Mastering Division: Step-by-Step Solutions & Examples

October 15, 2025 by TextBrain Team 54 views

Hey guys! Let's dive into the world of division. This guide breaks down several division problems step-by-step, making it easy for you to understand and practice. Whether you're a student, a teacher, or just someone looking to brush up on your math skills, you're in the right place. We'll cover a range of problems, from straightforward divisions to those with remainders, ensuring you get a solid grasp of the concept. Division is a fundamental math operation, and mastering it opens doors to more complex mathematical challenges. So, grab your pencils and let's get started! We will tackle the following divisions: 3507:5, 80/4:9, 8753:7, 2567:7, 7893:5, 8432:9, 9579:7, 9767:4, 2498:3, 7807:3, 9551:3, 7503:2, and 5625:3. Each problem provides a chance to practice your skills and build confidence. Remember, the key to mastering division is practice, practice, and more practice! Let's break down each problem, providing detailed solutions and explanations. This will help you understand the process and apply the concepts to similar problems.

Division Problem Breakdown

1. 3507 : 5

Let's begin with our first problem, 3507 divided by 5. This type of division is a perfect place to start when practicing division. The number 3507 is the dividend, and 5 is the divisor. Here's how we solve it:

Divide 35 by 5: 35 divided by 5 equals 7. Write 7 above the 5 in the dividend (3507).
Multiply 7 by 5: 7 times 5 equals 35. Write 35 below the 35 in the dividend.
Subtract: 35 minus 35 equals 0.
Bring down the next digit: Bring down the 0 from the dividend.
Divide 0 by 5: 0 divided by 5 equals 0. Write 0 next to the 7 above.
Multiply 0 by 5: 0 times 5 equals 0. Write 0 below the 0.
Subtract: 0 minus 0 equals 0.
Bring down the next digit: Bring down the 7 from the dividend.
Divide 7 by 5: 7 divided by 5 equals 1 (with a remainder of 2). Write 1 next to the 0 above.
Multiply 1 by 5: 1 times 5 equals 5. Write 5 below the 7.
Subtract: 7 minus 5 equals 2. The remainder is 2.

So, 3507 divided by 5 equals 701 with a remainder of 2. We can write this as 701 R 2. Remember, the remainder is what's left over after the division is complete. Mastering the remainder aspect of division is crucial, as it appears frequently in higher-level math. Understanding remainders will help you avoid common pitfalls as you solve more complex problems. When you get a remainder, always make sure it is smaller than the divisor; otherwise, your division is not complete.

2. 80 / 4 : 9

Next up, we have 80 divided by 4, and then the result divided by 9. This is a slightly different format, but it still relies on the same division principles. Let's break it down:

First, divide 80 by 4: 80 divided by 4 equals 20.
Now, divide 20 by 9: 20 divided by 9 equals 2 with a remainder of 2.

So, 80/4:9 equals 2 with a remainder of 2, which can be written as 2 R 2. It is essential to complete the first operation before the second one. This is why we do 80 / 4 first. The result of this initial operation is the dividend of the second operation. Always remember to maintain the order of operations. This is especially important when dealing with more complex problems. Taking the time to understand the order of operations will make solving more complex equations a breeze. Remember that when you divide by a larger number, the quotient will always be less than 1. If you struggle with division with remainders, try using the concept of multiplication.

3. 8753 : 7

Now, let's work on 8753 divided by 7: Let's solve the equation step by step.

Divide 8 by 7: 8 divided by 7 equals 1 (with a remainder of 1). Write 1 above the 8.
Multiply 1 by 7: 1 times 7 equals 7. Write 7 below the 8.
Subtract: 8 minus 7 equals 1.
Bring down the next digit: Bring down the 7 from the dividend to make 17.
Divide 17 by 7: 17 divided by 7 equals 2 (with a remainder of 3). Write 2 next to the 1 above.
Multiply 2 by 7: 2 times 7 equals 14. Write 14 below the 17.
Subtract: 17 minus 14 equals 3.
Bring down the next digit: Bring down the 5 from the dividend to make 35.
Divide 35 by 7: 35 divided by 7 equals 5. Write 5 next to the 2 above.
Multiply 5 by 7: 5 times 7 equals 35. Write 35 below the 35.
Subtract: 35 minus 35 equals 0.
Bring down the next digit: Bring down the 3 from the dividend.
Divide 3 by 7: 3 divided by 7 equals 0 (with a remainder of 3). Write 0 next to the 5 above.

So, 8753 divided by 7 equals 1250 with a remainder of 3, or 1250 R 3. The concept of remainders is very important to understand. There will be some numbers left over that cannot be equally divided. Having a good grasp on remainders will prepare you for more advanced math problems. It's all about breaking down the problem into smaller, more manageable steps. Practicing these steps repeatedly will help you become a pro at division!

4. 2567 : 7

Let's go through the division of 2567 divided by 7 step by step:

Divide 25 by 7: 25 divided by 7 equals 3 (with a remainder of 4). Write 3 above the 5.
Multiply 3 by 7: 3 times 7 equals 21. Write 21 below the 25.
Subtract: 25 minus 21 equals 4.
Bring down the next digit: Bring down the 6 from the dividend to make 46.
Divide 46 by 7: 46 divided by 7 equals 6 (with a remainder of 4). Write 6 next to the 3 above.
Multiply 6 by 7: 6 times 7 equals 42. Write 42 below the 46.
Subtract: 46 minus 42 equals 4.
Bring down the next digit: Bring down the 7 from the dividend to make 47.
Divide 47 by 7: 47 divided by 7 equals 6 (with a remainder of 5). Write 6 next to the 6 above.
Multiply 6 by 7: 6 times 7 equals 42. Write 42 below the 47.
Subtract: 47 minus 42 equals 5.

So, 2567 divided by 7 equals 366 with a remainder of 5, or 366 R 5. Keep up the great work, guys! Always double-check your work by multiplying the quotient by the divisor and adding the remainder. This will confirm you have the right answer. If it doesn't match, then you should review your math.

5. 7893 : 5

Let's proceed with 7893 divided by 5:

Divide 7 by 5: 7 divided by 5 equals 1 (with a remainder of 2). Write 1 above the 7.
Multiply 1 by 5: 1 times 5 equals 5. Write 5 below the 7.
Subtract: 7 minus 5 equals 2.
Bring down the next digit: Bring down the 8 from the dividend to make 28.
Divide 28 by 5: 28 divided by 5 equals 5 (with a remainder of 3). Write 5 next to the 1 above.
Multiply 5 by 5: 5 times 5 equals 25. Write 25 below the 28.
Subtract: 28 minus 25 equals 3.
Bring down the next digit: Bring down the 9 from the dividend to make 39.
Divide 39 by 5: 39 divided by 5 equals 7 (with a remainder of 4). Write 7 next to the 5 above.
Multiply 7 by 5: 7 times 5 equals 35. Write 35 below the 39.
Subtract: 39 minus 35 equals 4.
Bring down the next digit: Bring down the 3 from the dividend to make 43.
Divide 43 by 5: 43 divided by 5 equals 8 (with a remainder of 3). Write 8 next to the 7 above.
Multiply 8 by 5: 8 times 5 equals 40. Write 40 below the 43.
Subtract: 43 minus 40 equals 3.

So, 7893 divided by 5 equals 1578 with a remainder of 3, or 1578 R 3. Always remember to organize your work, making the steps clearer and easier to follow. Practicing will help you develop this skill more efficiently.

6. 8432 : 9

Now, let's tackle 8432 divided by 9:

Divide 84 by 9: 84 divided by 9 equals 9 (with a remainder of 3). Write 9 above the 4.
Multiply 9 by 9: 9 times 9 equals 81. Write 81 below the 84.
Subtract: 84 minus 81 equals 3.
Bring down the next digit: Bring down the 3 from the dividend to make 33.
Divide 33 by 9: 33 divided by 9 equals 3 (with a remainder of 6). Write 3 next to the 9 above.
Multiply 3 by 9: 3 times 9 equals 27. Write 27 below the 33.
Subtract: 33 minus 27 equals 6.
Bring down the next digit: Bring down the 2 from the dividend to make 62.
Divide 62 by 9: 62 divided by 9 equals 6 (with a remainder of 8). Write 6 next to the 3 above.
Multiply 6 by 9: 6 times 9 equals 54. Write 54 below the 62.
Subtract: 62 minus 54 equals 8.

So, 8432 divided by 9 equals 936 with a remainder of 8, or 936 R 8. Practicing these problems repeatedly helps build fluency in division. The more you do it, the easier it gets! Keep up the momentum. Also, you can use a calculator to check your work, but make sure you understand the process without it.

7. 9579 : 7

Next up, 9579 divided by 7:

Divide 9 by 7: 9 divided by 7 equals 1 (with a remainder of 2). Write 1 above the 9.
Multiply 1 by 7: 1 times 7 equals 7. Write 7 below the 9.
Subtract: 9 minus 7 equals 2.
Bring down the next digit: Bring down the 5 from the dividend to make 25.
Divide 25 by 7: 25 divided by 7 equals 3 (with a remainder of 4). Write 3 next to the 1 above.
Multiply 3 by 7: 3 times 7 equals 21. Write 21 below the 25.
Subtract: 25 minus 21 equals 4.
Bring down the next digit: Bring down the 7 from the dividend to make 47.
Divide 47 by 7: 47 divided by 7 equals 6 (with a remainder of 5). Write 6 next to the 3 above.
Multiply 6 by 7: 6 times 7 equals 42. Write 42 below the 47.
Subtract: 47 minus 42 equals 5.
Bring down the next digit: Bring down the 9 from the dividend to make 59.
Divide 59 by 7: 59 divided by 7 equals 8 (with a remainder of 3). Write 8 next to the 6 above.
Multiply 8 by 7: 8 times 7 equals 56. Write 56 below the 59.
Subtract: 59 minus 56 equals 3.

So, 9579 divided by 7 equals 1368 with a remainder of 3, or 1368 R 3. This will help you to improve your skills. Keep up the hard work, guys! It's all about consistent practice. If you find the steps tedious, remember that the more you practice, the faster and more comfortable you'll become.

8. 9767 : 4

Let's solve 9767 divided by 4:

Divide 9 by 4: 9 divided by 4 equals 2 (with a remainder of 1). Write 2 above the 9.
Multiply 2 by 4: 2 times 4 equals 8. Write 8 below the 9.
Subtract: 9 minus 8 equals 1.
Bring down the next digit: Bring down the 7 from the dividend to make 17.
Divide 17 by 4: 17 divided by 4 equals 4 (with a remainder of 1). Write 4 next to the 2 above.
Multiply 4 by 4: 4 times 4 equals 16. Write 16 below the 17.
Subtract: 17 minus 16 equals 1.
Bring down the next digit: Bring down the 6 from the dividend to make 16.
Divide 16 by 4: 16 divided by 4 equals 4. Write 4 next to the 4 above.
Multiply 4 by 4: 4 times 4 equals 16. Write 16 below the 16.
Subtract: 16 minus 16 equals 0.
Bring down the next digit: Bring down the 7 from the dividend.
Divide 7 by 4: 7 divided by 4 equals 1 (with a remainder of 3). Write 1 next to the 4 above.
Multiply 1 by 4: 1 times 4 equals 4. Write 4 below the 7.
Subtract: 7 minus 4 equals 3.

So, 9767 divided by 4 equals 2441 with a remainder of 3, or 2441 R 3. Remember, the key is to take your time and go step by step. It might seem challenging at first, but with practice, you'll become more confident. If you find yourself struggling with these types of division problems, then try watching some videos on the topic, there are lots of them available on the internet.

9. 2498 : 3

Alright, let's calculate 2498 divided by 3:

Divide 24 by 3: 24 divided by 3 equals 8. Write 8 above the 4.
Multiply 8 by 3: 8 times 3 equals 24. Write 24 below the 24.
Subtract: 24 minus 24 equals 0.
Bring down the next digit: Bring down the 9 from the dividend.
Divide 9 by 3: 9 divided by 3 equals 3. Write 3 next to the 8 above.
Multiply 3 by 3: 3 times 3 equals 9. Write 9 below the 9.
Subtract: 9 minus 9 equals 0.
Bring down the next digit: Bring down the 8 from the dividend.
Divide 8 by 3: 8 divided by 3 equals 2 (with a remainder of 2). Write 2 next to the 3 above.
Multiply 2 by 3: 2 times 3 equals 6. Write 6 below the 8.
Subtract: 8 minus 6 equals 2.

So, 2498 divided by 3 equals 832 with a remainder of 2, or 832 R 2. Now that you have completed all the steps, take a moment to review your work. Try to spot any errors. Make corrections if you notice any. Do not skip these steps, this will help you in the long run.

10. 7807 : 3

Let's solve 7807 divided by 3:

Divide 7 by 3: 7 divided by 3 equals 2 (with a remainder of 1). Write 2 above the 7.
Multiply 2 by 3: 2 times 3 equals 6. Write 6 below the 7.
Subtract: 7 minus 6 equals 1.
Bring down the next digit: Bring down the 8 from the dividend to make 18.
Divide 18 by 3: 18 divided by 3 equals 6. Write 6 next to the 2 above.
Multiply 6 by 3: 6 times 3 equals 18. Write 18 below the 18.
Subtract: 18 minus 18 equals 0.
Bring down the next digit: Bring down the 0 from the dividend.
Divide 0 by 3: 0 divided by 3 equals 0. Write 0 next to the 6 above.
Multiply 0 by 3: 0 times 3 equals 0. Write 0 below the 0.
Subtract: 0 minus 0 equals 0.
Bring down the next digit: Bring down the 7 from the dividend.
Divide 7 by 3: 7 divided by 3 equals 2 (with a remainder of 1). Write 2 next to the 0 above.
Multiply 2 by 3: 2 times 3 equals 6. Write 6 below the 7.
Subtract: 7 minus 6 equals 1.

So, 7807 divided by 3 equals 2602 with a remainder of 1, or 2602 R 1. Great job, team! Practice makes perfect, and you are doing just great. Keep up the pace. You're building a strong foundation in division, which will be essential for future math concepts. Remember to break down the problem and focus on one step at a time.

11. 9551 : 3

Okay, let's proceed with 9551 divided by 3:

Divide 9 by 3: 9 divided by 3 equals 3. Write 3 above the 9.
Multiply 3 by 3: 3 times 3 equals 9. Write 9 below the 9.
Subtract: 9 minus 9 equals 0.
Bring down the next digit: Bring down the 5 from the dividend.
Divide 5 by 3: 5 divided by 3 equals 1 (with a remainder of 2). Write 1 next to the 3 above.
Multiply 1 by 3: 1 times 3 equals 3. Write 3 below the 5.
Subtract: 5 minus 3 equals 2.
Bring down the next digit: Bring down the 5 from the dividend to make 25.
Divide 5 by 3: 25 divided by 3 equals 8 (with a remainder of 1). Write 8 next to the 1 above.
Multiply 8 by 3: 8 times 3 equals 24. Write 24 below the 25.
Subtract: 25 minus 24 equals 1.
Bring down the next digit: Bring down the 1 from the dividend to make 11.
Divide 11 by 3: 11 divided by 3 equals 3 (with a remainder of 2). Write 3 next to the 8 above.
Multiply 3 by 3: 3 times 3 equals 9. Write 9 below the 11.
Subtract: 11 minus 9 equals 2.

So, 9551 divided by 3 equals 3183 with a remainder of 2, or 3183 R 2. Great work! If you are struggling with the division process, then try creating a multiplication chart of the number you are dividing by. This way you will have the answers ready at hand.

12. 7503 : 2

Let's work on 7503 divided by 2:

Divide 7 by 2: 7 divided by 2 equals 3 (with a remainder of 1). Write 3 above the 7.
Multiply 3 by 2: 3 times 2 equals 6. Write 6 below the 7.
Subtract: 7 minus 6 equals 1.
Bring down the next digit: Bring down the 5 from the dividend to make 15.
Divide 15 by 2: 15 divided by 2 equals 7 (with a remainder of 1). Write 7 next to the 3 above.
Multiply 7 by 2: 7 times 2 equals 14. Write 14 below the 15.
Subtract: 15 minus 14 equals 1.
Bring down the next digit: Bring down the 0 from the dividend to make 10.
Divide 10 by 2: 10 divided by 2 equals 5. Write 5 next to the 7 above.
Multiply 5 by 2: 5 times 2 equals 10. Write 10 below the 10.
Subtract: 10 minus 10 equals 0.
Bring down the next digit: Bring down the 3 from the dividend.
Divide 3 by 2: 3 divided by 2 equals 1 (with a remainder of 1). Write 1 next to the 5 above.
Multiply 1 by 2: 1 times 2 equals 2. Write 2 below the 3.
Subtract: 3 minus 2 equals 1.

So, 7503 divided by 2 equals 3751 with a remainder of 1, or 3751 R 1. Good job! Now you are getting through all the divisions. Take a moment to celebrate all your hard work. When you come across larger numbers, don't be intimidated. Use the same steps as before, break the problem down, and take it one step at a time.

13. 5625 : 3

Finally, let's solve 5625 divided by 3:

Divide 5 by 3: 5 divided by 3 equals 1 (with a remainder of 2). Write 1 above the 5.
Multiply 1 by 3: 1 times 3 equals 3. Write 3 below the 5.
Subtract: 5 minus 3 equals 2.
Bring down the next digit: Bring down the 6 from the dividend to make 26.
Divide 26 by 3: 26 divided by 3 equals 8 (with a remainder of 2). Write 8 next to the 1 above.
Multiply 8 by 3: 8 times 3 equals 24. Write 24 below the 26.
Subtract: 26 minus 24 equals 2.
Bring down the next digit: Bring down the 2 from the dividend to make 22.
Divide 22 by 3: 22 divided by 3 equals 7 (with a remainder of 1). Write 7 next to the 8 above.
Multiply 7 by 3: 7 times 3 equals 21. Write 21 below the 22.
Subtract: 22 minus 21 equals 1.
Bring down the next digit: Bring down the 5 from the dividend to make 15.
Divide 15 by 3: 15 divided by 3 equals 5. Write 5 next to the 7 above.
Multiply 5 by 3: 5 times 3 equals 15. Write 15 below the 15.
Subtract: 15 minus 15 equals 0.

So, 5625 divided by 3 equals 1875, or 1875. Great work finishing all the divisions! Remember that division is about breaking down numbers, and you've shown you can do it. Keep practicing and stay curious. Also, feel free to ask any questions. You are doing fantastic! Keep up the great work, and happy calculating!