Introduction
Multi-Digit Division is an important Grade 6 math skill because students are moving from simple answers toward explaining how the math works.
In this lesson, students use models, real questions, worked examples, practice problems, and two online quizzes to build confidence with multi-digit division.
What Is Multi-Digit Division?
Multi-Digit Division means choosing a model, naming what each number means, and explaining the strategy.
The goal is not only to get the answer. Students should be able to show the idea, explain the strategy, and check whether the answer makes sense.
Understanding Multi-Digit Division
Before solving, students should slow down and decide what each number, shape, unit, or label represents.
- Read the question carefully and identify what is being asked.
- Choose a model, equation, table, or diagram that matches the situation.
- Solve one step at a time and keep units or labels attached.
- Use the answer explanation to check that the result makes sense.
Visual Models
Visual Model 1
Question: What is the quotient?
| \(28 \div 12\) | \(= 2\), remainder \(4\) |
|---|---|
| Bring down \(5\): \(45 \div 12\) | \(= 3\), remainder \(9\) |
| Bring down \(6\): \(96 \div 12\) | \(= 8\), remainder \(0\) |
| Quotient: | \(\mathbf{238}\) |
- A. \(238\)
- B. \(240\)
- C. \(242\)
- D. \(250\)
Why it works: \(2{,}856 \div 12 = 238\). The long division shows quotient 238 with no remainder.
Answer: \(238\)
Visual Model 2
Question: What is the quotient of \(3{,}456 \div 16\)?
| \(34 \div 16\) | \(= 2\), remainder \(2\) |
|---|---|
| Bring down \(5\): \(25 \div 16\) | \(= 1\), remainder \(9\) |
| Bring down \(6\): \(96 \div 16\) | \(= 6\), remainder \(0\) |
| Quotient: | \(\mathbf{216}\) |
- A. \(216\)
- B. \(214\)
- C. \(220\)
- D. \(224\)
Why it works: The long division shows \(16 \times 216 = 3{,}456\), so the quotient is exactly 216 with no remainder.
Answer: \(216\)
Worked Examples
Example 1
Question: What is \(5{,}472 \div 24\) using partial quotients?
| \(24 \times 200 = 4{,}800\) | \(\Rightarrow\) | \(5{,}472 - 4{,}800 = 672\) |
|---|---|---|
| \(24 \times 20 = 480\) | \(\Rightarrow\) | \(672 - 480 = 192\) |
| \(24 \times 8 = 192\) | \(\Rightarrow\) | \(192 - 192 = 0\) |
| \multicolumn{3}{c}{Quotient: \(200 + 20 + 8 = \mathbf{228}\)} |
- A. \(226\)
- B. \(232\)
- C. \(230\)
- D. \(228\)
- Using partial quotients: \(200 + 20 + 8 = 228\).
- Verify: \(24 \times 228 = 5{,}472\).
Answer: \(228\)
Example 2
Question: Using the area model above, what is the quotient \(2{,}688 \div 32\)?
- A. \(84\)
- B. \(86\)
- C. \(88\)
- D. \(90\)
- The area model shows \(80 + 4 = 84\).
- Verify: \(32 \times 80 = 2{,}560\) and \(32 \times 4 = 128\), so \(2{,}560 + 128 = 2{,}688\).
Answer: \(84\)
Example 3
Question: What is \(7{,}524 \div 44\)?
| Step 1: | \(44\) goes into \(75\) once. \(44 \times 1 = 44\) |
|---|---|
| Step 2: | \(75 - 44 = 31\). Bring down \(2 \Rightarrow 312\) |
| Step 3: | \(44\) goes into \(312\) seven times. \(44 \times 7 = 308\) |
| Step 4: | \(312 - 308 = 4\). Bring down \(4 \Rightarrow 44\) |
| Step 5: | \(44 \div 44 = 1\), remainder \(0\) |
| \multicolumn{2}{c}{Quotient: \(\mathbf{171}\)} |
- A. \(171\)
- B. \(170\)
- C. \(169\)
- D. \(175\)
- Following the long division steps: \(7{,}524 \div 44 = 171\) with no remainder.
- Verify: \(44 \times 171 = 7{,}524\).
Answer: \(171\)
Real-World Word Problems
Problem 1
Question: A school orders \(4{,}725\) pencils to distribute equally among 15 classrooms. How many pencils does each classroom receive?
- A. \(315\)
- B. \(305\)
- C. \(325\)
- D. \(335\)
Why it works: \(4{,}725 \div 15 = 315\). Each classroom receives 315 pencils.
Answer: \(315\) pencils
Problem 2
Question: An orchard has \(3{,}920\) apples to pack into crates of 20 apples each. How many crates are needed?
- A. \(196\)
- B. \(200\)
- C. \(204\)
- D. \(210\)
Why it works: \(3{,}920 \div 20 = 196\). The orchard needs 196 crates.
Answer: \(196\) crates
Common Mistakes
- Rushing before identifying what the numbers represent.
- Choosing an operation that does not match the situation.
- Dropping labels, units, or context from the answer.
- Skipping the estimate or reasonableness check.
Strategy Tips
- Underline the question being asked.
- Use a model before jumping to computation.
- Write an equation that matches the story or picture.
- Explain the final answer in a sentence.
Practice Questions
Question 1
What is \(1{,}248 \div 24\)?
- A. \(52\)
- B. \(48\)
- C. \(42\)
- D. \(62\)
Question 2
Divide \(3{,}564\) by \(12\).
- A. \(297\)
- B. \(287\)
- C. \(305\)
- D. \(312\)
Question 3
What is \(5{,}280 \div 16\)?
- A. \(315\)
- B. \(320\)
- C. \(330\)
- D. \(345\)
Question 4
Divide \(2{,}805\) by \(15\).
- A. \(187\)
- B. \(185\)
- C. \(175\)
- D. \(195\)
Question 5
What is \(4{,}368 \div 21\)?
- A. \(206\)
- B. \(208\)
- C. \(212\)
- D. \(216\)
Question 6
Divide \(6{,}750 \div 25\).
- A. \(260\)
- B. \(268\)
- C. \(275\)
- D. \(270\)
Full Answer Explanations Click to show all answers and explanations
Question 1
Answer: \(52\)
Use long division or estimation: \(24\times50=1{,}200\), leaving \(48\). Then \(48\div24=2\), so \(1{,}248\div24=52\).
Question 2
Answer: \(297\)
\(3{,}564 \div 12 = 297\). Check: \(12 \times 297 = 3{,}564\).
Question 3
Answer: \(330\)
\(5{,}280 \div 16 = 330\). Verify: \(16 \times 330 = 5{,}280\).
Question 4
Answer: \(187\)
\(2{,}805 \div 15 = 187\). Check: \(15 \times 187 = 2{,}805\).
Question 5
Answer: \(208\)
\(4{,}368 \div 21 = 208\). Verify: \(21 \times 208 = 4{,}368\).
Question 6
Answer: \(270\)
\(6{,}750 \div 25 = 270\). Check: \(25 \times 270 = 6{,}750\).
Connection to Standards
This lesson supports Grade 6 math expectations for reasoning, modeling, problem solving, and explaining answers clearly. It connects classroom skills to the kind of questions students see on state math assessments.
Summary
Multi-Digit Division becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
GOLDEN RULE
Understand the model before choosing the operation.
