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💡 4th Grade Math: Long Division With Remainders Practice Questions

1
Solved Example
Easy Level
💡 Question 1: Divide 47 by 5. What is the quotient and the remainder?
Let's find out how many groups of 5 we can make from 47!
Solution & Explanation
Here's how to solve \(47 \div 5\):
  • 👉 Step 1: Think: How many times does 5 go into 47 without going over?
  • 👉 Step 2: We know that \(5 \times 9 = 45\).
  • 👉 Step 3: Write 9 as the quotient.
  • 👉 Step 4: Subtract 45 from 47: \(47 - 45 = 2\).
  • 👉 Step 5: The number 2 is less than 5, so it is our remainder.

✅ Answer: The quotient is 9 and the remainder is 2.

We can write this as \(47 \div 5 = 9\) R \(2\).

\[ \begin{array}{r} 9 \\ 5 \overline{\smash{)} 47} \\ -45 \\ 2 \end{array} \]
2
Solved Example
Easy Level
📌 Question 2: Find the result of \(125 \div 3\). Remember to find both the quotient and the remainder.
Solution & Explanation
Let's solve \(125 \div 3\):
  • 👉 Step 1: Start with the first digit of the dividend, 1. Can 3 go into 1? No.
  • 👉 Step 2: Look at the first two digits, 12. How many times does 3 go into 12? \(3 \times 4 = 12\).
  • 👉 Step 3: Write 4 above the 2 in 125. Subtract \(12 - 12 = 0\).
  • 👉 Step 4: Bring down the next digit, 5. Now we have 5.
  • 👉 Step 5: How many times does 3 go into 5? \(3 \times 1 = 3\).
  • 👉 Step 6: Write 1 next to the 4 in the quotient. Subtract \(5 - 3 = 2\).
  • 👉 Step 7: The number 2 is less than 3, so it is our remainder.

✅ Answer: The quotient is 41 and the remainder is 2.

We can write this as \(125 \div 3 = 41\) R \(2\).

\[ \begin{array}{r} 41 \\ 3 \overline{\smash{)} 125} \\ -12 \downarrow \\ 05 \\ -3 \\ 2 \end{array} \]
3
Solved Example
Medium Level
💡 Question 3: Divide 345 by 4. What is your quotient and remainder?
Solution & Explanation
Let's figure out \(345 \div 4\):
  • 👉 Step 1: Can 4 go into 3? No. So, look at the first two digits, 34.
  • 👉 Step 2: How many times does 4 go into 34? \(4 \times 8 = 32\).
  • 👉 Step 3: Write 8 above the 4 in 345. Subtract \(34 - 32 = 2\).
  • 👉 Step 4: Bring down the next digit, 5. Now we have 25.
  • 👉 Step 5: How many times does 4 go into 25? \(4 \times 6 = 24\).
  • 👉 Step 6: Write 6 next to the 8 in the quotient. Subtract \(25 - 24 = 1\).
  • 👉 Step 7: The number 1 is less than 4, so it is our remainder.

✅ Answer: The quotient is 86 and the remainder is 1.

We can write this as \(345 \div 4 = 86\) R \(1\).

\[ \begin{array}{r} 86 \\ 4 \overline{\smash{)} 345} \\ -32 \downarrow \\ 25 \\ -24 \\ 1 \end{array} \]
4
Solved Example
Medium Level
📌 Question 4: Calculate \(2567 \div 6\). Show your quotient and remainder.
Solution & Explanation
Let's solve \(2567 \div 6\):
  • 👉 Step 1: Can 6 go into 2? No. Look at the first two digits, 25.
  • 👉 Step 2: How many times does 6 go into 25? \(6 \times 4 = 24\).
  • 👉 Step 3: Write 4 above the 5. Subtract \(25 - 24 = 1\).
  • 👉 Step 4: Bring down the next digit, 6. Now we have 16.
  • 👉 Step 5: How many times does 6 go into 16? \(6 \times 2 = 12\).
  • 👉 Step 6: Write 2 next to the 4. Subtract \(16 - 12 = 4\).
  • 👉 Step 7: Bring down the next digit, 7. Now we have 47.
  • 👉 Step 8: How many times does 6 go into 47? \(6 \times 7 = 42\).
  • 👉 Step 9: Write 7 next to the 2. Subtract \(47 - 42 = 5\).
  • 👉 Step 10: The number 5 is less than 6, so it is our remainder.

✅ Answer: The quotient is 427 and the remainder is 5.

We can write this as \(2567 \div 6 = 427\) R \(5\).

\[ \begin{array}{r} 427 \\ 6 \overline{\smash{)} 2567} \\ -24 \downarrow \downarrow \\ 16 \\ -12 \downarrow \\ 47 \\ -42 \\ 5 \end{array} \]
5
Solved Example
Medium Level
🌟 Question 5: A baker made 50 yummy cookies. She wants to put them into bags, with 6 cookies in each bag. How many full bags can she make?
Solution & Explanation
This is a division problem where the remainder tells us how many cookies are left over, but we only care about the full bags!
  • 👉 Step 1: We need to divide the total number of cookies (50) by the number of cookies per bag (6). This is \(50 \div 6\).
  • 👉 Step 2: Think: How many times does 6 go into 50 without going over?
  • 👉 Step 3: We know that \(6 \times 8 = 48\).
  • 👉 Step 4: If we subtract \(50 - 48 = 2\), we have a remainder of 2.
  • 👉 Step 5: The quotient, 8, represents the number of full bags. The remainder, 2, means there are 2 cookies left over that cannot make a full bag.

✅ Answer: The baker can make 8 full bags of cookies.

6
Solved Example
Medium Level
🤔 Question 6: A group of 32 students needs to form teams of 5 for a fun game. After forming as many teams of 5 as possible, how many students will be left over?
Solution & Explanation
Here, we need to find out how many students are not in a complete team. This is exactly what the remainder tells us!
  • 👉 Step 1: We need to divide the total number of students (32) by the number of students per team (5). This is \(32 \div 5\).
  • 👉 Step 2: Think: How many times does 5 go into 32 without going over?
  • 👉 Step 3: We know that \(5 \times 6 = 30\).
  • 👉 Step 4: If we subtract \(32 - 30 = 2\), we have a remainder of 2.
  • 👉 Step 5: The quotient, 6, means they can form 6 full teams. The remainder, 2, means there are 2 students who don't fit into a full team.

✅ Answer: 2 students will be left over.

7
Solved Example
Real World Example
🎁 Question 7: Emily has 43 colorful stickers. She wants to share them equally among her 4 best friends. How many stickers will each friend get, and how many stickers will Emily have left for herself?
Solution & Explanation
This is a real-world sharing problem!
  • 👉 Step 1: We need to divide the total number of stickers (43) by the number of friends (4). This is \(43 \div 4\).
  • 👉 Step 2: Perform the long division:
    • How many times does 4 go into 4? 1 time. Write 1 above the 4. \(4 \times 1 = 4\). Subtract \(4 - 4 = 0\).
    • Bring down the 3. Now we have 3.
    • How many times does 4 go into 3? 0 times. Write 0 next to the 1 in the quotient. \(4 \times 0 = 0\). Subtract \(3 - 0 = 3\).
    • The number 3 is less than 4, so it is our remainder.
  • 👉 Step 3: The quotient (10) tells us how many stickers each friend gets. The remainder (3) tells us how many stickers Emily has left.

✅ Answer: Each friend will get 10 stickers, and Emily will have 3 stickers left for herself.

\[ \begin{array}{r} 10 \\ 4 \overline{\smash{)} 43} \\ -4 \downarrow \\ 03 \\ -0 \\ 3 \end{array} \]
8
Solved Example
Real World Example
📦 Question 8: A factory produces 150 small toy cars. Each shipping box can hold exactly 8 toy cars. How many full shipping boxes can the factory fill, and how many toy cars will be left over, not enough to fill another box?
Solution & Explanation
This problem asks for both the full boxes (quotient) and the leftover items (remainder).
  • 👉 Step 1: We need to divide the total number of toy cars (150) by the capacity of each box (8). This is \(150 \div 8\).
  • 👉 Step 2: Perform the long division:
    • Can 8 go into 1? No. Look at the first two digits, 15.
    • How many times does 8 go into 15? 1 time. Write 1 above the 5. \(8 \times 1 = 8\). Subtract \(15 - 8 = 7\).
    • Bring down the 0. Now we have 70.
    • How many times does 8 go into 70? \(8 \times 8 = 64\).
    • Write 8 next to the 1 in the quotient. Subtract \(70 - 64 = 6\).
    • The number 6 is less than 8, so it is our remainder.
  • 👉 Step 3: The quotient (18) tells us how many full boxes can be filled. The remainder (6) tells us how many toy cars are left over.

✅ Answer: The factory can fill 18 full shipping boxes, and there will be 6 toy cars left over.

\[ \begin{array}{r} 18 \\ 8 \overline{\smash{)} 150} \\ -8 \downarrow \\ 70 \\ -64 \\ 6 \end{array} \]

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