Long Division
Grade 4 · Math · Study Guide
Learn how to divide large numbers step by step using the long division method.
Division is the process of splitting a number into equal groups. When numbers get big, we use a method called long division to keep everything organized. Long division uses four steps that repeat: Divide, Multiply, Subtract, Bring down. Some people remember this as 'Does McDonald's Sell Burgers?'
Here's how it works with 84 ÷ 4. First, look at the first digit: does 4 go into 8? Yes, 2 times. Write 2 above the 8. Multiply 2 × 4 = 8. Subtract 8 − 8 = 0. Bring down the 4. Now does 4 go into 4? Yes, 1 time. Write 1 above the 4. Multiply 1 × 4 = 4. Subtract 4 − 4 = 0. No remainder, so 84 ÷ 4 = 21.
Sometimes division doesn't come out evenly. For example, 87 ÷ 4: you'd get 21 with a remainder of 3. We write this as 21 R3. The remainder is always smaller than the divisor.
Estimation helps you check your work. Before dividing 96 ÷ 3, think: 90 ÷ 3 = 30, so the answer should be close to 32. If you get something like 320, you know something went wrong!
| Step | Action | Result |
|---|---|---|
| 1 | Divide: 4 into 9? | 2 times |
| 2 | Multiply: 2 × 4 | 8 |
| 3 | Subtract: 9 − 8 | 1 |
| 4 | Bring down the 6 | 16 |
| 5 | Divide: 4 into 16? | 4 times |
| 6 | Final answer | 24 |
Key terms
- Dividend
- The number being divided (the big number inside the division bracket).
- Divisor
- The number you are dividing by (outside the bracket).
- Quotient
- The answer to a division problem.
- Remainder
- The amount left over when a number doesn't divide evenly.
Flashcards
- Dividend
- The number being divided; it goes inside the long division bracket.
- Divisor
- The number you divide by; it goes outside the bracket.
- Quotient
- The answer to a division problem; it goes on top of the bracket.
- Remainder
- The leftover amount after division; must be less than the divisor.
- DMSB
- Divide, Multiply, Subtract, Bring down — the four steps of long division.
- 72 ÷ 6
- 12
Practice questions
What is 72 ÷ 3?
- 22
- 24
- 26
- 28
Show answer
Answer: 24
72 ÷ 3: 3 goes into 7 twice (6), remainder 1; bring down 2 to get 12; 3 goes into 12 four times. Answer: 24.
The remainder in a division problem must always be less than the divisor.
Show answer
Answer: True
If the remainder were equal to or larger than the divisor, you could divide at least one more time.
In the problem 85 ÷ 5 = 17, the number 5 is called the ___.
Show answer
Answer: divisor
The divisor is the number you divide by. In 85 ÷ 5 = 17, the 5 is the divisor.
What is 96 ÷ 4?
- 22
- 24
- 26
- 28
Show answer
Answer: 24
96 ÷ 4: 4 into 9 is 2 (8), remainder 1; bring down 6 to get 16; 4 into 16 is 4. Answer: 24.
91 ÷ 7 = 13. The number 13 is called the ___.
Show answer
Answer: quotient
The quotient is the result of division. In 91 ÷ 7 = 13, the number 13 is the quotient.
Fun facts
- The division symbol ÷ is called an obelus. It was first used in math in 1659!
- Ancient Egyptians divided by doubling and halving numbers — no long division needed!
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