Solved Exercises on Basic Division Facts in Grade 3

Master basic division facts: division tables, fact families, and connections to multiplication through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Basic Division Facts
Exercise 1
Solve these basic division facts: 12 ÷ 3, 15 ÷ 5, 18 ÷ 6, 20 ÷ 4
Definition:

Division Facts: Basic division equations that involve dividing numbers from 1 to 100 by single-digit numbers. These facts are related to multiplication facts and should be memorized for fluency.

Division Fact Strategy:
  1. Think multiplication: What number times the divisor equals the dividend?
  2. Use known facts: Apply memorized multiplication facts to help
  3. Count groups: Visualize how many equal groups fit into the total
  4. Verify: Multiply your answer by the divisor to check
12 ÷ 3 = 4
Related: 3 × 4 = 12
15 ÷ 5 = 3
Related: 5 × 3 = 15
18 ÷ 6 = 3
Related: 6 × 3 = 18
20 ÷ 4 = 5
Related: 4 × 5 = 20
12
3
4
Problem 1
12 ÷ 3
Think
? × 3 = 12
Answer
4
Step 1: For 12 ÷ 3

What number times 3 equals 12? Since 4 × 3 = 12, then 12 ÷ 3 = 4

Step 2: For 15 ÷ 5

What number times 5 equals 15? Since 3 × 5 = 15, then 15 ÷ 5 = 3

Step 3: For 18 ÷ 6

What number times 6 equals 18? Since 3 × 6 = 18, then 18 ÷ 6 = 3

Step 4: For 20 ÷ 4

What number times 4 equals 20? Since 5 × 4 = 20, then 20 ÷ 4 = 5

12 ÷ 3 = 4, 15 ÷ 5 = 3, 18 ÷ 6 = 3, 20 ÷ 4 = 5
Final answer:

12 ÷ 3 = 4, 15 ÷ 5 = 3, 18 ÷ 6 = 3, 20 ÷ 4 = 5

Applied rules:

• Multiplication-Division Connection: Division facts are inverses of multiplication facts

• Fact Families: Three numbers create four related multiplication and division facts

• Verification: Multiply quotient by divisor to check answer

2 Fact Families
Exercise 2
Write the complete fact family for 3, 4, and 12 showing all related multiplication and division facts.
Definition:

Fact Family: A group of related multiplication and division facts that use the same three numbers. For numbers a, b, and c where a × b = c, the fact family includes: a × b = c, b × a = c, c ÷ a = b, and c ÷ b = a.

3 × 4 = 12
Multiplication
4 × 3 = 12
Multiplication
12 ÷ 3 = 4
Division
12 ÷ 4 = 3
Division
12
3
4

Connection: Multiplication and division are inverse operations that undo each other.

Multiplication Facts
3 × 4 = 12, 4 × 3 = 12
Division Facts
12 ÷ 3 = 4, 12 ÷ 4 = 3
Total Facts
4 facts
Step 1: Write multiplication facts

Using the commutative property: 3 × 4 = 12 and 4 × 3 = 12

Step 2: Write division facts

Using inverse relationship: 12 ÷ 3 = 4 and 12 ÷ 4 = 3

Step 3: Verify the relationships

Check that multiplication and division facts correspond correctly

Step 4: Confirm completeness

Ensure all four related facts are included

3 × 4 = 12, 4 × 3 = 12, 12 ÷ 3 = 4, 12 ÷ 4 = 3
Final answer:

The fact family for 3, 4, and 12 includes: 3 × 4 = 12, 4 × 3 = 12, 12 ÷ 3 = 4, 12 ÷ 4 = 3

Applied rules:

• Fact Family Rule: Three numbers create four related multiplication and division facts

• Commutative Property: a × b = b × a (creates two multiplication facts)

• Inverse Operations: Multiplication and division are opposite operations

3 Division Table
Exercise 3
Complete the division table for dividing by 3: 3 ÷ 3, 6 ÷ 3, 9 ÷ 3, 12 ÷ 3, 15 ÷ 3, 18 ÷ 3, 21 ÷ 3, 24 ÷ 3
Definition:

Division Table: A sequence of division facts that show the pattern when dividing consecutive multiples of a number by that same number.

3 ÷ 3 = 1
6 ÷ 3 = 2
9 ÷ 3 = 3
12 ÷ 3 = 4
15 ÷ 3 = 5
18 ÷ 3 = 6
21 ÷ 3 = 7
24 ÷ 3 = 8
3 ÷ 3 = 1
6 ÷ 3 = 2
9 ÷ 3 = 3
12 ÷ 3 = 4
Dividend pattern
3, 6, 9, 12, 15, 18, 21, 24
Divisor
3
Quotient pattern
1, 2, 3, 4, 5, 6, 7, 8
Step 1: Identify the divisor

We're dividing by 3 in all cases

Step 2: List the dividends

These are consecutive multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24

Step 3: Perform each division

3÷3=1, 6÷3=2, 9÷3=3, 12÷3=4, 15÷3=5, 18÷3=6, 21÷3=7, 24÷3=8

Step 4: Observe the pattern

The quotient increases by 1 each time the dividend increases by 3

1, 2, 3, 4, 5, 6, 7, 8
Final answer:

3 ÷ 3 = 1, 6 ÷ 3 = 2, 9 ÷ 3 = 3, 12 ÷ 3 = 4, 15 ÷ 3 = 5, 18 ÷ 3 = 6, 21 ÷ 3 = 7, 24 ÷ 3 = 8

Applied rules:

• Division Pattern: Dividing consecutive multiples by the same number creates a counting sequence

• Pattern Recognition: Helps with memorization and fluency

• Sequential Division: Each result is one more than the previous

Division Facts Overview
If a × b = c, then c ÷ a = b and c ÷ b = a
Inverse Relationship
Family 1
2, 4, 8
2×4=8, 4×2=8, 8÷2=4, 8÷4=2
Family 2
3, 5, 15
3×5=15, 5×3=15, 15÷3=5, 15÷5=3
Family 3
4, 6, 24
4×6=24, 6×4=24, 24÷4=6, 24÷6=4
Family 4
5, 7, 35
5×7=35, 7×5=35, 35÷5=7, 35÷7=5
Key definitions:

Division: The operation of splitting a number into equal groups

Dividend: The number being divided

Divisor: The number that divides the dividend

Quotient: The result of division

Fact Family: Related multiplication and division facts using the same numbers

Division Fact Strategies:
  1. Think multiplication: Use known multiplication facts to solve division
  2. Count groups: Visualize how many equal groups fit into the total
  3. Use patterns: Recognize patterns in division tables
  4. Relate to sharing: Connect to equal sharing situations
  5. Verify answers: Multiply back to check division results
Key Pattern: Division facts are inverses of multiplication facts.
Fact Family: Three numbers create four related facts.
Tip 1: Practice multiplication facts first, as they help with division.
Tip 2: Use fact families to connect multiplication and division.
Tip 3: Look for patterns in division tables to aid memorization.
Tip 4: Always verify division by multiplying back.
Solution: Exercises 4 to 5
4 Verification Practice
Exercise 4
Verify these division facts by multiplying back: (a) 16 ÷ 4 = 4, (b) 21 ÷ 7 = 3, (c) 18 ÷ 2 = 9
Definition:

Verification: Checking division answers by multiplying the quotient by the divisor to ensure the result equals the dividend.

16 ÷ 4 = 4
→
4 × 4 = 16
21 ÷ 7 = 3
→
3 × 7 = 21
18 ÷ 2 = 9
→
9 × 2 = 18
Part (a)
16 ÷ 4 = 4 → 4 × 4 = 16 ✓
Part (b)
21 ÷ 7 = 3 → 3 × 7 = 21 ✓
Part (c)
18 ÷ 2 = 9 → 9 × 2 = 18 ✓
Step 1: Verify 16 ÷ 4 = 4

Multiply back: 4 × 4 = 16 ✓

Step 2: Verify 21 ÷ 7 = 3

Multiply back: 3 × 7 = 21 ✓

Step 3: Verify 18 ÷ 2 = 9

Multiply back: 9 × 2 = 18 ✓

Step 4: Confirm all verifications

All division facts are correct since multiplication checks pass

All facts verified: 4×4=16, 3×7=21, 9×2=18
Final answer:

All division facts are correct: (a) 16 ÷ 4 = 4, (b) 21 ÷ 7 = 3, (c) 18 ÷ 2 = 9

Applied rules:

• Verification Method: Multiply quotient by divisor to get dividend

• Inverse Operations: Multiplication and division undo each other

• Self-Checking: Use multiplication to verify division answers

5 Mixed Practice
Exercise 5
Solve and identify the related multiplication fact: (a) 24 ÷ 6 = ?, (b) 35 ÷ 5 = ?, (c) 28 ÷ 4 = ?
Definition:

Mixed Practice: Combining division facts with their related multiplication counterparts to strengthen understanding of the inverse relationship.

24 ÷ 6 = 4
Related: 6 × 4 = 24
35 ÷ 5 = 7
Related: 5 × 7 = 35
28 ÷ 4 = 7
Related: 4 × 7 = 28
Part (a)
24 ÷ 6 = 4 → 6 × 4 = 24
Part (b)
35 ÷ 5 = 7 → 5 × 7 = 35
Part (c)
28 ÷ 4 = 7 → 4 × 7 = 28
Step 1: Solve 24 ÷ 6

Think: What times 6 equals 24? Answer: 4, so 24 ÷ 6 = 4. Related: 6 × 4 = 24

Step 2: Solve 35 ÷ 5

Think: What times 5 equals 35? Answer: 7, so 35 ÷ 5 = 7. Related: 5 × 7 = 35

Step 3: Solve 28 ÷ 4

Think: What times 4 equals 28? Answer: 7, so 28 ÷ 4 = 7. Related: 4 × 7 = 28

Step 4: Verify each fact family

Confirm that each division fact has its corresponding multiplication fact

(a) 4, (b) 7, (c) 7
Final answer:

(a) 24 ÷ 6 = 4 (related: 6 × 4 = 24), (b) 35 ÷ 5 = 7 (related: 5 × 7 = 35), (c) 28 ÷ 4 = 7 (related: 4 × 7 = 28)

Applied rules:

• Multiplication-division relationship: Each division fact corresponds to a multiplication fact

• Fact family completion: Knowing one fact helps find the others

• Inverse operations: Division and multiplication are opposite operations

Advanced Division Facts Concepts
a ÷ b = c ↔ a = b × c
Bidirectional Relationship
Key definitions:

Quotient: The result of a division operation

Remainder: What's left over when division is not exact

Fact Family: A set of related multiplication and division equations

Divisibility: When one number divides another evenly with no remainder

Advanced Strategies:
  1. Use multiplication tables: Leverage known multiplication facts
  2. Recognize patterns: Notice relationships between numbers
  3. Apply fact families: Use related facts to solve unknowns
  4. Check with multiplication: Always verify division results
  5. Connect to real problems: Apply facts to word problems
Tip 1: Division facts are just multiplication facts in reverse.
Tip 2: Practice with arrays and equal groups to visualize division.
Tip 3: Use skip counting to help with division facts.
Tip 4: Memorize the basic facts to improve computational fluency.
Memory Technique: Connect division facts to multiplication facts you already know.
Pattern Recognition: Notice that division by the same number creates counting sequences.
Important rules:

• Inverse Relationship: Division and multiplication are opposite operations

• Fact Families: Three numbers create four related facts

• Verification: Multiply quotient by divisor to check dividend

• Commutativity: Applies to multiplication but not division

Example
Division
Related Multiplication
Basic
12 ÷ 3 = 4
3 × 4 = 12
Medium
20 ÷ 4 = 5
4 × 5 = 20
Advanced
36 ÷ 6 = 6
6 × 6 = 36

Questions & Answers

Question: Why do we need to memorize division facts? Can't we just count or use other methods?

Answer: Memorizing division facts is important for several reasons:

  • SPEED: You can solve problems much faster when you know the facts
  • ACCURACY: Less chance of making counting errors
  • COMPLEX PROBLEMS: You'll need these basics for harder math later
  • CONFIDENCE: Knowing facts makes you feel more confident in math
  • PROBLEM SOLVING: You can focus on the problem strategy, not basic calculations

Think of it like knowing your alphabet - it makes reading much easier!

Question: How can I help my child practice division facts at home?

Answer: Here are effective practice methods:

  • Flashcards: Practice with division fact cards daily
  • Games: Use online math games or apps for engagement
  • Real-world problems: Share items equally and ask division questions
  • Fact family triangles: Show the relationship between multiplication and division
  • Worksheets: Regular practice with structured exercises
  • Verbal practice: Ask division facts during car rides or meals

Consistency is more important than long sessions - even 10 minutes daily helps!

Question: Do division facts work with bigger numbers too?

Answer: Yes! The same principles apply to larger numbers:

  • Basic facts help: 24 ÷ 6 = 4 helps with 240 ÷ 6 = 40
  • Patterns continue: The relationships between numbers stay the same
  • Fact families work: 7 × 8 = 56 means 56 ÷ 7 = 8
  • Verification works: Always multiply back to check

Knowing basic facts makes it easier to tackle larger division problems!