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

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

Solution: Exercises 1 to 3
1 Division with Remainders
Exercise 1
Solve: 13 ÷ 3 = ? and 17 ÷ 4 = ?
Definition:

Division with Remainders: When a number cannot be divided evenly, there is a remainder left over. The answer includes both a quotient and a remainder.

Division with Remainder method:
  1. Divide the dividend by the divisor
  2. Find the largest multiple of the divisor that fits in the dividend
  3. Subtract to find the remainder
  4. Write the answer as quotient R remainder
Problem 1
13 ÷ 3
Largest multiple
3 × 4 = 12
Remainder
13 - 12 = 1
Step 1: How many 3s fit in 13?

3 × 1 = 3, 3 × 2 = 6, 3 × 3 = 9, 3 × 4 = 12, 3 × 5 = 15

Step 2: Find the largest multiple that fits

3 × 4 = 12 fits in 13, but 3 × 5 = 15 is too big

Step 3: Calculate the remainder

13 - 12 = 1

Step 4: Write the answer

13 ÷ 3 = 4 R1

13 ÷ 3 = 4 R1
Problem 2
17 ÷ 4
Largest multiple
4 × 4 = 16
Remainder
17 - 16 = 1
Step 1: How many 4s fit in 17?

4 × 1 = 4, 4 × 2 = 8, 4 × 3 = 12, 4 × 4 = 16, 4 × 5 = 20

Step 2: Find the largest multiple that fits

4 × 4 = 16 fits in 17, but 4 × 5 = 20 is too big

Step 3: Calculate the remainder

17 - 16 = 1

Step 4: Write the answer

17 ÷ 4 = 4 R1

17 ÷ 4 = 4 R1
Final answers:

13 ÷ 3 = 4 R1 and 17 ÷ 4 = 4 R1

Applied rules:

• Remainder Rule: Remainder must be less than the divisor

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

• Maximum remainder: Remainder is always smaller than the divisor

2 Division Word Problems
Exercise 2
There are 24 apples to be shared equally among 6 children. How many apples does each child get?
Definition:

Division Word Problems: Real-world problems that require division to find equal groups or equal shares.

Total items
24 apples
Number of groups
6 children
Items per group
4 apples
Step 1: Identify the problem

We need to divide 24 apples equally among 6 children

Step 2: Set up the division

24 ÷ 6 = ?

Step 3: Solve using multiplication facts

What number times 6 equals 24? 6 × 4 = 24

Step 4: Write the answer

Each child gets 4 apples

24 ÷ 6 = 4
Verification
4 × 6 = 24
Step 5: Check your answer

4 apples per child × 6 children = 24 apples ✓

Final answer:

Each child gets 4 apples

Applied rules:

• Keywords: "shared equally", "divided among", "each" indicate division

• Verification: Always multiply to check your division answer

• Units: Include the correct units in your final answer

3 Division Patterns and Properties
Exercise 3
Solve: 36 ÷ 6 = ?, 42 ÷ 7 = ?, 54 ÷ 9 = ?, and identify the pattern.
Definition:

Division Patterns: Recognizing relationships between dividends, divisors, and quotients to make division easier.

Problem 1
36 ÷ 6 = 6
Problem 2
42 ÷ 7 = 6
Problem 3
54 ÷ 9 = 6
Step 1: Solve 36 ÷ 6

What number times 6 equals 36? 6 × 6 = 36, so 36 ÷ 6 = 6

Step 2: Solve 42 ÷ 7

What number times 7 equals 42? 6 × 7 = 42, so 42 ÷ 7 = 6

Step 3: Solve 54 ÷ 9

What number times 9 equals 54? 6 × 9 = 54, so 54 ÷ 9 = 6

Step 4: Identify the pattern

All problems result in quotient 6. The dividend increases by 6 each time, and the divisor increases by 1 each time.

Step 5: Extend the pattern

Next would be 66 ÷ 11 = 6, then 78 ÷ 13 = 6

36 ÷ 6 = 6, 42 ÷ 7 = 6, 54 ÷ 9 = 6
Final answers:

36 ÷ 6 = 6, 42 ÷ 7 = 6, 54 ÷ 9 = 6

Applied rules:

• Pattern Recognition: Look for relationships between numbers

• Multiplication Connection: Use known facts to solve division

• Verification: Always check with multiplication

Complete Summary: Division Facts for Class 3
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).

Division Symbol: ÷ (read as "divided by") or represented as a fraction bar.

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

Step-by-Step Division Methods:
  1. Identify the problem: Read the division sentence (e.g., 12 ÷ 3)
  2. Understand what it means: "How many groups of 3 are in 12?" or "If 12 is shared equally among 3 people, how much does each get?"
  3. Choose a method: Equal groups, repeated subtraction, skip counting, or fact families
  4. Solve: Use your chosen method to find the answer
  5. Verify: Multiply the quotient by the divisor to check your answer
  6. For remainders: If there's a remainder, check that (quotient × divisor) + remainder = dividend
Tip 1: Use multiplication facts to help with division (fact families).
Tip 2: For division with remainders, always check that remainder is smaller than divisor.
Tip 3: Look for patterns in division facts to make solving easier.
Tip 4: Always check your answer by multiplying the quotient and divisor (add remainder if present).
Common Division Facts to Remember: 2÷2=1, 4÷2=2, 6÷2=3, 8÷2=4, 10÷2=5, 12÷2=6, 14÷2=7, 16÷2=8, 18÷2=9, 20÷2=10
Division Patterns: Numbers divisible by 2: even numbers. Numbers divisible by 5: end in 0 or 5. Numbers divisible by 10: end in 0.
Advanced Division Strategies:
  1. Long division method: For larger numbers, use step-by-step division
  2. Breaking apart numbers: Split larger numbers into smaller, easier-to-divide parts
  3. Using place value: Divide tens and ones separately when possible
  4. Estimation first: Round numbers to estimate before calculating precisely
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
Zero Rule
0 ÷ a = 0
Zero divided by any number is zero
Advanced Concepts:

Fact Families: Sets of related multiplication and division facts using the same numbers (e.g., 2×3=6, 3×2=6, 6÷2=3, 6÷3=2)

Remainders: In class 3, students learn that sometimes division doesn't result in equal groups, leaving a remainder.

Word Problems: Division is often used in sharing, grouping, and rate problems.

Place Value: Understanding how to divide tens and ones separately.

Different Division Strategies:
  1. Equal Groups: Make equal groups and count items in each group
  2. Arrays: Arrange objects in rows and columns
  3. Repeated Subtraction: Keep subtracting the divisor until reaching zero or remainder
  4. Fact Families: Use known multiplication facts to solve division problems
  5. Number Lines: Skip count backwards from the dividend
  6. Breaking Apart: Divide larger numbers by breaking them into smaller parts
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, confusing dividend and divisor, remainder larger than divisor.
Success Strategies: Master multiplication facts first, practice regularly, use multiple methods to verify, pay attention to remainders.
Essential Division Facts for Class 3:

• 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

Questions & Answers

Common Questions About Division

Question: What happens when I can't divide a number evenly? Like 7 ÷ 2?

Answer: When you can't divide evenly, you get a remainder! Let's solve 7 ÷ 2:

  • You can make 2 equal groups, but you'll have some left over
  • 2 × 3 = 6 (fits in 7)
  • 2 × 4 = 8 (too big for 7)
  • So 7 ÷ 2 = 3 R1 (3 with remainder 1)
  • Check: 3 × 2 + 1 = 6 + 1 = 7 ✓

The remainder (R1) is the part that couldn't be divided equally!

Question: My child is struggling with division word problems. How can I help them identify when to use division?

Answer: Look for these key words and phrases that signal division:

  • Sharing equally: "divided among", "shared between", "split evenly"
  • Groups: "in each group", "per group", "how many groups"
  • Rate: "each", "per", "for every"
  • Examples: "12 cookies shared among 4 friends" means 12 ÷ 4

Also, ask: "Are we making equal groups?" or "How many in each group?" If yes, it's likely division!

Question: What are the most important division facts for class 3 students to master?

Answer: Focus on these essential division facts for class 3:

  • Division by 2: Halving numbers (4÷2=2, 6÷2=3, 8÷2=4, etc.)
  • Division by 3: Through 30 (6÷3=2, 9÷3=3, 12÷3=4, etc.)
  • Division by 4: Through 40 (8÷4=2, 12÷4=3, 16÷4=4, etc.)
  • Division by 5: Through 50 (10÷5=2, 15÷5=3, 20÷5=4, etc.)
  • Division by 10: Through 100 (20÷10=2, 30÷10=3, 40÷10=4, etc.)
  • Special cases: Any number divided by 1 equals itself, any number divided by itself equals 1

Mastering these facts provides a strong foundation for more complex division problems!