Division Facts 1-10: Complete Guide with Exercises and Solutions

Master division facts 1-10 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: 20 ÷ 4 = ?
Also solve: 30 ÷ 5 = ?, 35 ÷ 7 = ?, 40 ÷ 8 = ?
Definition:

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

Division fact: A basic division equation that uses numbers 1-10.

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
20 ÷ 4
Think
? × 4 = 20
Answer
5
Step 1: Identify parts

Dividend = 20 (the total number)

Divisor = 4 (how many in each group)

Step 2: Think multiplication

What number times 4 equals 20?

4 × 5 = 20, so 20 ÷ 4 = 5

Step 3: Check your answer

5 × 4 = 20 ✓

20 ÷ 4 = 5
Final answers:

20 ÷ 4 = 5

30 ÷ 5 = 6 (because 5 × 6 = 30)

35 ÷ 7 = 5 (because 7 × 5 = 35)

40 ÷ 8 = 5 (because 8 × 5 = 40)

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:
10 ÷ 1 = 10
10 ÷ 2 = 5
10 ÷ 5 = 2
10 ÷ 10 = ?
15 ÷ 1 = ?
15 ÷ 3 = ?
Definition:

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

Pattern
10 ÷ ?
Quotient
?
Step 1: Observe the pattern

10 ÷ 1 = 10 (largest quotient)

10 ÷ 2 = 5 (smaller divisor, smaller quotient)

10 ÷ 5 = 2 (even smaller quotient)

Step 2: Continue the pattern

10 ÷ 10 = ? → Think: 10 × ? = 10 → Answer: 1

15 ÷ 1 = ? → Think: 1 × ? = 15 → Answer: 15

15 ÷ 3 = ? → Think: 3 × ? = 15 → Answer: 5

Step 3: Verify the pattern

As divisor increases, quotient decreases: 10 → 5 → 2 → 1

10 ÷ 10 = 1
15 ÷ 1 = 15
15 ÷ 3 = 5
Final answer:

10 ÷ 10 = 1, 15 ÷ 1 = 15, 15 ÷ 3 = 5

Applied rules:

• Division pattern rule: Larger divisor = Smaller quotient

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

• Commutative relationship: 10 ÷ 2 = 5 and 10 ÷ 5 = 2

Pattern recognition: Look for decreasing quotients as divisors increase!
Factor pairs: Remember that 2×5=10 and 5×2=10, so 10÷2=5 and 10÷5=2
3 Word Problems
Exercise 3
Maria has 24 crayons. She wants to put them equally into 6 boxes. How many crayons go in each box?
There are 36 students in gym class. They form teams of 4. How many teams are there?
A baker has 45 cookies. She puts 5 cookies in each bag. How many bags does she fill?
Definition:

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

Maria's problem
24 ÷ 6
Teams problem
36 ÷ 4
Baker's problem
45 ÷ 5
Step 1: Maria's crayon problem

Total crayons = 24 (dividend)

Number of boxes = 6 (divisor)

Crayons per box: 24 ÷ 6 = 4 crayons

Step 2: Team formation problem

Total students = 36 (dividend)

Students per team = 4 (divisor)

Number of teams: 36 ÷ 4 = 9 teams

Step 3: Cookie bagging problem

Total cookies = 45 (dividend)

Cookies per bag = 5 (divisor)

Number of bags: 45 ÷ 5 = 9 bags

Step 4: Verify all answers

Maria: 6 boxes × 4 crayons = 24 crayons ✓

Teams: 9 teams × 4 students = 36 students ✓

Baker: 9 bags × 5 cookies = 45 cookies ✓

Maria: 24 ÷ 6 = 4 crayons per box
Teams: 36 ÷ 4 = 9 teams
Baker: 45 ÷ 5 = 9 bags
Final answer:

Maria puts 4 crayons in each box.

There are 9 teams in gym class.

The baker fills 9 bags with cookies.

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 1-10 Summary

📋
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 1-10.

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: 10 ÷ 2 = 5 (think: 2 × 5 = 10)

Medium: 24 ÷ 6 = 4 (think: 6 × 4 = 24)

Harder: 42 ÷ 7 = 6 (think: 7 × 6 = 42)

Advanced: 56 ÷ 8 = 7 (think: 8 × 7 = 56)

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 6×4=24, 4×6=24, 24÷6=4, 24÷4=6 together.

Patterns: Notice how divisors and quotients are factor pairs.

Practice: Daily drills improve recall speed.

Verification: Always multiply back to check!

Division Facts 1-10: 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 1-10

📊
Dividend ÷ 1 ÷ 2 ÷ 3 ÷ 4 ÷ 5
10 10 5 3.33 2.5 2
12 12 6 4 3 2.4
15 15 7.5 5 3.75 3
16 16 8 5.33 4 3.2
18 18 9 6 4.5 3.6
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 1-10.

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

• 10÷1=10, 10÷2=5, 10÷5=2, 10÷10=1

• 12÷2=6, 12÷3=4, 12÷4=3, 12÷6=2

• 15÷3=5, 15÷5=3

• 16÷2=8, 16÷4=4, 16÷8=2

• 18÷2=9, 18÷3=6, 18÷6=3, 18÷9=2

• 20÷2=10, 20÷4=5, 20÷5=4, 20÷10=2

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 1-10: 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 1-10.

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!