Solved Exercises on Basic Division Facts in Grade 3

Master basic division facts: understanding division, division facts up to 12, and division word problems through these 3 detailed exercises.

Solution: Exercises 1 to 3
1 Understanding Division
Exercise 1
Solve: 12 ÷ 3 = ?
Show how division works using grouping and repeated subtraction.
Definition:

Division: Division is the process of splitting a number into equal groups. It's the opposite of multiplication.

Division Symbol: ÷ (divided by), / (fraction bar), or a horizontal line

Parts of Division: Dividend ÷ Divisor = Quotient (Remainder if any)

Division methods:
  1. Grouping Method: Make equal groups from the dividend
  2. Repeated Subtraction: Keep subtracting the divisor from the dividend
  3. Using Multiplication Facts: Think of what number times the divisor equals the dividend
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12 items
3 groups
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Step 1: Understand the problem

We need to find how many items are in each group when 12 items are divided into 3 equal groups.

Step 2: Grouping method

Take 12 items and make 3 equal groups:
Group 1: ●●● (3 items)
Group 2: ●●● (3 items)
Group 3: ●●● (3 items)
Remaining: ●●● (3 items) → Total 4 groups of 3 items each

Wait! Let me correct this: We want 3 groups total, so:
12 items ÷ 3 groups = 4 items per group

Step 3: Repeated subtraction method

Start with 12 and keep subtracting 3:
12 - 3 = 9 (1st subtraction)
9 - 3 = 6 (2nd subtraction)
6 - 3 = 3 (3rd subtraction)
3 - 3 = 0 (4th subtraction)
We subtracted 3 four times to reach 0, so 12 ÷ 3 = 4

Step 4: Using multiplication facts

Think: What number × 3 = 12?
3 × 1 = 3
3 × 2 = 6
3 × 3 = 9
3 × 4 = 12 ← This is our answer!
So 12 ÷ 3 = 4

12 ÷ 3 = 4
Final answer:

12 ÷ 3 = 4 because 4 groups of 3 make 12 (4 × 3 = 12)

Applied rules:

• Division as grouping: Split the dividend into equal groups equal to the divisor

• Division as repeated subtraction: Count how many times you can subtract the divisor

• Relationship with multiplication: Division undoes multiplication

• Fact families: 3 × 4 = 12, 4 × 3 = 12, 12 ÷ 3 = 4, 12 ÷ 4 = 3

Tip: Always check your division by multiplying: quotient × divisor = dividend
Common mistake: Confusing dividend and divisor - dividend is the big number being divided
2 Division Facts Practice
Exercise 2
Solve: 24 ÷ 6 = ?
Use fact families and multiplication tables to solve.
Definition:

Division Facts: Basic division equations that relate to multiplication facts

Fact Family: A set of related multiplication and division facts using the same numbers

Division Table: A table showing division facts for a particular number

6 × 4 = 24
Multiplier × Multiplicand = Product
4 × 6 = 24
Commutative Property
24 ÷ 6 = 4
Product ÷ Multiplier = Multiplicand
24 ÷ 4 = 6
Product ÷ Multiplicand = Multiplier
24
Dividend
÷
Operation
6
Divisor
=
Equals
4
Quotient
Step 1: Identify the division fact

We need to divide 24 by 6. Think of the multiplication fact where 6 is one factor.

Step 2: Use multiplication facts

What number times 6 equals 24?
6 × 1 = 6
6 × 2 = 12
6 × 3 = 18
6 × 4 = 24 ← This is our answer!
So 24 ÷ 6 = 4

Step 3: Verify with fact family

If 24 ÷ 6 = 4, then 4 × 6 should equal 24
4 × 6 = 24 ✓
Also: 6 × 4 = 24 ✓
And: 24 ÷ 4 = 6 ✓

Step 4: Check with grouping

If we have 24 items and put them into 6 equal groups:
Each group would have 4 items
6 groups × 4 items = 24 items total ✓

24 ÷ 6 = 4
Final answer:

24 ÷ 6 = 4 because 6 × 4 = 24

Applied rules:

• Multiplication-division relationship: Division facts come from multiplication facts

• Fact families: Numbers in a fact family can be arranged in 4 related facts

• Division as inverse of multiplication: Division undoes multiplication

• Memorization trick: Know your multiplication tables to master division facts

Tip: Master multiplication facts first - division becomes much easier!
Pattern: In division facts, the largest number is always the dividend
3 Word Problem Division
Exercise 3
Sarah has 18 cookies. She wants to share them equally among 3 friends. How many cookies does each friend get?
Definition:

Word Problems: Real-life situations that require mathematical operations to solve

Equal Sharing: A type of division problem where items are distributed equally

Keywords for Division: share, split, divide, distribute, each, per, average

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Step 1: Identify what we know

Total cookies: 18
Number of friends: 3
Need to find: Cookies per friend

Step 2: Set up the division

We need to divide 18 cookies among 3 friends
This means: 18 ÷ 3 = ?

Step 3: Solve using multiplication facts

Think: What number × 3 = 18?
3 × 1 = 3
3 × 2 = 6
3 × 3 = 9
3 × 4 = 12
3 × 5 = 15
3 × 6 = 18 ← This is our answer!
So 18 ÷ 3 = 6

Step 4: Verify the answer

If each friend gets 6 cookies and there are 3 friends:
6 × 3 = 18 cookies total ✓
This matches our original number of cookies.

Each friend gets 6 cookies
Final answer:

Each friend gets 6 cookies because 18 ÷ 3 = 6

Applied rules:

• Equal sharing: Total amount ÷ Number of groups = Amount per group

• Keyword identification: "share equally" indicates division

• Verification: Always multiply back to check your answer

• Real-world connection: Division helps us distribute things fairly

Tip: Draw pictures to visualize word problems - it makes solving easier!
Key words: Look for "each," "per," "shared equally," "divided among"
Division Facts and Properties
\(a ÷ b = c\) means \(c × b = a\)
Division Relationship
Division by 1
\(a ÷ 1 = a\)
Any number divided by 1 equals itself
Division by Self
\(a ÷ a = 1\)
Any non-zero number divided by itself equals 1
Zero Divided
\(0 ÷ a = 0\)
Zero divided by any number equals zero
Key definitions:

Dividend: The number being divided (the larger number)

Divisor: The number dividing into the dividend

Quotient: The result of the division

Remainder: What's left over when division doesn't result in a whole number

Division strategies:
  1. Visual grouping: Draw circles and place objects in each group
  2. Repeated subtraction: Keep subtracting the divisor until reaching zero
  3. Multiplication connection: Think of the related multiplication fact
  4. Number line jumps: Skip count backwards on a number line
Tip 1: Practice division facts daily - they build fluency!
Tip 2: Use arrays and grouping models to understand division visually.
Tip 3: Remember: multiplication and division are inverse operations.
Tip 4: Always check division by multiplying the quotient by the divisor.
Division facts to memorize: Division facts up to 12 ÷ 12 are foundational for higher math.
Important note: Division by zero is undefined - you cannot divide by zero.
Essential division facts:

• 2 ÷ 1 = 2, 4 ÷ 2 = 2, 6 ÷ 2 = 3, 8 ÷ 2 = 4, 10 ÷ 2 = 5, 12 ÷ 2 = 6

• 3 ÷ 1 = 3, 6 ÷ 2 = 3, 9 ÷ 3 = 3, 12 ÷ 3 = 4, 15 ÷ 3 = 5, 18 ÷ 3 = 6

• 4 ÷ 1 = 4, 8 ÷ 2 = 4, 12 ÷ 3 = 4, 16 ÷ 4 = 4, 20 ÷ 4 = 5, 24 ÷ 4 = 6

• 5 ÷ 1 = 5, 10 ÷ 2 = 5, 15 ÷ 3 = 5, 20 ÷ 4 = 5, 25 ÷ 5 = 5, 30 ÷ 5 = 6

• 6 ÷ 1 = 6, 12 ÷ 2 = 6, 18 ÷ 3 = 6, 24 ÷ 4 = 6, 30 ÷ 5 = 6, 36 ÷ 6 = 6

Division Concepts and Applications
\(a ÷ b = c\) if and only if \(c × b = a\)
Fundamental Division Property
Division fundamentals:

Division as Equal Sharing: Distributing items equally among groups

Division as Grouping: Finding how many groups of a certain size can be made

Division as Repeated Subtraction: How many times can the divisor be subtracted from the dividend

Division as Inverse of Multiplication: Using multiplication facts to solve division problems

Step-by-step division approach:
  1. Read carefully: Understand what the problem is asking
  2. Identify parts: Find the dividend, divisor, and what you need to find
  3. Choose strategy: Select the best method for the specific problem
  4. Solve systematically: Follow the chosen method step by step
  5. Check answer: Verify by multiplying quotient and divisor
Memorization trick: Practice with flashcards for quick recall of division facts.
Visual aid: Use manipulatives like counters or drawing circles to model division.
Connection strategy: Always connect division to the related multiplication fact.
Verification method: Multiply your answer by the divisor to check accuracy.
Common errors: Forgetting to check answers, confusing dividend with divisor, miscounting groups.
Test preparation: Practice word problems, memorize facts up to 12, understand relationships.
Division patterns to recognize:

• Any number divided by 1 equals itself: n ÷ 1 = n

• Any number divided by itself equals 1: n ÷ n = 1 (when n ≠ 0)

• Zero divided by any number equals zero: 0 ÷ n = 0 (when n ≠ 0)

• Division by zero is undefined: n ÷ 0 = undefined

• Even numbers divided by 2 result in whole numbers

Division Fact Families

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Fact Family Relationships
3 × 4 = 12
Multiplication
4 × 3 = 12
Commutative
12 ÷ 3 = 4
Division
12 ÷ 4 = 3
Division
Division Strategies

• Visual grouping: Draw circles and distribute items

• Repeated subtraction: Keep subtracting the divisor

• Multiplication connection: Think of related facts

• Skip counting: Count by the divisor

Practice Makes Perfect! 🌟
Division Laws, Methods, and Key Expressions
\(a ÷ b = c \Rightarrow a = b × c\)
Division-Multiplication Relationship
Key definitions:

Division: The operation of splitting a quantity into equal parts

Fact Family: A group of related multiplication and division facts

Quotient: The answer in a division problem

Dividend: The number being divided

Divisor: The number that divides the dividend

Complete methodology:
  1. Understand the problem: Identify what is being asked
  2. Identify the operation: Determine if division is needed
  3. Set up the equation: Write the division sentence
  4. Choose strategy: Select the most efficient method
  5. Solve: Carry out the division
  6. Check: Verify by multiplying the quotient and divisor
Tip 1: Use multiplication facts to quickly solve division problems.
Tip 2: Draw pictures or use objects to visualize division problems.
Tip 3: Always check your work by multiplying quotient × divisor = dividend.
Tip 4: Practice regularly to build automaticity with basic facts.
Common errors: Misidentifying dividend/divisor, forgetting to check answers, calculation mistakes.
Exam preparation: Master facts up to 12, practice word problems, understand relationships.
Division laws and properties:

• Identity Property: n ÷ 1 = n

• Inverse Property: n ÷ n = 1 (n ≠ 0)

• Zero Property: 0 ÷ n = 0 (n ≠ 0)

• Undefined: n ÷ 0 is undefined

• Commutativity: Division is NOT commutative (a ÷ b ≠ b ÷ a)

• Associativity: Division is NOT associative ((a ÷ b) ÷ c ≠ a ÷ (b ÷ c))

Questions & Answers

Question: I don't understand why 12 ÷ 3 = 4. Can you explain it differently?

Answer: Great question! Let me explain it in multiple ways:

  • Sharing: Imagine you have 12 cookies and want to share them equally among 3 friends. Each friend gets 4 cookies because 3 × 4 = 12.
  • Groups: If you have 12 objects and make groups of 3, you can make exactly 4 groups.
  • Counting backward: Start at 12 and count backward by 3s: 12, 9, 6, 3, 0. You counted back 4 times, so 12 ÷ 3 = 4.
  • Multiplication connection: Since 3 × 4 = 12, then 12 ÷ 3 = 4 (they're opposite operations).

Division is just another way of thinking about how many equal groups you can make or how many are in each group!

Question: Why can't we divide by zero? What happens if we try?

Answer: Division by zero is undefined, and here's why:

  • If we say 12 ÷ 0 = ?, we're asking "What number times 0 equals 12?"
  • But any number times 0 equals 0, not 12!
  • So there's no answer that makes sense.
  • It's like trying to share 12 cookies among 0 people - it doesn't make practical sense.

Think of it this way: How many groups of zero can you make from 12? That question has no meaningful answer, so mathematicians say division by zero is undefined.

Question: How can I help my child memorize division facts faster?

Answer: Here are effective strategies for learning division facts:

  • Connect to multiplication: Teach division facts alongside multiplication facts since they're inverses
  • Use visual aids: Draw groups, arrays, or use manipulatives like blocks or counters
  • Practice regularly: Short, frequent practice sessions (5-10 minutes daily) work better than long sessions
  • Make it fun: Use games, apps, songs, or flashcards to make practice enjoyable
  • Real-world applications: Connect division to sharing food, distributing toys, etc.

Start with smaller facts (÷1, ÷2) and gradually work up. Consistency and positive reinforcement are key!