Division Facts for Class 4 - Complete Guide for 3rd Grade Students

Master division facts for class 4 with step-by-step examples, exercises, and solutions designed specifically for 3rd grade students learning advanced division concepts.

Solution: Exercises 1 to 3
1 Long Division Method
Exercise 1
Solve: 84 ÷ 4 = ? using the long division method.
Definition:

Long Division: A method for dividing large numbers by breaking the problem into simpler steps: divide, multiply, subtract, bring down.

Long Division Steps:
  1. Divide the first digit(s) of the dividend by the divisor
  2. Multiply the quotient by the divisor
  3. Subtract the result from the dividend
  4. Bring down the next digit
  5. Repeat until all digits are used
Step 1
8 ÷ 4 = 2
Step 2
2 × 4 = 8
Step 3
8 - 8 = 0
Step 1: Divide 8 by 4

8 ÷ 4 = 2, write 2 above the 8

Step 2: Multiply 2 by 4

2 × 4 = 8, write 8 below the 8

Step 3: Subtract

8 - 8 = 0

Step 4: Bring down 4

Now divide 4 by 4 = 1, write 1 above the 4

Step 5: Multiply and subtract

1 × 4 = 4, then 4 - 4 = 0

84 ÷ 4 = 21
Verification
21 × 4 = 84
Final answer:

84 ÷ 4 = 21

Applied rules:

• DMBS: Divide, Multiply, Subtract, Bring Down

• Verification: Quotient × Divisor = Dividend

• Place value: Align digits properly in columns

2 Division with Larger Numbers
Exercise 2
Solve: 156 ÷ 6 = ? and identify the divisibility rule for 6.
Definition:

Divisibility Rules: Quick ways to determine if a number can be divided evenly by another number without doing the full calculation.

Divisibility Rule
Divisible by 2 AND 3
Calculate
156 ÷ 6
Result
26
Step 1: Check divisibility by 6

Rule: Number must be divisible by both 2 and 3

156 is even (divisible by 2), sum of digits: 1+5+6=12 (divisible by 3)

Step 2: Use long division

156 ÷ 6 = 26

Step 3: Divide 15 by 6

15 ÷ 6 = 2 remainder 3, write 2 above the 5

Step 4: Bring down 6

Make 36, then 36 ÷ 6 = 6

Step 5: Final calculation

2 × 6 = 12, 15-12=3, bring down 6 to make 36, 36÷6=6

156 ÷ 6 = 26
Verification
26 × 6 = 156
Final answer:

156 ÷ 6 = 26

Applied rules:

• Divisibility by 6: Must be divisible by both 2 and 3

• Divisibility by 2: Number ends in 0, 2, 4, 6, or 8

• Divisibility by 3: Sum of digits is divisible by 3

3 Division with Remainders
Exercise 3
Solve: 247 ÷ 5 = ? and express the answer with remainder, decimal, and fraction forms.
Definition:

Multiple Answer Forms: Division results can be expressed as quotient with remainder, decimal, or mixed number.

With Remainder
49 R2
As Decimal
49.4
As Fraction
49 2/5
Step 1: Use long division

247 ÷ 5 = 49 R2

Step 2: Convert remainder to decimal

2 ÷ 5 = 0.4, so 49 R2 = 49.4

Step 3: Express as mixed number

49 R2 = 49 2/5

Step 4: Verify with multiplication

49 × 5 = 245, 245 + 2 = 247 ✓

Step 5: Verify decimal form

49.4 × 5 = 247 ✓

247 ÷ 5 = 49 R2 = 49.4 = 49 2/5
Final answers:

247 ÷ 5 = 49 R2 (with remainder), 49.4 (decimal), or 49 2/5 (mixed number)

Applied rules:

• Remainder conversion: Remainder ÷ divisor = decimal part

• Fraction form: Quotient + (remainder/divisor)

• Verification: Always check with multiplication

Complete Summary: Division Facts for Class 4
Key Concepts and Definitions:

Division: The mathematical operation that splits a number into equal groups or shares it equally.

Dividend: The number being divided (the whole amount).

Divisor: The number we divide by (tells us how many groups or how many in each group).

Quotient: The answer to a division problem (how many in each group or how many groups).

Remainder: What's left over when division doesn't result in equal groups (remainder is always less than the divisor).

Long Division: A systematic method for dividing larger numbers using the steps: Divide, Multiply, Subtract, Bring Down.

Divisibility Rules: Quick tests to determine if a number can be divided evenly by another number.

Core Rules and Principles:

• Division is inverse of multiplication: If 3 × 4 = 12, then 12 ÷ 3 = 4 and 12 ÷ 4 = 3

• Division by 1: Any number divided by 1 equals itself (a ÷ 1 = a)

• Division by itself: Any non-zero number divided by itself equals 1 (a ÷ a = 1)

• Division by 0: Cannot divide by zero (undefined)

• Zero divided by a number: 0 ÷ a = 0 (for any non-zero a)

• Remainder rule: The remainder is always less than the divisor

• DMBS: Long division follows the pattern: Divide, Multiply, Subtract, Bring Down

Step-by-Step Division Methods:
  1. Identify the problem: Read the division sentence (e.g., 124 ÷ 4)
  2. Set up long division: Write dividend inside bracket, divisor outside
  3. Divide: How many times does divisor go into first digit(s)?
  4. Multiply: Multiply quotient by divisor
  5. Subtract: Subtract result from dividend
  6. Bring down: Bring down next digit
  7. Repeat: Continue until all digits are used
  8. Verify: Multiply quotient by divisor to check your answer
Tip 1: Use divisibility rules to quickly check if numbers divide evenly.
Tip 2: Always verify your answer by multiplying quotient × divisor.
Tip 3: Use estimation to check if your answer is reasonable.
Tip 4: Write neatly and align digits in columns for long division.
Divisibility Rules: By 2: ends in 0,2,4,6,8. By 3: sum of digits divisible by 3. By 4: last two digits divisible by 4. By 5: ends in 0 or 5. By 6: divisible by both 2 and 3. By 9: sum of digits divisible by 9. By 10: ends in 0.
Common Division Facts: Know multiplication tables up to 12×12 to help with division facts.
Advanced Division Strategies:
  1. Partial Quotients: Break the division into smaller, easier parts
  2. Estimation first: Round numbers to estimate before calculating precisely
  3. Using multiples: Find multiples of the divisor to make division easier
  4. Checking work: Always verify with multiplication
Advanced Division Rules and Methods
Dividend ÷ Divisor = Quotient R Remainder
Division with Remainders
Division Fact
a ÷ b = c
Means a = b × c
With Remainder
a ÷ b = c R r
Means a = b × c + r
Decimal Form
a ÷ b = c.d
Means a = b × (c.d)
Advanced Concepts:

Fact Families: Sets of related multiplication and division facts using the same numbers (e.g., 4×6=24, 6×4=24, 24÷4=6, 24÷6=4)

Remainders: In class 4, students learn to convert remainders to decimals and fractions.

Word Problems: Complex problems requiring multiple steps including division.

Estimation: Using rounding to estimate division results before calculating precisely.

Different Division Strategies:
  1. Long Division: Systematic method for dividing large numbers
  2. Partial Quotients: Break the dividend into smaller parts
  3. Repeated Subtraction: Keep subtracting the divisor until reaching zero or remainder
  4. Fact Families: Use known multiplication facts to solve division problems
  5. Estimation: Round numbers to make division easier
  6. Using Multiples: Find multiples of the divisor to make division faster
Memorization Tip: Practice division facts daily with flashcards or games.
Visualization Tip: Draw pictures or use objects to represent division problems.
Pattern Tip: Notice that division by 2 gives half the number.
Verification Tip: Always multiply your answer by the divisor to check accuracy.
Common Mistakes: Dividing by zero, forgetting to check answers, misaligning digits in long division, remainder larger than divisor.
Success Strategies: Master multiplication facts first, practice regularly, use multiple methods to verify, pay attention to remainders and place value.
Essential Division Facts for Class 4:

• Division by 1: a ÷ 1 = a (any number divided by 1 is itself)

• Division by itself: a ÷ a = 1 (any non-zero number divided by itself is 1)

• Zero rule: 0 ÷ a = 0 (zero divided by any number is zero)

• Inverse relationship: If a × b = c, then c ÷ a = b and c ÷ b = a

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

• Verification: (Quotient × Divisor) + Remainder = Dividend

• Decimal conversion: Remainder ÷ Divisor = decimal part

Questions & Answers

Common Questions About Division

Question: I don't understand why we need to learn long division. Can't we just use a calculator?

Answer: Long division is important for several reasons:

  • Understanding: It helps you understand how division really works
  • Problem-solving: Builds logical thinking and step-by-step reasoning skills
  • Foundation: Prepares you for more advanced math like algebra
  • Checking: You can verify calculator answers when needed
  • Tests: You may not always have a calculator available

Long division teaches patience and precision - valuable life skills!

Question: My child is struggling with the long division algorithm. How can I help them remember the steps?

Answer: Here are memory aids for the long division steps:

  • DMBS: Remember "Does McDonald's Sell Burgers?" - Divide, Multiply, Subtract, Bring Down
  • Visual cues: Write the letters DMBS at the top of the problem
  • Practice with smaller numbers: Start with 2-digit dividends before moving to larger numbers
  • Check each step: Verify each multiplication and subtraction before proceeding
  • Use grid paper: Helps keep numbers aligned in columns

Consistent practice with guidance will build confidence!

Question: What are the most important divisibility rules for class 4 students to master?

  • By 2: Number ends in 0, 2, 4, 6, or 8 (even numbers)
  • By 3: Sum of digits is divisible by 3 (e.g., 123: 1+2+3=6, divisible by 3)
  • By 4: Last two digits form a number divisible by 4 (e.g., 132: 32÷4=8)
  • By 5: Number ends in 0 or 5
  • By 6: Number is divisible by both 2 and 3
  • By 9: Sum of digits is divisible by 9 (e.g., 189: 1+8+9=18, divisible by 9)
  • By 10: Number ends in 0

    • These rules make division much faster and help verify answers!