Solved Exercises on Dividing Multi-Digit Numbers in Grade 4

Master division of multi-digit numbers: long division, remainders, place value, and division strategies through these 5 detailed exercises.

Division Concepts, Rules and Methods
\( \text{Dividend} \div \text{Divisor} = \text{Quotient} \) 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

Long Division Steps:
  1. Divide: How many times does divisor go into dividend part?
  2. Multiply: Multiply divisor by quotient digit
  3. Subtract: Subtract the product from the dividend part
  4. Bring Down: Bring down the next digit
  5. Repeat: Continue until no more digits to bring down
Tip 1: Remember the acronym "Does McDonald's Sell Cheeseburgers?" (Divide, Multiply, Subtract, Check, Bring down).
Tip 2: Always check your work by multiplying quotient × divisor + remainder = dividend.
Tip 3: If the divisor doesn't fit into the current part, write 0 in the quotient.
Place Value: Understanding tens, hundreds, and thousands helps determine how many times a divisor fits.
Estimation: Round numbers to estimate the quotient before doing exact calculations.
Important Division Rules:

• Any number divided by 1 equals itself

• Zero divided by any non-zero number equals zero

• Division by zero is undefined

• Dividend = Divisor × Quotient + Remainder

• Remainder is always less than the divisor

Solution: Exercises 1 to 3
1 Basic Long Division
Exercise 1
Divide: 84 ÷ 4
Definition:

Long Division: A method to divide multi-digit numbers systematically

Division method:
  1. Divide the first digit by the divisor
  2. Multiply the quotient by the divisor
  3. Subtract to find the remainder
  4. Bring down the next digit
  5. Repeat the process
84 ÷ 4
÷
= 21
Step 1: Look at the first digit (8)
Step 2: How many times does 4 go into 8? Answer: 2
Step 3: Multiply: 2 × 4 = 8
Step 4: Subtract: 8 - 8 = 0
Step 5: Bring down the next digit (4)
Step 6: How many times does 4 go into 4? Answer: 1
Step 7: Multiply: 1 × 4 = 4
Step 8: Subtract: 4 - 4 = 0
Check: 21 × 4 = 84 ✓
84 ÷ 4 = 21
Final answer:

84 ÷ 4 = 21 with no remainder

Applied rules:

• Division: How many times does the divisor fit into the dividend?

• Multiplication: Used to check our work

• Place Value: Understanding tens and ones helps with division

2 Division with Remainder
Exercise 2
Divide: 97 ÷ 5
Definition:

Remainder: What's left over when division doesn't result in a whole number

97 ÷ 5
÷
= 19 remainder 2
Step 1: Look at the first digit (9)
Step 2: How many times does 5 go into 9? Answer: 1
Step 3: Multiply: 1 × 5 = 5
Step 4: Subtract: 9 - 5 = 4
Step 5: Bring down the next digit (7) to make 47
Step 6: How many times does 5 go into 47? Answer: 9
Step 7: Multiply: 9 × 5 = 45
Step 8: Subtract: 47 - 45 = 2
Step 9: No more digits to bring down, remainder is 2
Check: (19 × 5) + 2 = 95 + 2 = 97 ✓
Remainder: 2 (since 2 < 5, division is complete)
97 ÷ 5 = 19 remainder 2
Final answer:

97 ÷ 5 = 19 remainder 2

Applied rules:

• Remainder Rule: Remainder must always be smaller than the divisor

• Verification: Divisor × Quotient + Remainder = Dividend

• Place Value: Understanding tens and ones helps organize the process

3 Three-Digit Division
Exercise 3
Divide: 486 ÷ 3
Definition:

Three-Digit Division: Extending long division to larger numbers

486 ÷ 3
÷
= 162
Step 1: Look at the first digit (4)
Step 2: How many times does 3 go into 4? Answer: 1
Step 3: Multiply: 1 × 3 = 3
Step 4: Subtract: 4 - 3 = 1
Step 5: Bring down the next digit (8) to make 18
Step 6: How many times does 3 go into 18? Answer: 6
Step 7: Multiply: 6 × 3 = 18
Step 8: Subtract: 18 - 18 = 0
Step 9: Bring down the next digit (6)
Step 10: How many times does 3 go into 6? Answer: 2
Step 11: Multiply: 2 × 3 = 6
Step 12: Subtract: 6 - 6 = 0
Check: 162 × 3 = 486 ✓
486 ÷ 3 = 162
Final answer:

486 ÷ 3 = 162 with no remainder

Applied rules:

• Systematic Approach: Work from left to right, one digit at a time

• Place Value: Hundreds, tens, and ones must be considered separately

• Verification: Always check by multiplying quotient by divisor

Solution: Exercises 4 to 5
4 Division with Zeros
Exercise 4
Divide: 804 ÷ 4
Definition:

Division with Zeros: Special case when dividend contains zeros

804 ÷ 4
÷
= 201
Step 1: Look at the first digit (8)
Step 2: How many times does 4 go into 8? Answer: 2
Step 3: Multiply: 2 × 4 = 8
Step 4: Subtract: 8 - 8 = 0
Step 5: Bring down the next digit (0)
Step 6: How many times does 4 go into 0? Answer: 0
Step 7: Write 0 in the quotient
Step 8: Bring down the next digit (4)
Step 9: How many times does 4 go into 4? Answer: 1
Step 10: Multiply: 1 × 4 = 4
Step 11: Subtract: 4 - 4 = 0
Check: 201 × 4 = 804 ✓
804 ÷ 4 = 201
Final answer:

804 ÷ 4 = 201 with no remainder

Applied rules:

• Zero Handling: If divisor doesn't go into current number, write 0 in quotient

• Continuity: Always bring down the next digit even if current result is 0

• Verification: Multiplication check confirms accuracy

5 Word Problem Division
Exercise 5
Sarah has 365 stickers. She wants to put them equally in 5 albums. How many stickers will go in each album?
Definition:

Word Problems: Real-life applications requiring division skills

365 ÷ 5
÷
= 73
Step 1: Set up: 365 ÷ 5
Step 2: Look at first digit (3), but 5 doesn't go into 3
Step 3: Look at first two digits (36)
Step 4: How many times does 5 go into 36? Answer: 7
Step 5: Multiply: 7 × 5 = 35
Step 6: Subtract: 36 - 35 = 1
Step 7: Bring down the next digit (5) to make 15
Step 8: How many times does 5 go into 15? Answer: 3
Step 9: Multiply: 3 × 5 = 15
Step 10: Subtract: 15 - 15 = 0
Check: 73 × 5 = 365 ✓
Each album gets 73 stickers
Final answer:

Each album will have 73 stickers

Applied rules:

• Problem Analysis: Identify dividend (365 stickers) and divisor (5 albums)

• Contextual Meaning: Quotient represents stickers per album

• Verification: Check that 73 × 5 = 365 stickers total

Division Laws, Methods, and Key Concepts
\( \text{Dividend} = \text{Divisor} \times \text{Quotient} + \text{Remainder} \)
Division Verification
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

Complete methodology:
  1. Set up the problem: Write dividend inside division bracket, divisor outside
  2. Divide: See how many times divisor goes into first digit(s)
  3. Multiply: Multiply divisor by quotient digit
  4. Subtract: Subtract product from current dividend part
  5. Bring down: Bring down next digit
  6. Repeat: Continue until no more digits to bring down
  7. Check: Verify using multiplication
Tip 1: Estimate first! 84 ÷ 4 is close to 80 ÷ 4 = 20, so expect answer near 20.
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.
Common errors: Forgetting to bring down digits, miscalculating multiplication, ignoring remainders.
Exam preparation: Practice with remainders, word problems, and checking work.
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

Questions & Answers

Question: I don't understand why sometimes I get a remainder when dividing. Can you explain?

Answer: Great question! A remainder occurs when the divisor doesn't divide evenly into the dividend. Think of it like sharing cookies:

  • If you have 9 cookies and want to share equally among 4 friends, each friend gets 2 cookies (4 × 2 = 8), and you have 1 cookie left over.
  • This leftover amount (1 cookie) is the remainder.
  • In math: 9 ÷ 4 = 2 remainder 1

The remainder tells us what's left after making as many equal groups as possible. The remainder is always smaller than the divisor because if it were equal to or larger than the divisor, we could make another group!

Question: My child struggles with the "bring down" step in long division. How can I help them understand this better?

Answer: The "bring down" step is often challenging! Try these approaches:

  • Visual approach: Use physical objects like base-10 blocks to represent numbers and physically move them down
  • Storytelling: Frame it as "uncovering the next digit" to continue the division process
  • Step-by-step: Emphasize that after subtracting, we always look for the next digit to include in our calculation

The key concept is that we're working with place value - when we bring down a digit, we're combining it with the remainder to form the next number to divide. Practice with smaller numbers first, then gradually increase complexity.

Question: How do I know if my division answer is correct? Sometimes I'm not sure about my work.

Answer: The best way to check your division is to use multiplication! Remember this relationship:

If Dividend ÷ Divisor = Quotient remainder Remainder

Then: (Quotient × Divisor) + Remainder = Original Dividend

For example: 97 ÷ 5 = 19 remainder 2

Check: (19 × 5) + 2 = 95 + 2 = 97 ✓

Additional tips:

  • Estimate first: 97 ÷ 5 should be close to 100 ÷ 5 = 20, so 19 makes sense
  • Make sure your remainder is smaller than your divisor
  • Try solving the same problem twice using different methods