Also solve: 21 ÷ 3 = ?, 28 ÷ 4 = ?, 32 ÷ 8 = ?
Division: Splitting a number into equal groups. The dividend ÷ divisor = quotient.
Division fact: A basic division equation that uses numbers 1-10.
- 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 = 16 (the total number)
Divisor = 4 (how many in each group)
What number times 4 equals 16?
4 × 4 = 16, so 16 ÷ 4 = 4
4 × 4 = 16 ✓
16 ÷ 4 = 4
21 ÷ 3 = 7 (because 3 × 7 = 21)
28 ÷ 4 = 7 (because 4 × 7 = 28)
32 ÷ 8 = 4 (because 8 × 4 = 32)
• 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)
18 ÷ 1 = 18
18 ÷ 2 = 9
18 ÷ 3 = 6
18 ÷ 6 = ?
18 ÷ 9 = ?
18 ÷ 18 = ?
Division patterns: As the divisor increases, the quotient decreases proportionally.
18 ÷ 1 = 18 (largest quotient)
18 ÷ 2 = 9 (smaller divisor, smaller quotient)
18 ÷ 3 = 6 (even smaller quotient)
18 ÷ 6 = ? → Think: 6 × ? = 18 → Answer: 3
18 ÷ 9 = ? → Think: 9 × ? = 18 → Answer: 2
18 ÷ 18 = ? → Think: 18 × ? = 18 → Answer: 1
As divisor increases, quotient decreases: 18 → 9 → 6 → 3 → 2 → 1
18 ÷ 9 = 2
18 ÷ 18 = 1
18 ÷ 6 = 3, 18 ÷ 9 = 2, 18 ÷ 18 = 1
• 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
There are 24 students in class. They sit in groups of 6. How many groups are there?
A farmer has 40 eggs. He packs them in cartons of 8 eggs each. How many cartons does he fill?
Division word problems: Real-life situations requiring equal sharing or grouping.
Total books = 30 (dividend)
Number of shelves = 5 (divisor)
Books per shelf: 30 ÷ 5 = 6 books
Total students = 24 (dividend)
Students per group = 6 (divisor)
Number of groups: 24 ÷ 6 = 4 groups
Total eggs = 40 (dividend)
Eggs per carton = 8 (divisor)
Number of cartons: 40 ÷ 8 = 5 cartons
Books: 5 shelves × 6 books = 30 books ✓
Groups: 4 groups × 6 students = 24 students ✓
Eggs: 5 cartons × 8 eggs = 40 eggs ✓
Groups: 24 ÷ 6 = 4 groups
Eggs: 40 ÷ 8 = 5 cartons
Each shelf gets 6 books.
There are 4 groups of students.
The farmer fills 5 cartons with eggs.
• 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 1-10 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 1-10.
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: 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)
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 1-10.
- 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
• 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
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.
- 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!