Division Facts 1-9: Complete Guide with Exercises and Solutions

Master division facts 1-9 with visual learning, step-by-step solutions, and comprehensive practice for 3rd grade mathematics.

Solution: Exercises 1 to 3
1 Basic Division Facts
Exercise 1
Solve: 18 ÷ 3 = ?
Also solve: 27 ÷ 9 = ?, 36 ÷ 4 = ?, 45 ÷ 5 = ?
Definition:

Division: Splitting a number into equal groups. The dividend ÷ divisor = quotient.

Division fact: A basic division equation that uses numbers 1-9.

Division method:
  1. Identify the dividend (total number) and divisor (number of groups)
  2. Think: "How many times does the divisor go into the dividend?"
  3. Use multiplication facts to find the quotient
  4. Check: Quotient × Divisor = Dividend
Problem
18 ÷ 3
Think
? × 3 = 18
Answer
6
Step 1: Identify parts

Dividend = 18 (the total number)

Divisor = 3 (how many in each group)

Step 2: Think multiplication

What number times 3 equals 18?

3 × 6 = 18, so 18 ÷ 3 = 6

Step 3: Check your answer

6 × 3 = 18 ✓

18 ÷ 3 = 6
Final answers:

18 ÷ 3 = 6

27 ÷ 9 = 3 (because 9 × 3 = 27)

36 ÷ 4 = 9 (because 4 × 9 = 36)

45 ÷ 5 = 9 (because 5 × 9 = 45)

Applied rules:

• Division is inverse of multiplication: If a × b = c, then c ÷ a = b

• Division by 1: Any number divided by 1 equals itself

• Division by itself: Any number divided by itself equals 1

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

Tip: Use multiplication tables to help with division facts!
Memory trick: Think "How many groups of the divisor fit in the dividend?"
2 Division Patterns
Exercise 2
Complete the pattern:
18 ÷ 1 = 18
18 ÷ 2 = 9
18 ÷ 3 = 6
18 ÷ 6 = ?
18 ÷ 9 = ?
18 ÷ 18 = ?
Definition:

Division patterns: As the divisor increases, the quotient decreases proportionally.

Pattern
18 ÷ ?
Quotient
?
Step 1: Observe the pattern

18 ÷ 1 = 18 (largest quotient)

18 ÷ 2 = 9 (smaller divisor, smaller quotient)

18 ÷ 3 = 6 (even smaller quotient)

Step 2: Continue the pattern

18 ÷ 6 = ? → Think: 6 × ? = 18 → Answer: 3

18 ÷ 9 = ? → Think: 9 × ? = 18 → Answer: 2

18 ÷ 18 = ? → Think: 18 × ? = 18 → Answer: 1

Step 3: Verify the pattern

As divisor increases, quotient decreases: 18 → 9 → 6 → 3 → 2 → 1

18 ÷ 6 = 3
18 ÷ 9 = 2
18 ÷ 18 = 1
Final answer:

18 ÷ 6 = 3, 18 ÷ 9 = 2, 18 ÷ 18 = 1

Applied rules:

• Division pattern rule: Larger divisor = Smaller quotient

• Factor pairs: Divisors and quotients are factor pairs of the dividend

• Commutative relationship: 18 ÷ 3 = 6 and 18 ÷ 6 = 3

Pattern recognition: Look for decreasing quotients as divisors increase!
Factor pairs: Remember that 2×9=18 and 9×2=18, so 18÷2=9 and 18÷9=2
3 Word Problems
Exercise 3
Maria has 36 stickers. She wants to share them equally among 6 friends. How many stickers does each friend get?
There are 45 chairs arranged in 9 rows. How many chairs are in each row?
A teacher has 54 pencils. She gives them equally to 9 students. How many pencils does each student get?
Definition:

Division word problems: Real-life situations requiring equal sharing or grouping.

Stickers problem
36 ÷ 6
Chairs problem
45 ÷ 9
Pencils problem
54 ÷ 9
Step 1: Sticker sharing problem

Total stickers = 36 (dividend)

Number of friends = 6 (divisor)

Stickers per friend: 36 ÷ 6 = 6 stickers

Step 2: Chair arrangement problem

Total chairs = 45 (dividend)

Number of rows = 9 (divisor)

Chairs per row: 45 ÷ 9 = 5 chairs

Step 3: Pencil distribution problem

Total pencils = 54 (dividend)

Number of students = 9 (divisor)

Pencils per student: 54 ÷ 9 = 6 pencils

Step 4: Verify all answers

Stickers: 6 friends × 6 stickers = 36 stickers ✓

Chairs: 9 rows × 5 chairs = 45 chairs ✓

Pencils: 9 students × 6 pencils = 54 pencils ✓

Stickers: 36 ÷ 6 = 6 stickers per friend
Chairs: 45 ÷ 9 = 5 chairs per row
Pencils: 54 ÷ 9 = 6 pencils per student
Final answer:

Each friend gets 6 stickers.

Each row has 5 chairs.

Each student gets 6 pencils.

Applied rules:

• Equal sharing: Total ÷ Number of groups = Amount per group

• Grouping: Total ÷ Size of each group = Number of groups

• Word problem keywords: "share equally", "divide among", "per", "each"

Keyword spotting: Look for words like "each", "per", "equally" for division!
Draw pictures: Draw groups to visualize the division problem!

Division Facts 1-9 Summary

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Key Definitions

Division: Splitting a number into equal groups.

Dividend: The number being divided (top number).

Divisor: The number dividing the dividend (bottom number).

Quotient: The answer to a division problem.

Division Fact: A basic division equation with numbers 1-9.

Core Rules

Inverse Property: If a × b = c, then c ÷ a = b and c ÷ b = a.

Division by 1: Any number ÷ 1 = itself.

Division by self: Any number ÷ itself = 1.

Division by 0: Undefined (impossible).

Zero property: 0 ÷ any number = 0.

Step-by-Step Method

1. Identify dividend and divisor

2. Think: "What number × divisor = dividend?"

3. Use multiplication facts to find the quotient

4. Check: Quotient × divisor = dividend

5. Write the answer clearly

Examples

Easy: 9 ÷ 1 = 9 (think: 1 × 9 = 9)

Medium: 18 ÷ 2 = 9 (think: 2 × 9 = 18)

Harder: 27 ÷ 3 = 9 (think: 3 × 9 = 27)

Advanced: 36 ÷ 4 = 9 (think: 4 × 9 = 36)

Tips & Pitfalls

Tip 1: Use multiplication tables to help with division.

Tip 2: Draw circles/dots to visualize equal groups.

Pitfall: Don't confuse dividend and divisor!

Common error: Forgetting to check answers.

Memory Aids

Fact families: Know 3×6=18, 6×3=18, 18÷3=6, 18÷6=3 together.

Patterns: Notice how divisors and quotients are factor pairs.

Practice: Daily drills improve recall speed.

Verification: Always multiply back to check!

Division Facts 1-9: Rules and Methods
Dividend ÷ Divisor = Quotient
Basic Division Structure
Division by 1
n ÷ 1 = n
Any number divided by 1 equals itself
Division by self
n ÷ n = 1
Any number divided by itself equals 1
Division by 0
n ÷ 0 = undefined
Cannot divide by zero
Inverse operation
If a × b = c, then c ÷ a = b
Division is opposite of multiplication
Key definitions:

Dividend: The number being divided

Divisor: The number dividing the dividend

Quotient: The result of division

Remainder: Leftover amount when division doesn't divide evenly

Division methods:
  1. Repeated subtraction: Keep subtracting divisor from dividend
  2. Multiplication thinking: Find what number times divisor equals dividend
  3. Fact families: Use related multiplication facts
  4. Visual grouping: Draw equal groups to represent division
Tip 1: Practice division facts daily using flashcards!
Tip 2: Use multiplication tables to help solve division problems.
Tip 3: Draw circles or dots to visualize equal groups.
Tip 4: Check your work by multiplying quotient × divisor = dividend.
Common errors: Forgetting to check answers, confusing dividend and divisor, dividing by zero.
Memorization tips: Focus on patterns (like 2s, 5s, 9s first), use songs or rhymes.
Division facts to memorize:

• Division by 1: n ÷ 1 = n

• Division by self: n ÷ n = 1

• Division by 0: Undefined

• Zero divided by any number: 0 ÷ n = 0

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

Division Facts Chart 1-9

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Dividend ÷ 1 ÷ 2 ÷ 3 ÷ 4 ÷ 5 ÷ 6 ÷ 7 ÷ 8 ÷ 9
9 9 - 3 - - - - - 1
18 18 9 6 - - 3 - - 2
27 27 - 9 - - - - - 3
36 36 18 12 9 - 6 - - 4
45 45 - 15 - 9 - - - 5
Division Facts Mastery Guide
a ÷ b = c means a = b × c
Division-Multiplication Relationship
Key definitions:

Division: The process of splitting a number into equal parts.

Fact family: Related multiplication and division facts using the same numbers.

Division fact: A division equation with numbers 1-9.

Complete methodology:
  1. Read the problem: Identify dividend and divisor
  2. Think multiplication: What number times divisor equals dividend?
  3. Recall fact: Use memorized division facts
  4. Check answer: Multiply quotient by divisor to get dividend
Tip 1: Start with easier facts (÷1, ÷2, ÷5, ÷9) before moving to harder ones.
Tip 2: Practice with visual models like arrays or equal groups.
Tip 3: Use skip counting backwards to solve division problems.
Tip 4: Always verify your answer by multiplying back.
Common mistakes: Confusing dividend/divisor, forgetting remainder concept, division by zero errors.
Test preparation: Memorize facts 1-9, practice word problems, understand inverse relationship.
Essential facts to memorize:

• 9÷1=9, 9÷3=3, 9÷9=1

• 18÷1=18, 18÷2=9, 18÷3=6, 18÷6=3, 18÷9=2

• 27÷1=27, 27÷3=9, 27÷9=3

• 36÷1=36, 36÷2=18, 36÷3=12, 36÷4=9, 36÷6=6, 36÷9=4

• 45÷1=45, 45÷3=15, 45÷5=9, 45÷9=5

Division Strategies

🎯
Step-by-Step Division Process
1
Identify Parts
2
Think Multiplication
3
Find Quotient
4
Check Answer
Visual Division Model
Draw equal groups or arrays to represent division problems
Practice Daily for Mastery!
Division Facts 1-9: Complete Reference Guide
If a × b = c, then c ÷ a = b and c ÷ b = a
Inverse Relationship
Key definitions:

Division: Splitting a number into equal groups.

Quotient: The answer to a division problem.

Fact family: Related multiplication and division facts.

Division fact: Basic division equation with numbers 1-9.

Complete methodology:
  1. Analyze the problem: Identify what needs to be divided
  2. Choose strategy: Visual model, multiplication thinking, or repeated subtraction
  3. Apply method: Follow chosen strategy to find quotient
  4. Verify result: Multiply quotient by divisor to check
Tip 1: To divide by 10, move the decimal point one place left.
Tip 2: Numbers divisible by 3 have digits that add up to a multiple of 3.
Tip 3: Use fact triangles to remember related multiplication and division facts.
Tip 4: Practice with manipulatives like counters or blocks for hands-on learning.
Common errors: Forgetting that division is not commutative, division by zero confusion.
Success strategies: Daily practice, visual models, checking work, using fact families.
Division facts to know by heart:

• Division by 1: n ÷ 1 = n

• Division by self: n ÷ n = 1

• Zero property: 0 ÷ n = 0

• Undefined: n ÷ 0 is undefined

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

Questions & Answers

Question: I keep mixing up division and multiplication. How do I remember which is which when solving problems?

Answer: Great question! Here's how to remember the difference:

  • Multiplication: Combining equal groups to make a larger total (3 groups of 4 = 12)
  • Division: Splitting a total into equal groups (12 split into 3 groups = 4 each)

Think of it this way: Multiplication makes numbers bigger (combining), while division makes numbers smaller (splitting).

Example: If you have 3 bags with 4 apples each, multiplication tells you total apples (3×4=12). If you have 12 apples and want 3 bags with equal amounts, division tells you how many in each bag (12÷3=4).

Key tip: Look for keywords! "Total," "groups of," "times" often indicate multiplication. "Each," "per," "shared equally," "divided among" usually mean division.

Question: Why do I have to memorize all these division facts? Can't I just figure them out each time?

Answer: That's an excellent question! While you can figure out division facts each time, memorizing them has huge benefits:

  • Speed: Memorized facts let you solve problems quickly
  • Confidence: Knowing facts builds confidence in math abilities
  • Foundation: Division facts are building blocks for more complex math
  • Problem-solving: Frees up mental space for solving harder problems

Think of it like knowing your alphabet - you could sound out every letter, but knowing them instantly helps you read fluently!

Start by memorizing easy facts (÷1, ÷2, ÷5, ÷9) and build from there. Use games, songs, and practice to make memorization fun!

Question: I sometimes get confused when dividing by 0. Why can't we do it?

Answer: Division by zero is impossible because it creates logical contradictions. Here's why:

If we said 10 ÷ 0 = some number, then that number × 0 should equal 10. But any number multiplied by 0 always equals 0, not 10!

Think of it practically: If you have 10 cookies and try to share them among 0 people, the situation doesn't make sense. How can you share something with nobody?

In mathematical terms, division by zero leads to contradictions, so mathematicians say it's "undefined" - it has no meaning.

Always remember: You can divide any number by any non-zero number, but division by zero is never allowed!