ANSWER: 9
Show your work using pictures and number sentences.
Division: Division is the process of sharing equally or grouping objects into equal parts. It's the opposite of multiplication.
Division Symbol: ÷ means "divided by" or "shared equally among"
- Sharing Equally: Distribute items evenly among groups
- Repeated Subtraction: Keep subtracting the divisor until reaching zero
- Using Multiplication Facts: Think "What times 4 equals 36?"
We need to find how many groups of 4 can be made from 36, or how many items each person gets if 36 items are shared equally among 4 people.
Draw 36 circles and group them into sets of 4:
○○○○ | ○○○○ | ○○○○ | ○○○○ | ○○○○ | ○○○○ | ○○○○ | ○○○○ | ○○○○
We can make 9 groups of 4.
If 36 ÷ 4 = 9, then 9 × 4 should equal 36.
9 × 4 = 36 ✓
36 ÷ 4 = 9 because 9 groups of 4 make 36.
• Division Relationship: Dividend ÷ Divisor = Quotient
• Multiplication Check: Quotient × Divisor = Dividend
• Equal Groups: Division creates equal-sized groups
ANSWER: 5 R4
How many are left over?
Division with Remainder: When division doesn't result in equal groups, some items are left over.
Remainder: The amount left over after division.
5 × 1 = 5
5 × 2 = 10
5 × 3 = 15
5 × 4 = 20
5 × 5 = 25
5 × 6 = 30 (too big!)
29 - 25 = 4 (the leftover amount)
29 ÷ 5 = 5 remainder 4, or 5 R4
29 ÷ 5 = 5 R4 because 5 groups of 5 make 25, leaving 4 remaining.
• Division Formula: Dividend = (Divisor × Quotient) + Remainder
• Remainder Rule: Remainder must be less than the divisor
• Verification: 5 × 5 + 4 = 25 + 4 = 29 ✓
ANSWER: 5 pages
Word Problem Strategy: Identify key words like "each," "per," "groups of," or "shared equally" to determine if division is needed.
We need to find how many groups of 9 can be made from 45.
Total ÷ Items per group = Number of groups
45 ÷ 9 = ?
We know that 9 × 5 = 45, so 45 ÷ 9 = 5
Sarah needs 5 pages to hold all 45 stickers.
Sarah needs 5 pages because 45 ÷ 9 = 5.
• Word Problem Steps: Read → Identify → Plan → Solve → Check
• Division Keywords: "per," "each," "in all groups," "shared equally"
• Context: Always answer in the context of the problem
Dividend: The number being divided
Divisor: The number we divide by
Quotient: The result of division
Remainder: What's left over
Fact Family: A set of related multiplication and division facts using the same numbers.
- Equal Sharing: Distribute items equally
- Grouping: Make equal-sized groups
- Repeated Subtraction: Subtract the divisor repeatedly
- Multiplication Facts: Use known multiplication facts
| Division | Answer | Check |
|---|---|---|
| 5 ÷ 5 | 1 | 1 × 5 = 5 |
| 10 ÷ 5 | 2 | 2 × 5 = 10 |
| 15 ÷ 5 | 3 | 3 × 5 = 15 |
| 20 ÷ 5 | 4 | 4 × 5 = 20 |
| 25 ÷ 5 | 5 | 5 × 5 = 25 |
| 30 ÷ 5 | 6 | 6 × 5 = 30 |
| 35 ÷ 5 | 7 | 7 × 5 = 35 |
| 40 ÷ 5 | 8 | 8 × 5 = 40 |
| 45 ÷ 5 | 9 | 9 × 5 = 45 |
| 50 ÷ 5 | 10 | 10 × 5 = 50 |
• Dividing by 5 gives one-fifth of the original number
• These facts are essential for grade 3 division mastery
• Practice until these become automatic
| Division | Answer | Check |
|---|---|---|
| 6 ÷ 6 | 1 | 1 × 6 = 6 |
| 12 ÷ 6 | 2 | 2 × 6 = 12 |
| 18 ÷ 6 | 3 | 3 × 6 = 18 |
| 24 ÷ 6 | 4 | 4 × 6 = 24 |
| 30 ÷ 6 | 5 | 5 × 6 = 30 |
| 36 ÷ 6 | 6 | 6 × 6 = 36 |
| 42 ÷ 6 | 7 | 7 × 6 = 42 |
| 48 ÷ 6 | 8 | 8 × 6 = 48 |
| 54 ÷ 6 | 9 | 9 × 6 = 54 |
| 60 ÷ 6 | 10 | 10 × 6 = 60 |
• Dividing by 6 gives one-sixth of the original number
• These facts are essential for grade 3 division mastery
• Notice that answers increase by 1 each time
Division: Splitting into equal parts or groups
Sharing: Giving equal amounts to each person/group
Grouping: Making equal-sized groups from a total
Fact Families: Related multiplication and division facts
- Understand the Problem: Identify what needs to be divided
- Choose the Method: Sharing, grouping, or using multiplication facts
- Apply the Method: Follow the steps of the chosen technique
- Check Your Work: Multiply quotient by divisor
• Any number divided by 1 equals itself
• Any number divided by itself equals 1
• Zero divided by any number (except 0) equals 0
• Division by zero is undefined
• Dividend = Divisor × Quotient + Remainder
Questions & Answers
Question: How can I help my students understand the connection between multiplication and division? They seem to struggle with seeing them as inverse operations.
Answer: Great question! Use fact families to show the relationship:
- Start with a multiplication fact: 5 × 6 = 30
- Show how it creates two division facts: 30 ÷ 5 = 6 and 30 ÷ 6 = 5
- Use visual models: 5 rows of 6 dots = 30 dots total
- Then ask: "If I have 30 dots and want 5 rows, how many in each row?" (30 ÷ 5 = 6)
- Or: "If I have 30 dots and want 6 in each row, how many rows?" (30 ÷ 6 = 5)
Concrete examples work best: "I have 30 cookies and 5 friends. How many does each friend get?" versus "I have 30 cookies and want to give 6 to each friend. How many friends can I feed?"
Question: Why do we sometimes have remainders in division? What do they mean?
Answer: Remainders occur when numbers don't divide evenly! Think of it like sharing:
- If you have 29 candies and share them equally among 5 friends, each friend gets 5 candies (5 × 5 = 25), and you have 4 candies left over
- The remainder (4) represents what can't be shared equally
- Remainders are always smaller than the divisor - otherwise, you could divide further!
- So 29 ÷ 5 = 5 R4 means 5 groups of 5 with 4 left over
Remainders are completely normal in division - they just mean the division isn't perfectly even!
Question: My child gets confused about whether to divide or multiply in word problems. How can I help them identify the operation?
Answer: Teach your child to look for key words and visualize the problem:
- Division words: "shared equally," "each," "per," "in each group," "split into," "divided among"
- Multiplication words: "total," "altogether," "product," "times," "groups of"
- Ask: "Am I finding the total, or am I splitting something up?"
- Have them draw pictures - if they're distributing items, it's division
- If they're combining equal groups, it's multiplication
Practice with real objects: "I have 45 cookies and want to put 9 on each plate - how many plates?" (45 ÷ 9 = 5 plates)
Division Problem Answers - Complete Summary
Division: The process of splitting a number into equal groups or parts.
Dividend: The number being divided.
Divisor: The number we divide by.
Quotient: The result of division.
Remainder: The amount left over after division.
Fact Family: A set of related multiplication and division facts using the same numbers.
Division Algorithm: The systematic method for solving division problems.
Division-Multiplication Connection: 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
Zero Division: 0 ÷ any number = 0
Division Formula: Dividend = Divisor × Quotient + Remainder
Remainder Rule: Remainder is always less than the divisor
1. Fact Family Method: Think of related multiplication facts
2. Repeated Subtraction: Keep subtracting the divisor
3. Equal Sharing: Distribute items equally among groups
4. Grouping Method: Make equal-sized groups
5. Verification: Always multiply quotient × divisor to check
Simple: 12 ÷ 3 = 4 (basic fact)
Medium: 36 ÷ 4 = 9 (intermediate fact)
With Remainder: 29 ÷ 5 = 5 R4 (with remainder)
Word Problem: 45 ÷ 9 = 5 (real-world context)
Advanced: Multi-step problems requiring multiple operations
Memory Aid: "What times the divisor gives me the dividend?"
Check Your Work: Always verify: Divisor × Quotient + Remainder = Dividend
Practice Tables: Master multiplication tables to improve division
Look for Patterns: Notice relationships in division facts
Visualize: Draw pictures to represent division situations
Confusing Dividend/Divisor: Pay attention to which number is being divided
Ignoring Remainders: Don't forget to include remainders when they exist
Not Checking: Always verify your answer by multiplying back
Mixing Operations: Be careful to identify whether to multiply or divide
Remainder Size: Remainders must always be smaller than divisors