Khan Academy-Style Lessons: Dividing Multi-Digit Numbers in Grade 4

Learn division of multi-digit numbers through step-by-step lessons with clear explanations, examples, and practice problems.

Khan Academy Introduction to Division

Welcome to Division!

Division is the process of splitting a number into equal parts. In this lesson, we'll learn how to divide large numbers using long division.

Division is the opposite of multiplication. If 3 × 4 = 12, then 12 ÷ 3 = 4 and 12 ÷ 4 = 3.

\( \text{Dividend} \div \text{Divisor} = \text{Quotient} \) remainder \( \text{Remainder} \)
Division Formula
Key Definitions:

Dividend: The number being divided

Divisor: The number we divide by

Quotient: The result of division

Remainder: What's left over after division

Long Division: Step-by-step method for dividing large numbers

Place Value: Understanding tens, hundreds, and thousands

Understanding Place Value

Before dividing, it's important to understand place value. In 345, the 3 is in the hundreds place, the 4 is in the tens place, and the 5 is in the ones place.

Khan Tip:

Always estimate your answer first! For 846 ÷ 3, think about 900 ÷ 3 = 300, so your answer should be close to 300.

Khan Lessons: 1 to 3
1 Introduction to Long Division
Lesson 1: Basic Long Division
Divide: 84 ÷ 4

The Long Division Process

Long division follows the same pattern every time: Divide, Multiply, Subtract, Bring Down, Repeat.

1 Divide: How many times does 4 go into 8? Answer: 2
2 Multiply: 2 × 4 = 8
3 Subtract: 8 - 8 = 0
4 Bring Down: Bring down the 4
5 Divide: How many times does 4 go into 4? Answer: 1
6 Multiply: 1 × 4 = 4
7 Subtract: 4 - 4 = 0
84 ÷ 4 = 21

Check Your Work:

21 × 4 = 84 ✓

Checkpoint Question:

What is 63 ÷ 3? Try solving it using the same steps!

2 Division with Remainders
Lesson 2: Division with Remainders
Divide: 97 ÷ 4

What Are Remainders?

When division doesn't come out evenly, we have a remainder. This is the amount left over after making as many equal groups as possible.

1 Divide: How many times does 4 go into 9? Answer: 2
2 Multiply: 2 × 4 = 8
3 Subtract: 9 - 8 = 1
4 Bring Down: Bring down the 7 to make 17
5 Divide: How many times does 4 go into 17? Answer: 4
6 Multiply: 4 × 4 = 16
7 Subtract: 17 - 16 = 1
97 ÷ 4 = 24 remainder 1

Check Your Work:

(24 × 4) + 1 = 96 + 1 = 97 ✓

Important:

The remainder is always smaller than the divisor. In this case, 1 < 4.

3 Three-Digit Division
Lesson 3: Three-Digit Division
Divide: 486 ÷ 3

Extending to Three Digits

The same long division process works for larger numbers. We just repeat the steps for each digit.

1 Divide: How many times does 3 go into 4? Answer: 1
2 Multiply: 1 × 3 = 3
3 Subtract: 4 - 3 = 1
4 Bring Down: Bring down the 8 to make 18
5 Divide: How many times does 3 go into 18? Answer: 6
6 Multiply: 6 × 3 = 18
7 Subtract: 18 - 18 = 0
8 Bring Down: Bring down the 6
9 Divide: How many times does 3 go into 6? Answer: 2
10 Multiply: 2 × 3 = 6
11 Subtract: 6 - 6 = 0
486 ÷ 3 = 162

Check Your Work:

162 × 3 = 486 ✓

Practice Problem:

Now try 528 ÷ 4. Follow the same steps!

Khan Lessons: 4 to 5
4 Division with Zeros
Lesson 4: Division with Zeros
Divide: 804 ÷ 4

Handling Zeros in Division

When you encounter a zero in the dividend, you still follow the same steps. Sometimes the divisor won't go into the zero, so you write 0 in the quotient.

1 Divide: How many times does 4 go into 8? Answer: 2
2 Multiply: 2 × 4 = 8
3 Subtract: 8 - 8 = 0
4 Bring Down: Bring down the 0
5 Divide: How many times does 4 go into 0? Answer: 0
6 Write 0 in quotient: Put 0 in the tens place
7 Bring Down: Bring down the 4
8 Divide: How many times does 4 go into 4? Answer: 1
9 Multiply: 1 × 4 = 4
10 Subtract: 4 - 4 = 0
804 ÷ 4 = 201

Check Your Work:

201 × 4 = 804 ✓

Key Point:

When the divisor doesn't go into a number, write 0 in the quotient and continue with the next digit.

5 Word Problems
Lesson 5: Word Problems
Sarah has 365 stickers. She wants to put them equally in 5 albums. How many stickers will go in each album?

Applying Division to Real Life

Word problems require us to identify the dividend (total items) and divisor (number of groups) before solving.

1 Identify: Dividend = 365 stickers, Divisor = 5 albums
2 Set up: 365 ÷ 5
3 Divide: How many times does 5 go into 3? Answer: 0 (go to 36)
4 Divide: How many times does 5 go into 36? Answer: 7
5 Multiply: 7 × 5 = 35
6 Subtract: 36 - 35 = 1
7 Bring Down: Bring down the 5 to make 15
8 Divide: How many times does 5 go into 15? Answer: 3
9 Multiply: 3 × 5 = 15
10 Subtract: 15 - 15 = 0
Each album gets 73 stickers

Check Your Work:

73 × 5 = 365 stickers ✓

Challenge Problem:

A bakery made 486 muffins. They pack them in boxes of 6. How many boxes do they need?

Khan Academy Complete Division Summary
\( \text{Dividend} = \text{Divisor} \times \text{Quotient} + \text{Remainder} \)
Division Verification

The Division Process

Remember the steps: Divide, Multiply, Subtract, Bring Down, Repeat. This is often remembered as "Dad, Mom, Sister, Brother, Run!"

Key definitions:

Division: Splitting a number into equal groups

Long Division: Methodical approach to divide multi-digit numbers

Remainder: Amount left over after division

Place Value: Position of digits determines their value

Estimation: Approximating answers before calculating

Fact Families: Related multiplication and division facts

Complete methodology:
  1. Understand the problem: Identify what is being asked
  2. Estimate: Make a reasonable guess for the answer
  3. Set up: Write dividend inside division bracket, divisor outside
  4. Divide: See how many times divisor goes into first digit(s)
  5. Multiply: Multiply divisor by quotient digit
  6. Subtract: Subtract product from current dividend part
  7. Bring down: Bring down next digit
  8. Repeat: Continue until no more digits to bring down
  9. Check: Verify using multiplication
Tip 1: Estimate first! 486 ÷ 3 is close to 500 ÷ 3 ≈ 167, so expect answer near 167.
Tip 2: If divisor doesn't go into current number, write 0 and bring down next digit.
Tip 3: Always verify by multiplying quotient × divisor + remainder = dividend.
Tip 4: Practice basic facts (multiplication tables) to speed up division.
Tip 5: Use fact families: if 3 × 4 = 12, then 12 ÷ 3 = 4 and 12 ÷ 4 = 3.
Common errors: Forgetting to bring down digits, miscalculating multiplication, ignoring remainders, incorrect place value.
Success strategies: Practice regularly, use estimation, check work, understand place value.
Essential division facts:

• Dividend = Divisor × Quotient + Remainder

• Remainder is always less than the divisor

• Any number divided by itself equals 1

• Any number divided by 1 equals itself

• Zero divided by any number (except 0) equals 0

• Division by zero is undefined

Practice Problems:

  • 728 ÷ 4 = ?
  • 546 ÷ 6 = ?
  • 903 ÷ 3 = ?
  • 672 ÷ 8 = ?

Questions & Answers

Question: Why do we need to learn long division? Isn't there an easier way to divide big numbers?

Answer: Long division is important because it teaches you the systematic thinking needed for more complex math. It breaks down big problems into smaller, manageable steps. While calculators exist, understanding the process helps you:

  • Understand what division really means (making equal groups)
  • Build a foundation for higher math concepts
  • Develop problem-solving and logical thinking skills
  • Catch errors when using calculators
  • Understand remainders and their meaning

Think of long division as a recipe - following the steps helps you understand how the final answer comes together!

Question: How can I help my child practice division at home in a Khan Academy style?

Answer: You can create a Khan Academy-style environment at home:

  • Start with concepts: Explain the idea before diving into problems
  • Use step-by-step approach: Break problems into clear, numbered steps
  • Provide examples: Show multiple examples from simple to complex
  • Encourage checking: Always verify answers
  • Offer practice: Provide several similar problems

The key is to be patient and encouraging, just like Khan Academy videos!

Question: What should I do when I get stuck on a division problem?

Answer: Here's a step-by-step plan when you're stuck:

  • Take a breath: Don't panic! Everyone gets stuck sometimes
  • Reread the problem: Make sure you understand what's being asked
  • Look for patterns: Does this remind you of a problem you've solved before?
  • Check your work: Go back to the last step you know was correct
  • Estimate: Make a reasonable guess to see if your answer makes sense
  • Ask for help: Talk to your teacher, parent, or a friend

Remember, getting stuck is part of learning! Each time you work through a difficult problem, you get stronger at math.