Division Problems: Let's Solve Them Together!

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Hey guys! Today, we're diving into some division problems. Division can seem tricky, but we're going to break it down step by step. We've got six problems to tackle: 113 ÷ 7, 845 ÷ 8, 624 ÷ 6, 534 ÷ 4, 249 ÷ 3, and 437 ÷ 5. So, grab your pencils and paper, and let's get started!

Breaking Down Division

Before we jump into the problems, let's quickly recap what division is all about. Division is basically splitting a number into equal groups. Think of it like sharing a bag of candy with your friends. The number you're splitting (the total number of candies) is called the dividend. The number of groups you're splitting it into (the number of friends) is the divisor. And the result you get (how many candies each friend gets) is the quotient. Sometimes, you might have some leftovers – that's called the remainder.

Understanding these terms is super important because they help us understand what we're actually doing when we divide. It's not just about following a procedure; it's about understanding the why behind it. When we understand the concept, problems become much easier to solve.

Long Division: Our Go-To Method

For these problems, we'll be using a method called long division. Long division is a step-by-step process that helps us divide larger numbers. It might seem a bit intimidating at first, but trust me, once you get the hang of it, it's like riding a bike! We will go through every steps to make it super clear. Remember, practice makes perfect, so don't worry if you don't get it right away.

Problem 1: 113 ÷ 7

Let's start with our first problem: 113 ÷ 7. This means we want to see how many times 7 fits into 113.

  1. Set up the problem: Write 113 inside the division bracket and 7 outside.
  2. Divide the first digit(s): Look at the first digit of 113, which is 1. Can 7 fit into 1? Nope. So, we move to the first two digits, 11. How many times does 7 fit into 11? It fits in once (1 x 7 = 7).
  3. Write the quotient: Write 1 above the 1 in 113.
  4. Multiply: Multiply the quotient (1) by the divisor (7): 1 x 7 = 7.
  5. Subtract: Subtract the result (7) from 11: 11 - 7 = 4.
  6. Bring down: Bring down the next digit (3) from 113 to make 43.
  7. Repeat: Now we have 43. How many times does 7 fit into 43? It fits in 6 times (6 x 7 = 42).
  8. Write the quotient: Write 6 next to the 1 above the division bracket.
  9. Multiply: Multiply the quotient (6) by the divisor (7): 6 x 7 = 42.
  10. Subtract: Subtract the result (42) from 43: 43 - 42 = 1.
  11. Remainder: We have 1 left over, which is our remainder.

So, 113 ÷ 7 = 16 with a remainder of 1. We can write this as 16 R1.

Problem 2: 845 ÷ 8

Next up, we have 845 ÷ 8. Let's follow the same steps:

  1. Set up: 845 inside, 8 outside.
  2. Divide: 8 fits into 8 once (1 x 8 = 8).
  3. Write: Write 1 above the 8 in 845.
  4. Multiply: 1 x 8 = 8.
  5. Subtract: 8 - 8 = 0.
  6. Bring down: Bring down the 4 to make 04 (which is just 4).
  7. Divide: How many times does 8 fit into 4? It doesn't! So, we write 0 above the 4 in 845.
  8. Bring down: Bring down the 5 to make 45.
  9. Divide: How many times does 8 fit into 45? It fits in 5 times (5 x 8 = 40).
  10. Write: Write 5 next to the 0 above the division bracket.
  11. Multiply: 5 x 8 = 40.
  12. Subtract: 45 - 40 = 5.
  13. Remainder: We have 5 left over.

So, 845 ÷ 8 = 105 with a remainder of 5, or 105 R5.

Problem 3: 624 ÷ 6

Let's keep the ball rolling with 624 ÷ 6.

  1. Set up: 624 inside, 6 outside.
  2. Divide: 6 fits into 6 once (1 x 6 = 6).
  3. Write: Write 1 above the 6 in 624.
  4. Multiply: 1 x 6 = 6.
  5. Subtract: 6 - 6 = 0.
  6. Bring down: Bring down the 2.
  7. Divide: How many times does 6 fit into 2? It doesn't! Write 0 above the 2 in 624.
  8. Bring down: Bring down the 4 to make 24.
  9. Divide: How many times does 6 fit into 24? It fits in 4 times (4 x 6 = 24).
  10. Write: Write 4 next to the 0 above the division bracket.
  11. Multiply: 4 x 6 = 24.
  12. Subtract: 24 - 24 = 0.
  13. Remainder: No remainder!

So, 624 ÷ 6 = 104. Nice and clean!

Problem 4: 534 ÷ 4

Alright, let's tackle 534 ÷ 4.

  1. Set up: 534 inside, 4 outside.
  2. Divide: 4 fits into 5 once (1 x 4 = 4).
  3. Write: Write 1 above the 5 in 534.
  4. Multiply: 1 x 4 = 4.
  5. Subtract: 5 - 4 = 1.
  6. Bring down: Bring down the 3 to make 13.
  7. Divide: How many times does 4 fit into 13? It fits in 3 times (3 x 4 = 12).
  8. Write: Write 3 next to the 1 above the division bracket.
  9. Multiply: 3 x 4 = 12.
  10. Subtract: 13 - 12 = 1.
  11. Bring down: Bring down the 4 to make 14.
  12. Divide: How many times does 4 fit into 14? It fits in 3 times (3 x 4 = 12).
  13. Write: Write 3 next to the 3 above the division bracket.
  14. Multiply: 3 x 4 = 12.
  15. Subtract: 14 - 12 = 2.
  16. Remainder: We have 2 left over.

So, 534 ÷ 4 = 133 with a remainder of 2, or 133 R2.

Problem 5: 249 ÷ 3

We're on a roll! Let's do 249 ÷ 3.

  1. Set up: 249 inside, 3 outside.
  2. Divide: How many times does 3 fit into 2? It doesn't. So, we look at 24.
  3. Divide: How many times does 3 fit into 24? It fits in 8 times (8 x 3 = 24).
  4. Write: Write 8 above the 4 in 249.
  5. Multiply: 8 x 3 = 24.
  6. Subtract: 24 - 24 = 0.
  7. Bring down: Bring down the 9.
  8. Divide: How many times does 3 fit into 9? It fits in 3 times (3 x 3 = 9).
  9. Write: Write 3 next to the 8 above the division bracket.
  10. Multiply: 3 x 3 = 9.
  11. Subtract: 9 - 9 = 0.
  12. Remainder: No remainder!

So, 249 ÷ 3 = 83.

Problem 6: 437 ÷ 5

Last but not least, let's tackle 437 ÷ 5.

  1. Set up: 437 inside, 5 outside.
  2. Divide: How many times does 5 fit into 4? It doesn't. So, we look at 43.
  3. Divide: How many times does 5 fit into 43? It fits in 8 times (8 x 5 = 40).
  4. Write: Write 8 above the 3 in 437.
  5. Multiply: 8 x 5 = 40.
  6. Subtract: 43 - 40 = 3.
  7. Bring down: Bring down the 7 to make 37.
  8. Divide: How many times does 5 fit into 37? It fits in 7 times (7 x 5 = 35).
  9. Write: Write 7 next to the 8 above the division bracket.
  10. Multiply: 7 x 5 = 35.
  11. Subtract: 37 - 35 = 2.
  12. Remainder: We have 2 left over.

So, 437 ÷ 5 = 87 with a remainder of 2, or 87 R2.

Final Results

Okay, guys, we did it! We solved all six division problems. Here's a recap of our answers:

  • 113 ÷ 7 = 16 R1
  • 845 ÷ 8 = 105 R5
  • 624 ÷ 6 = 104
  • 534 ÷ 4 = 133 R2
  • 249 ÷ 3 = 83
  • 437 ÷ 5 = 87 R2

Keep Practicing!

Division might seem challenging at first, but the more you practice, the easier it becomes. Remember to take it step by step, and don't be afraid to ask for help if you get stuck. You've got this!

If you want more practice, try making up your own division problems or searching online for worksheets. The key is to keep your brain engaged and keep practicing those skills. You'll be a division master in no time! This is just the beginning; imagine what else you can conquer in math with a solid foundation in division.