Division Facts for Multiplication - Complete Guide for 3rd Grade Students

Master division facts for multiplication with step-by-step examples, exercises, and solutions designed specifically for 3rd grade students learning the inverse relationship between division and multiplication.

Solution: Exercises 1 to 3
1 Fact Family Relationships
Exercise 1
Complete the fact family for 3 × 4 = 12: 3 × 4 = 12, 4 × 3 = 12, 12 ÷ 3 = ?, 12 ÷ 4 = ?
Definition:

Fact Family: A set of related multiplication and division facts that use the same three numbers. Knowing multiplication facts helps solve division facts.

Fact Family Method:
  1. Start with the multiplication fact (3 × 4 = 12)
  2. Write the commutative multiplication fact (4 × 3 = 12)
  3. Write the two related division facts (12 ÷ 3 = 4 and 12 ÷ 4 = 3)
  4. Use multiplication to verify division facts
Multiplication Facts
3 × 4 = 12
Commutative Fact
4 × 3 = 12
Division Facts
12 ÷ 3 = 4, 12 ÷ 4 = 3
Step 1: Start with the given fact

3 × 4 = 12

Step 2: Write the commutative fact

4 × 3 = 12

Step 3: Write the first division fact

12 ÷ 3 = 4 (because 3 × 4 = 12)

Step 4: Write the second division fact

12 ÷ 4 = 3 (because 4 × 3 = 12)

Step 5: Verify all facts

3 × 4 = 12 ✓, 4 × 3 = 12 ✓, 12 ÷ 3 = 4 ✓, 12 ÷ 4 = 3 ✓

12 ÷ 3 = 4 and 12 ÷ 4 = 3
Final answers:

12 ÷ 3 = 4 and 12 ÷ 4 = 3

Applied rules:

• Inverse relationship: Multiplication and division are inverse operations

• Fact families: Three numbers create four related facts

• Verification: Always check division by multiplying

2 Using Multiplication to Solve Division
Exercise 2
Solve: 24 ÷ 6 = ? using the multiplication fact that helps.
Definition:

Division Using Multiplication: To solve division problems, think "What number times the divisor equals the dividend?"

Division Problem
24 ÷ 6 = ?
Related Multiplication
? × 6 = 24
Solution
4 × 6 = 24
Step 1: Rewrite as a multiplication problem

24 ÷ 6 = ? means ? × 6 = 24

Step 2: Think of multiplication facts

What number times 6 equals 24?

Step 3: Recall multiplication facts

6 × 4 = 24

Step 4: Write the division answer

24 ÷ 6 = 4

Step 5: Verify the answer

4 × 6 = 24 ✓

24 ÷ 6 = 4
Final answer:

24 ÷ 6 = 4

Applied rules:

• Division as missing factor: 24 ÷ 6 asks "6 × ? = 24"

• Use known facts: Apply multiplication knowledge to solve division

• Verification: Always multiply to check division answer

3 Division Facts Through Multiplication Tables
Exercise 3
Use the multiplication table for 7 to solve: 21 ÷ 7 = ?, 28 ÷ 7 = ?, 35 ÷ 7 = ?, 42 ÷ 7 = ?
Definition:

Multiplication Table Division: Using known multiplication facts to quickly solve related division problems.

Multiplication Facts
7×3=21, 7×4=28, 7×5=35, 7×6=42
Division Facts
21÷7=3, 28÷7=4, 35÷7=5, 42÷7=6
Step 1: Recall the 7 multiplication facts

7 × 3 = 21, 7 × 4 = 28, 7 × 5 = 35, 7 × 6 = 42

Step 2: Convert to division facts

If 7 × 3 = 21, then 21 ÷ 7 = 3

If 7 × 4 = 28, then 28 ÷ 7 = 4

If 7 × 5 = 35, then 35 ÷ 7 = 5

If 7 × 6 = 42, then 42 ÷ 7 = 6

Step 3: Verify each division fact

3 × 7 = 21 ✓, 4 × 7 = 28 ✓, 5 × 7 = 35 ✓, 6 × 7 = 42 ✓

21 ÷ 7 = 3, 28 ÷ 7 = 4, 35 ÷ 7 = 5, 42 ÷ 7 = 6
Final answers:

21 ÷ 7 = 3, 28 ÷ 7 = 4, 35 ÷ 7 = 5, 42 ÷ 7 = 6

Applied rules:

• Table connection: Each multiplication fact creates a division fact

• Pattern recognition: Division facts follow the same sequence as multiplication

• Memory aid: Mastering multiplication tables helps with division facts

Complete Summary: Division Facts for Multiplication
Key Concepts and Definitions:

Division: The mathematical operation that splits a number into equal groups or shares it equally.

Multiplication: The mathematical operation that combines equal groups to find a total.

Fact Family: A set of related multiplication and division facts that use the same three numbers.

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

Dividend: The number being divided (the whole amount).

Divisor: The number we divide by (tells us how many groups or how many in each group).

Quotient: The answer to a division problem (how many in each group or how many groups).

Product: The answer to a multiplication problem.

Core Rules and Principles:

• Division is inverse of multiplication: If 3 × 4 = 12, then 12 ÷ 3 = 4 and 12 ÷ 4 = 3

• Fact families: Three numbers create four related facts (two multiplication, two division)

• Division as missing factor: a ÷ b = ? is equivalent to ? × b = a

• Division by 1: Any number divided by 1 equals itself (a ÷ 1 = a)

• Division by itself: Any non-zero number divided by itself equals 1 (a ÷ a = 1)

• Zero divided by a number: 0 ÷ a = 0 (for any non-zero a)

Step-by-Step Methods:
  1. Identify the division problem: Read the division sentence (e.g., 18 ÷ 3)
  2. Rewrite as multiplication: Think "? × 3 = 18"
  3. Recall multiplication facts: Remember 6 × 3 = 18
  4. Write the division answer: 18 ÷ 3 = 6
  5. Verify: Multiply the quotient by the divisor to check (6 × 3 = 18)
Tip 1: Master multiplication tables first - they make division much easier!
Tip 2: Always verify division by multiplying your answer by the divisor.
Tip 3: Use fact families to see the relationship between multiplication and division.
Tip 4: Think of division as "finding the missing factor" in a multiplication equation.
Common Fact Families: 2×3=6→6÷2=3, 6÷3=2; 4×5=20→20÷4=5, 20÷5=4; 6×7=42→42÷6=7, 42÷7=6
Memorization Strategy: Learn multiplication tables to automatically know division facts.
Advanced Strategies:
  1. Fact Family Recognition: Quickly identify the related multiplication and division facts
  2. Mental Math: Use known multiplication facts for instant division recall
  3. Pattern Recognition: Notice that division facts follow the same sequence as multiplication
  4. Verification Technique: Always check division answers by multiplying
Multiplication-Related Division Rules and Methods
If a × b = c, then c ÷ a = b and c ÷ b = a
Inverse Relationship Formula
Fact Family
2×4=8, 4×2=8, 8÷2=4, 8÷4=2
Four related facts using same numbers
Division as Missing Factor
15 ÷ 3 = ? means ? × 3 = 15
Find the unknown factor
Verification
If 20 ÷ 4 = 5, then 5 × 4 = 20
Always check with multiplication
Advanced Concepts:

Fact Families: Sets of related multiplication and division facts using the same three numbers (e.g., 3×4=12, 4×3=12, 12÷3=4, 12÷4=3)

Multiplication Connection: Division facts are the reverse of multiplication facts.

Missing Factor Strategy: Thinking of division as finding the missing factor in a multiplication equation.

Verification: Always multiplying the quotient by the divisor to check division answers.

Different Division Strategies Using Multiplication:
  1. Fact Family Method: Use the three related numbers to find all four facts
  2. Missing Factor: Think "What number times the divisor equals the dividend?"
  3. Table Lookup: Use known multiplication tables to solve division problems
  4. Reverse Thinking: Instead of dividing, think about multiplication
  5. Verification: Always multiply to check your division answer
Memorization Tip: Practice fact families together to strengthen connections between multiplication and division.
Strategy Tip: When stuck on division, think "What number times the divisor gives me the dividend?"
Pattern Tip: Notice that division facts follow the same sequence as their multiplication counterparts.
Verification Tip: Always multiply your answer by the divisor to check if you get the dividend back.
Common Mistakes: Forgetting to check answers with multiplication, mixing up dividend and divisor, not mastering multiplication facts first.
Success Strategies: Master multiplication tables first, practice fact families together, always verify answers with multiplication.
Essential Multiplication-Division Connections:

• Division by 1: a ÷ 1 = a (same as multiplication: a × 1 = a)

• Division by itself: a ÷ a = 1 (same as multiplication: a × 1/a = 1)

• Zero rule: 0 ÷ a = 0 (same as multiplication: 0 × a = 0)

• Inverse relationship: If a × b = c, then c ÷ a = b and c ÷ b = a

• Verification: Quotient × Divisor = Dividend

• Missing factor: a ÷ b = ? means ? × b = a

Questions & Answers

Common Questions About Division Facts for Multiplication

Question: Why do I need to learn multiplication to do division? Can't I just do division on its own?

Answer: Multiplication and division are like best friends - they help each other! Here's why:

  • They're opposites: If 3 × 4 = 12, then 12 ÷ 3 = 4
  • Division asks: "How many groups of 3 make 12?" which is the same as "What number times 3 equals 12?"
  • It's faster: If you know 7 × 8 = 56, you instantly know 56 ÷ 7 = 8
  • Verification: You can always check your division by multiplying

Learning multiplication first makes division much easier!

Question: My child knows multiplication but still struggles with division. How can I help them make the connection?

Answer: Help your child see the connection with these strategies:

  • Fact families: Practice sets like 3×4=12, 4×3=12, 12÷3=4, 12÷4=3 together
  • Missing factor thinking: Change "12 ÷ 3 = ?" to "3 × ? = 12"
  • Visual models: Use arrays to show how multiplication and division are related
  • Practice together: Do multiplication and division facts in pairs
  • Verbalize: Have your child say "Since 4 × 3 = 12, then 12 ÷ 3 = 4"

The key is helping them see that division is just multiplication working backwards!

Question: What are the most important multiplication facts to know for division success?

Answer: Focus on these essential multiplication facts for division:

  • Basic facts: 1× through 10× tables (especially 2×, 3×, 4×, 5×, 6×, 7×, 8×, 9×, 10×)
  • Squares: 2×2=4, 3×3=9, 4×4=16, 5×5=25, etc. (helps with perfect square division)
  • Easy patterns: Multiples of 10, doubles (2×), and 5× facts
  • Common divisors: Know facts for numbers 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

Mastering these facts automatically gives you the corresponding division facts!