Also solve: 36 ÷ 6 = ?, 42 ÷ 7 = ?, 48 ÷ 8 = ?
Division: Splitting a number into equal groups. The dividend ÷ divisor = quotient.
Division fact: A basic division equation that uses numbers 1-12.
- Identify the dividend (total number) and divisor (number of groups)
- Think: "How many times does the divisor go into the dividend?"
- Use multiplication facts to find the quotient
- Check: Quotient × Divisor = Dividend
Dividend = 30 (the total number)
Divisor = 5 (how many in each group)
What number times 5 equals 30?
5 × 6 = 30, so 30 ÷ 5 = 6
6 × 5 = 30 ✓
30 ÷ 5 = 6
36 ÷ 6 = 6 (because 6 × 6 = 36)
42 ÷ 7 = 6 (because 7 × 6 = 42)
48 ÷ 8 = 6 (because 8 × 6 = 48)
• 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)
48 ÷ 1 = 48
48 ÷ 2 = 24
48 ÷ 3 = 16
48 ÷ 4 = ?
48 ÷ 6 = ?
48 ÷ 8 = ?
Division patterns: As the divisor increases, the quotient decreases proportionally.
48 ÷ 1 = 48 (largest quotient)
48 ÷ 2 = 24 (smaller divisor, smaller quotient)
48 ÷ 3 = 16 (even smaller quotient)
48 ÷ 4 = ? → Think: 4 × ? = 48 → Answer: 12
48 ÷ 6 = ? → Think: 6 × ? = 48 → Answer: 8
48 ÷ 8 = ? → Think: 8 × ? = 48 → Answer: 6
As divisor increases, quotient decreases: 48 → 24 → 16 → 12 → 8 → 6
48 ÷ 6 = 8
48 ÷ 8 = 6
48 ÷ 4 = 12, 48 ÷ 6 = 8, 48 ÷ 8 = 6
• Division pattern rule: Larger divisor = Smaller quotient
• Factor pairs: Divisors and quotients are factor pairs of the dividend
• Commutative relationship: 48 ÷ 4 = 12 and 48 ÷ 12 = 4
There are 63 students in gym class. They form teams of 7. How many teams are there?
A baker has 72 cookies. He packs them in bags of 8 cookies each. How many bags does he make?
Division word problems: Real-life situations requiring equal sharing or grouping.
Total crayons = 54 (dividend)
Number of boxes = 9 (divisor)
Crayons per box: 54 ÷ 9 = 6 crayons
Total students = 63 (dividend)
Students per team = 7 (divisor)
Number of teams: 63 ÷ 7 = 9 teams
Total cookies = 72 (dividend)
Cookies per bag = 8 (divisor)
Number of bags: 72 ÷ 8 = 9 bags
Crayons: 9 boxes × 6 crayons = 54 crayons ✓
Teams: 9 teams × 7 students = 63 students ✓
Cookies: 9 bags × 8 cookies = 72 cookies ✓
Teams: 63 ÷ 7 = 9 teams
Cookies: 72 ÷ 8 = 9 bags
Each box gets 6 crayons.
There are 9 teams in gym class.
The baker makes 9 bags of cookies.
• 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"
Division Facts and Answers Summary
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 1-12.
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.
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
Easy: 12 ÷ 3 = 4 (think: 3 × 4 = 12)
Medium: 24 ÷ 6 = 4 (think: 6 × 4 = 24)
Harder: 42 ÷ 7 = 6 (think: 7 × 6 = 42)
Advanced: 56 ÷ 8 = 7 (think: 8 × 7 = 56)
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.
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: 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.
- Read the problem: Identify dividend and divisor
- Think multiplication: What number times divisor equals dividend?
- Recall fact: Use memorized division facts
- Check answer: Multiply quotient by divisor to get dividend
• 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÷3=12, 36÷4=9, 36÷6=6, 36÷9=4, 36÷12=3
• 48÷4=12, 48÷6=8, 48÷8=6, 48÷12=4
• 60÷5=12, 60÷6=10, 60÷10=6, 60÷12=5
Division Strategies
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.
- Analyze the problem: Identify what needs to be divided
- Choose strategy: Visual model, multiplication thinking, or repeated subtraction
- Apply method: Follow chosen strategy to find quotient
- Verify result: Multiply quotient by divisor to check
• 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!