Long Division

For Elementary Students

What Is Long Division?

Long division is a way to divide BIG numbers that are too hard to do in your head!

Think about it like this: Long division is like breaking a big problem into smaller, easier steps — one digit at a time!

The Magic Words: Divide, Multiply, Subtract, Bring Down

Remember these four steps! We'll do them over and over until we're done:

D → Divide
M → Multiply
S → Subtract
B → Bring down

Memory trick: "Does McDonald's Sell Burgers?"

Let's Try an Example: 96 ÷ 4

Step 1 — Divide: How many 4s go into 9?

• Think: 4 × 2 = 8 (that works!)
• Write 2 on top

    2
   ---
4 | 96

Step 2 — Multiply: 2 × 4 = 8

• Write 8 under the 9

    2
   ---
4 | 96
    8

Step 3 — Subtract: 9 − 8 = 1

    2
   ---
4 | 96
  − 8
    1

Step 4 — Bring down the next number (6)

    2
   ---
4 | 96
  − 8 ↓
    16

Now repeat the steps with 16:

Divide: How many 4s go into 16?

• 4 × 4 = 16 → Write 4 on top

Multiply: 4 × 4 = 16

Subtract: 16 − 16 = 0 ← All done!

    24  ← Answer!
   ----
4 | 96
  − 8 ↓
    16
  − 16
     0

Answer: 96 ÷ 4 = 24

What If There's a Leftover?

Sometimes there's a remainder (leftover) at the end!

Example: 23 ÷ 4

    5 R3  ← 5 remainder 3
   -----
4 | 23
  −20
    3   ← Leftover!

• 4 goes into 23 five times (because 4 × 5 = 20)
• We have 3 left over (because 23 − 20 = 3)

Answer: 5 remainder 3 (written as "5 R3")

Checking Your Answer

To check: Multiply your answer by the divisor, then add the remainder.

Check: 5 × 4 + 3 = 20 + 3 = 23 ✓ Correct!

Simple Steps to Remember

1. Divide: How many times does it go in?
2. Multiply: Multiply and write the result
3. Subtract: Subtract to find what's left
4. Bring down: Bring down the next digit
5. Repeat until done!

For Junior High Students

When to Use Long Division

Long division is the method you use when the numbers are too large to divide in your head. It works for any division problem.

Vocabulary:

• Dividend — the number being divided (inside the division symbol)
• Divisor — the number you're dividing by (outside the division symbol)
• Quotient — the answer
• Remainder — what's left over (if any)

The Four Steps: Divide, Multiply, Subtract, Bring Down

Remember the cycle: D-M-S-B (Divide, Multiply, Subtract, Bring down). Repeat until there are no more digits to bring down.

Mnemonic: "Does McDonald's Sell Burgers?" or "Dad, Mom, Sister, Brother"

The Process

Setup:

    quotient
   ----------
divisor | dividend

Steps:

1. Divide — How many times does the divisor go into the current digits?
2. Multiply — Multiply divisor by that digit, write below
3. Subtract — Subtract to find the remainder
4. Bring down — Bring down the next digit
5. Repeat until done

Worked Example: 96 ÷ 4

Step 1 — Divide: 4 into 9 = 2 times (4 × 2 = 8)
    2
   ---
4 | 96

Step 2 — Multiply: 2 × 4 = 8
    2
   ---
4 | 96
    8

Step 3 — Subtract: 9 − 8 = 1
    2
   ---
4 | 96
  − 8
    1

Step 4 — Bring down the 6
    2
   ---
4 | 96
  − 8 ↓
    16

Now repeat with 16:

• Divide: 4 into 16 = 4 times
• Multiply: 4 × 4 = 16
• Subtract: 16 − 16 = 0

    24
   ----
4 | 96
  − 8 ↓
    16
  − 16
     0

Answer: 24

Worked Example: 175 ÷ 5

Step 1: Can 5 go into 1? No! So look at the first two digits (17).

Step-by-step:
5 into 17 = 3 times (5 × 3 = 15)
    3
   ---
5 | 175
   15
    2

Bring down the 5:

5 into 25 = 5 times (5 × 5 = 25)
    35
   ----
5 | 175
  − 15 ↓
    25
  − 25
     0

Answer: 35

Important tip: If the divisor doesn't go into the first digit, combine the first two digits.

Division with Remainders

Example: 83 ÷ 6

Step 1: 6 into 8 = 1 time (6 × 1 = 6)
    1
   ---
6 | 83
    6
    2

Step 2: Bring down 3 to get 23
6 into 23 = 3 times (6 × 3 = 18)
    13
   ----
6 | 83
  − 6 ↓
    23
  − 18
     5  ← Remainder!

Answer: 13 remainder 5 (written as 13 R5)

Check: 13 × 6 + 5 = 78 + 5 = 83 ✓ Correct!

To check: multiply the quotient by the divisor and add the remainder. The result should equal the original dividend.

Multi-Digit Divisors

Example: 156 ÷ 12

12 into 15 = 1 time (12 × 1 = 12)
    1
   ----
12 | 156
    12
     3

Bring down 6 to get 36
12 into 36 = 3 times (12 × 3 = 36)
    13
   ----
12 | 156
  − 12 ↓
     36
   − 36
      0

Answer: 13

When the Quotient Has a Zero

Example: 408 ÷ 4

4 into 4 = 1
    1
   ---
4 | 408
    4
    0

Bring down 0 to get 0
4 into 0 = 0 times!
    10
   ----
4 | 408
  − 4 ↓
     0
   − 0
     0

Bring down 8 to get 8
4 into 8 = 2
    102
   -----
4 | 408
  − 4 ↓
     0 ↓
   − 0
     8
   − 8
     0

Answer: 102

Important: Don't forget to write 0 in the quotient when the divisor doesn't go into a number!

Tips for Success

Tip 1: Always check your answer by multiplying the quotient by the divisor and adding the remainder

Tip 2: If the divisor doesn't go into the first digit, combine the first two digits

Tip 3: Write neatly and keep columns aligned — this avoids mistakes

Tip 4: The remainder must always be smaller than the divisor

Tip 5: Estimate first! 175 ÷ 5 is about 200 ÷ 5 = 40, so answer should be close to 40

Real-Life Uses

Sharing: "Divide 96 cookies equally among 4 classes" → 96 ÷ 4 = 24 cookies per class

Budgeting: "$175 split among 5 people" → $175 ÷ 5 = $35 each

Packaging: "Pack 156 items in boxes of 12" → 156 ÷ 12 = 13 boxes

Time: "Drive 408 miles at 4 hours" → 408 ÷ 4 = 102 miles per hour

Common Mistakes

Mistake 1: Forgetting to bring down the next digit

Mistake 2: Not checking if the divisor goes into the first digit(s)

Mistake 3: Making subtraction errors (always double-check!)

Mistake 4: Forgetting to write 0 in the quotient when needed

Practice