Long Division

➗ Long Division

Part 1 of 5 — What Is Long Division?

When numbers get too big to divide in your head, we use a neat method called long division. It breaks a hard problem into small, easy steps that you repeat over and over.

In a division problem, every number has a name:

• The dividend is the number being split up (it goes inside the division box).
• The divisor is the number you are splitting by (it goes outside the box).
• The quotient is the answer (it goes on top of the box).

For example, in $84 \div 4 = 21$:

The Four Steps: D, M, S, B

Long division repeats four steps in the same order every time. A fun way to remember them is DMSB — Dad, Mom, Sister, Brother:

1. Divide — How many times does the divisor go in?
2. Multiply — Multiply that answer by the divisor.
3. Subtract — Subtract to see what is left.
4. Bring down — Bring down the next digit, then start over.

Worked Example: $84 \div 4$

• Divide: $8 \div 4 = 2$. Write 2 on top.
• Multiply: $2 \times 4 = 8$. Write it under the 8.
• Subtract: $8 - 8 = 0$.
• Bring down: Bring down the 4, making 04.
• Repeat — Divide: $4 \div 4 = 1$. Write 1 on top.
• Multiply & Subtract: $1 \times 4 = 4$, and $4 - 4 = 0$.

The quotient on top is 21, so $84 \div 4 = 21$. 🎉

Why the Steps Work

Long division is really just sharing into equal groups, one place value at a time. We start with the biggest place (the tens or hundreds) and work toward the smallest (the ones).

That is why we always work left to right through the dividend — the opposite direction from addition and subtraction!

Concept Check 🎯

✏️ Worked Examples

Part 2 of 5 — Step by Step

Let's carefully work through $72 \div 6$ using DMSB.

Step 1 — Divide: Can $6$ go into $7$? Yes, once. $7 \div 6 = 1$. Write 1 on top above the 7.

Step 2 — Multiply: $1 \times 6 = 6$. Write 6 below the 7.

Step 3 — Subtract: $7 - 6 = 1$.

Step 4 — Bring down: Bring down the 2, making 12.

Repeat — Divide: $12 \div 6 = 2$. Write 2 on top.

Multiply & Subtract: $2 \times 6 = 12$, and $12 - 12 = 0$.

The answer is $72 \div 6 = 12$. ✅

A Bigger Example: $156 \div 4$

So $156 \div 4 = 39$.

Tip: If the first digit is smaller than the divisor (like $1 < 4$ above), just include the next digit and divide that bigger chunk.

Your Turn 🧮

Work each one with DMSB and type just the quotient (the answer).

1. $48 \div 4 =$ ?

2. $90 \div 3 =$ ?

3. $128 \div 8 =$ ?

🧭 Guided Practice

Part 3 of 5 — Practice Together

Work each problem with DMSB, then choose the correct answer.

Name the Steps 🔤

Fill in the missing parts of the DMSB process for $96 \div 6$.

• After you Divide ($9 \div 6 = 1$), the next step is to ___.
• The answer to $96 \div 6$ is ___.

🌍 Word Problems

Part 4 of 5 — Division in Real Life

Division helps us share things equally or split things into groups. The trick is figuring out what is being shared (the dividend) and how many groups or how big each group is (the divisor).

Example: A teacher has 72 crayons to share equally among 6 tables. How many crayons does each table get?

This is $72 \div 6 = 12$. Each table gets 12 crayons. 🖍️

Remainders in real life: Sometimes things don't split evenly. If you have 17 stickers for 3 friends, then $17 \div 3 = 5$ R $2$. Each friend gets 5 stickers, and 2 stickers are left over.

Solve Each Problem 🧮

1. A baker puts 96 muffins into boxes of 8. How many full boxes are there?

2. 150 students ride in buses that hold 5 rows each... actually, they split evenly into 5 buses. How many students per bus?

3. 45 apples are shared equally among 9 baskets. How many apples in each basket?

Remainder Problem 🎯

🏆 Review & Challenge

Part 5 of 5 — Put It All Together

You learned how to break big division problems into small, repeating steps. Here is your quick reference:

Don't forget to check! Multiply your quotient by the divisor — you should get the dividend back.

• $84 \div 4 = 21$, and $21 \times 4 = 84$ ✓

If a number is left over at the end, that is the remainder ($17 \div 3 = 5$ R $2$).

Mixed Challenge 🎯

Use everything you know about long division.