Division Facts 1-12: Complete Guide with Exercises and Solutions

Master division facts 1-12 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: 24 ÷ 6 = ?
Also solve: 36 ÷ 4 = ?, 45 ÷ 9 = ?
Definition:

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

Division fact: A basic division equation that uses numbers 1-12.

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
24 ÷ 6
Think
? × 6 = 24
Answer
4
Step 1: Identify parts

Dividend = 24 (the total number)

Divisor = 6 (how many in each group)

Step 2: Think multiplication

What number times 6 equals 24?

6 × 4 = 24, so 24 ÷ 6 = 4

Step 3: Check your answer

4 × 6 = 24 ✓

24 ÷ 6 = 4
Final answers:

24 ÷ 6 = 4

36 ÷ 4 = 9 (because 4 × 9 = 36)

45 ÷ 9 = 5 (because 9 × 5 = 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:
12 ÷ 1 = 12
12 ÷ 2 = 6
12 ÷ 3 = 4
12 ÷ 4 = ?
12 ÷ 6 = ?
12 ÷ 12 = ?
Definition:

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

Pattern
12 ÷ ?
Quotient
?
Step 1: Observe the pattern

12 ÷ 1 = 12 (largest quotient)

12 ÷ 2 = 6 (smaller divisor, smaller quotient)

12 ÷ 3 = 4 (even smaller quotient)

Step 2: Continue the pattern

12 ÷ 4 = ? → Think: 4 × ? = 12 → Answer: 3

12 ÷ 6 = ? → Think: 6 × ? = 12 → Answer: 2

12 ÷ 12 = ? → Think: 12 × ? = 12 → Answer: 1

Step 3: Verify the pattern

As divisor increases, quotient decreases: 12 → 6 → 4 → 3 → 2 → 1

12 ÷ 4 = 3
12 ÷ 6 = 2
12 ÷ 12 = 1
Final answer:

12 ÷ 4 = 3, 12 ÷ 6 = 2, 12 ÷ 12 = 1

Applied rules:

• Division pattern rule: Larger divisor = Smaller quotient

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

• Commutative relationship: 12 ÷ 3 = 4 and 12 ÷ 4 = 3

Pattern recognition: Look for decreasing quotients as divisors increase!
Factor pairs: Remember that 3×4=12 and 4×3=12, so 12÷3=4 and 12÷4=3
3 Word Problems
Exercise 3
Sarah has 36 cookies. She wants to share them equally among 6 friends. How many cookies does each friend get?
Tom has 48 stickers. He puts 8 stickers on each page of his album. How many pages does he fill?
Definition:

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

Sarah's problem
36 ÷ 6
Tom's problem
48 ÷ 8
Results
? and ?
Step 1: Sarah's cookie problem

Total cookies = 36 (dividend)

Number of friends = 6 (divisor)

Each friend gets: 36 ÷ 6 = 6 cookies

Step 2: Tom's sticker problem

Total stickers = 48 (dividend)

Stickers per page = 8 (divisor)

Pages filled: 48 ÷ 8 = 6 pages

Step 3: Verify both answers

Sarah: 6 friends × 6 cookies = 36 cookies ✓

Tom: 6 pages × 8 stickers = 48 stickers ✓

Sarah: 36 ÷ 6 = 6 cookies per friend
Tom: 48 ÷ 8 = 6 pages
Final answer:

Sarah's friends each get 6 cookies.

Tom fills 6 pages with stickers.

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 1-12: 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, 10s 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 1-12

📊
Easy divisions (1-2)

n ÷ 1 = n (always)

Even numbers ÷ 2 = half of the number

Examples: 8÷2=4, 12÷2=6, 16÷2=8

Common patterns (3-5)

Numbers ending in 0 or 5 ÷ 5

Sum of digits divisible by 3 → number ÷ 3

Examples: 15÷3=5, 20÷5=4, 24÷3=8

Advanced facts (6-9)

Double the divisor to find doubles

Half the divisor for halves

Examples: 18÷6=3, 27÷9=3, 36÷6=6

Multiples of 10 (10-12)

Move decimal point for ÷ 10

Think in dozens for ÷ 12

Examples: 50÷10=5, 48÷12=4, 36÷12=3

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 1-12.

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, ÷10) 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 1-12, practice word problems, understand inverse relationship.
Essential facts to memorize:

• 12÷1=12, 12÷2=6, 12÷3=4, 12÷4=3, 12÷6=2, 12÷12=1

• 18÷2=9, 18÷3=6, 18÷6=3, 18÷9=2

• 24÷2=12, 24÷3=8, 24÷4=6, 24÷6=4, 24÷8=3, 24÷12=2

• 36÷4=9, 36÷6=6, 36÷9=4, 36÷12=3

• 48÷6=8, 48÷8=6, 48÷12=4

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 1-12: 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 1-12.

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, ÷10) 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!