Introduction

Multi-Digit Division is an important Grade 4 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: The long division diagram shows \(2{,}688\div3\). What is the quotient?

Visual Model 1

  • A. \(876\)
  • B. \(886\)
  • C. \(906\)
  • D. \(896\)

Why it works: Follow the diagram: \(26\div3=8\) r\(2\), \(28\div3=9\) r\(1\), \(18\div3=6\). Reading the quotient from the right side, we get \(\mathbf{896}\).

Answer: \(896\)

Visual Model 2

Question: A van can carry \(8\) students. If there are \(360\) students going on a field trip, how many vans are needed?

Visual Model 2

  • A. \(45\)
  • B. \(42\)
  • C. \(48\)
  • D. \(40\)

Why it works: Ask: \(8\times\,?=360\). Since \(8\times45=360\), we need \(\mathbf{45}\) vans for all the students.

Answer: \(45\)

Worked Examples

Example 1

Question: What is the remainder when \(2{,}047\) is divided by \(7\)?

Example 1

  • A. \(2\)
  • B. \(5\)
  • C. \(4\)
  • D. \(3\)
  1. Use long division: \(20\div7=2\) r\(6\), bring down the \(4\) to get \(64\div7=9\) r\(1\), bring down the \(7\) to get \(17\div7=2\) r\(3\).
  2. The remainder is \(\mathbf{3}\).

Answer: \(3\)

Example 2

Question: A small factory packs \(3{,}024\) toys into boxes. How many boxes of \(6\) toys per box can they fill?

Example 2

  • A. \(504\)
  • B. \(514\)
  • C. \(494\)
  • D. \(524\)
  1. Divide: \(30\div6=5\), bring down the \(2\) to get \(2\div6=0\) r\(2\), bring down the \(4\) to get \(24\div6=4\).
  2. The factory can fill \(\mathbf{504}\) boxes.

Answer: \(504\)

Example 3

Question: The area model below shows \(1{,}248\div8\). What is the quotient?

Example 3

  • A. \(156\)
  • B. \(166\)
  • C. \(146\)
  • D. \(176\)
  1. Divide: \(12\div8=1\) r\(4\), bring down the \(4\) to get \(44\div8=5\) r\(4\), bring down the \(8\) to get \(48\div8=6\).
  2. Each guest gets \(\mathbf{156}\) cookies.

Answer: \(156\)

Real-World Word Problems

Problem 1

Question: Ava has \(728\) stickers to put equally into \(8\) boxes. How many stickers go in each box?

  • A. \(87\)
  • B. \(80\)
  • C. \(99\)
  • D. \(91\)

Why it works: Think: \(72\div8=9\), bring down the \(8\) to get \(8\div8=1\). So each box holds \(\mathbf{91}\) stickers.

Answer: \(91\)

Problem 2

Question: Ming has \(936\) marbles. She wants to pack them into bags with \(9\) marbles each. How many full bags can she make?

  • A. \(104\)
  • B. \(99\)
  • C. \(108\)
  • D. \(114\)

Why it works: Divide: \(9\div9=1\), bring down the \(3\) to get \(3\div9=0\) r\(3\), bring down the \(6\) to get \(36\div9=4\). Ming makes \(\mathbf{104}\) full bags.

Answer: \(104\)

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 \(1{,}245\div5\)?

  • A. \(229\)
  • B. \(269\)
  • C. \(289\)
  • D. \(249\)

Question 2

What is \(3{,}456\div4\)?

  • A. \(836\)
  • B. \(846\)
  • C. \(856\)
  • D. \(864\)

Question 3

A baker divides \(540\) cookies equally among \(6\) friends. How many cookies does each friend receive?

  • A. \(80\)
  • B. \(95\)
  • C. \(90\)
  • D. \(85\)

Question 4

What is \(2{,}184\div7\)?

  • A. \(312\)
  • B. \(302\)
  • C. \(319\)
  • D. \(322\)

Question 5

Which expression shows the quotient and remainder for \(567\div8\)?

  • A. \(70\) r\(7\)
  • B. \(70\) r\(5\)
  • C. \(71\) r\(1\)
  • D. \(71\) r\(4\)

Question 6

Diego needs to divide \(1{,}625\) into \(5\) equal groups. What is the result?

  • A. \(315\)
  • B. \(305\)
  • C. \(335\)
  • D. \(325\)
Full Answer Explanations Click to show all answers and explanations

Question 1

Answer: \(249\)

We use long division: \(12\div5=2\) r\(2\), bring down the \(4\) to get \(24\div5=4\) r\(4\), then bring down the \(5\) to get \(45\div5=9\). So \(\mathbf{249}\) is our answer.

Question 2

Answer: \(864\)

Use long division step by step: \(3\div4=0\) r\(3\), bring down the \(4\) to get \(34\div4=8\) r\(2\), bring down the \(5\) to get \(25\div4=6\) r\(1\), bring down the \(6\) to get \(16\div4=4\). The quotient is \(\mathbf{864}\).

Question 3

Answer: \(90\)

Divide: \(54\div6=9\), and \(0\div6=0\) gives us \(90\). Each friend receives \(\mathbf{90}\) cookies.

Question 4

Answer: \(312\)

Long division: \(2\div7=0\) r\(2\), bring down the \(1\) to get \(21\div7=3\), bring down the \(8\) to get \(8\div7=1\) r\(1\), bring down the \(4\) to get \(14\div7=2\). The answer is \(\mathbf{312}\).

Question 5

Answer: \(70\) r\(7\)

Long division: \(56 \div 8 = 7\), bring down the \(7\) to get \(7 \div 8 = 0\) r\(7\). The quotient is \(\mathbf{70}\) with remainder \(\mathbf{7}\). Quick check: \(70 \times 8 + 7 = 560 + 7 = 567\). \checkmark

Question 6

Answer: \(325\)

Use long division: \(16\div5=3\) r\(1\), bring down the \(2\) to get \(12\div5=2\) r\(2\), bring down the \(5\) to get \(25\div5=5\). The result is \(\mathbf{325}\).

Timed practice quizzes

Related Quizzes

After studying Multi-Digit Division, open these two timed quizzes in a new tab for focused extra practice.

Connection to Standards

This lesson supports Grade 4 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.