0. The division is complete, and the quotient is 205. Therefore, 8,610 divided by 42 equals 205.

Problem 8 36)4,500

Here, we need to divide 4,500 by 36. Employing long division, we start by assessing how many times 36 fits into 45. We estimate 36 goes into 45 one time (36 * 1 = 36). Write 1 above the 5 in 4,500. Subtract 36 from 45, which leaves 9. Bring down the 0 to form 90. Determine how many times 36 goes into 90. We estimate 36 goes into 90 two times (36 * 2 = 72). Write 2 above the first 0 in 4,500. Subtract 72 from 90, which leaves 18. Bring down the next 0 to form 180. Determine how many times 36 goes into 180. We find that 36 goes into 180 exactly 5 times (36 * 5 = 180). Write 5 above the last 0 in 4,500. Subtract 180 from 180, which leaves 0. The division is complete, and the quotient is 125. Thus, 4,500 divided by 36 equals 125.

Problem 9 44)9,020

In this problem, we divide 9,020 by 44. Using long division, we first assess how many times 44 goes into 90. We estimate 44 goes into 90 two times (44 * 2 = 88). Write 2 above the 0 in 9,020. Subtract 88 from 90, which leaves 2. Bring down the 2 to form 22. Since 44 does not go into 22, write 0 above the 2 in 9,020. Bring down the 0 to form 220. Now, determine how many times 44 goes into 220. We find that 44 goes into 220 exactly 5 times (44 * 5 = 220). Write 5 above the 0 in 9,020. Subtract 220 from 220, which leaves 0. The division is complete, and the quotient is 205. Therefore, 9,020 divided by 44 equals 205.

Problem 10 29)1,363

To find the quotient of 1,363 divided by 29, we use long division. First, we determine how many times 29 goes into 136. We estimate that 29 goes into 136 four times (29 * 4 = 116). Write 4 above the 6 in 1,363. Subtract 116 from 136, which leaves 20. Bring down the 3 to form 203. Now, determine how many times 29 goes into 203. We find that 29 goes into 203 exactly 7 times (29 * 7 = 203). Write 7 above the 3 in 1,363. Subtract 203 from 203, which leaves 0. The division is complete, and the quotient is 47. Thus, 1,363 divided by 29 equals 47.

Problem 11 31)7,998

Here, we divide 7,998 by 31 using long division. We start by assessing how many times 31 goes into 79. We estimate that 31 goes into 79 two times (31 * 2 = 62). Write 2 above the 9 in 7,998. Subtract 62 from 79, which leaves 17. Bring down the 9 to form 179. Now, determine how many times 31 goes into 179. We estimate that 31 goes into 179 five times (31 * 5 = 155). Write 5 above the next 9 in 7,998. Subtract 155 from 179, which leaves 24. Bring down the 8 to form 248. Determine how many times 31 goes into 248. We find that 31 goes into 248 exactly 8 times (31 * 8 = 248). Write 8 above the 8 in 7,998. Subtract 248 from 248, which leaves 0. The division is complete, and the quotient is 258. Therefore, 7,998 divided by 31 equals 258.

Problem 12 58)1,624

Finally, we divide 1,624 by 58. Using long division, we first assess how many times 58 goes into 162. We estimate that 58 goes into 162 two times (58 * 2 = 116). Write 2 above the 2 in 1,624. Subtract 116 from 162, which leaves 46. Bring down the 4 to form 464. Now, determine how many times 58 goes into 464. We find that 58 goes into 464 exactly 8 times (58 * 8 = 464). Write 8 above the 4 in 1,624. Subtract 464 from 464, which leaves 0. The division is complete, and the quotient is 28. Thus, 1,624 divided by 58 equals 28.

Conclusion

Through this comprehensive guide, we've systematically tackled a variety of division problems, employing the long division method to find the quotients. From dividing 1,296 by 27 to dividing 1,624 by 58, we've honed our skills and deepened our understanding of this fundamental mathematical operation. With consistent practice and a firm grasp of the principles outlined here, you'll be well-equipped to conquer any division challenge that comes your way.