Relationship Between Multiplication and Division
Multiplication and division are inverse operations — they undo each other. If you know a multiplication fact, you can write two division facts from it. This connection is called a fact family.
Understanding this relationship helps you divide faster (using tables) and check your answers.
What is Relationship Between Multiplication and Division - Class 3 Maths (Division)?
Inverse operations are operations that reverse each other. Multiplication puts equal groups together; division breaks a total into equal groups.
If a × b = c, then c ÷ a = b and c ÷ b = a
Example: 4 × 7 = 28 → 28 ÷ 4 = 7 and 28 ÷ 7 = 4.
Types and Properties
Fact family: A set of related multiplication and division facts using the same three numbers.
| Fact Family for 3, 8, 24 | |||
|---|---|---|---|
| 3 × 8 = 24 | 8 × 3 = 24 | 24 ÷ 3 = 8 | 24 ÷ 8 = 3 |
Every fact family has 4 facts — 2 multiplication and 2 division (unless both factors are the same, like 5 × 5 = 25).
Solved Examples
Example 1: Write the Fact Family
Question: Write the fact family for 6, 9, and 54.
Think:
- 6 × 9 = 54
- 9 × 6 = 54
- 54 ÷ 6 = 9
- 54 ÷ 9 = 6
Answer: The fact family is: 6 × 9 = 54, 9 × 6 = 54, 54 ÷ 6 = 9, 54 ÷ 9 = 6.
Example 2: Use Multiplication to Divide
Question: Find 56 ÷ 8.
Think:
- Ask: 8 × ? = 56
- 8 × 7 = 56
Answer: 56 ÷ 8 = 7.
Example 3: Use Division to Check Multiplication
Question: Aman says 7 × 9 = 63. Check using division.
Think:
- If 7 × 9 = 63, then 63 ÷ 7 should be 9.
- 63 ÷ 7 = 9 ✓
Answer: Aman is correct.
Example 4: Word Problem — Using Inverse
Question: Priya buys 5 packets of biscuits. She gets 40 biscuits in total. How many biscuits in each packet?
Think:
- 5 × ? = 40
- 40 ÷ 5 = 8
Answer: Each packet has 8 biscuits.
Example 5: Find the Missing Number
Question: ___ × 6 = 42. Find the missing number.
Think:
- 42 ÷ 6 = 7
Answer: The missing number is 7.
Example 6: Fact Family with Equal Factors
Question: Write the fact family for 5, 5, and 25.
Think:
- 5 × 5 = 25
- 25 ÷ 5 = 5
- Since both factors are the same, there are only 2 unique facts.
Answer: 5 × 5 = 25 and 25 ÷ 5 = 5.
Example 7: Relating Multiplication Array to Division
Question: A classroom has 4 rows with 8 chairs in each row. Write one multiplication fact and two division facts.
Think:
- Multiplication: 4 × 8 = 32
- Division: 32 ÷ 4 = 8 (chairs per row)
- Division: 32 ÷ 8 = 4 (number of rows)
Answer: 4 × 8 = 32, 32 ÷ 4 = 8, 32 ÷ 8 = 4.
Example 8: True or False
Question: True or false — If 72 ÷ 9 = 8, then 9 × 8 = 72.
Think:
- Division and multiplication are inverse operations.
- If 72 ÷ 9 = 8, then 9 × 8 must equal 72.
- 9 × 8 = 72 ✓
Answer: True.
Example 9: Word Problem — Finding Total
Question: Each box has 6 apples. Ria has 8 boxes. How many apples in total? If she shares them equally among 4 friends, how many does each get?
Think:
- Total = 6 × 8 = 48 apples
- Each friend = 48 ÷ 4 = 12 apples
Answer: Total = 48 apples. Each friend gets 12 apples.
Key Points to Remember
- Multiplication and division are inverse (opposite) operations.
- If a × b = c, then c ÷ a = b and c ÷ b = a.
- A fact family has 2 multiplication facts and 2 division facts using the same 3 numbers.
- Use multiplication tables to divide quickly.
- Use division to check multiplication answers.
- When both factors are the same (e.g., 6 × 6 = 36), the fact family has only 2 unique facts.
Practice Problems
- Write the fact family for 7, 8, and 56.
- Find 72 ÷ 9 using the multiplication table of 9.
- If 8 × 6 = 48, what is 48 ÷ 8?
- ___ × 4 = 36. Find the missing number using division.
- Write a multiplication and a division fact for: 5 rows of 9 chairs = 45 chairs.
- Kavi says 63 ÷ 7 = 8. Check using multiplication. Is he correct?
- Write the fact family for 9, 9, and 81.
Frequently Asked Questions
Q1. What does 'inverse operation' mean?
An inverse operation reverses or undoes another operation. Multiplication builds a total from groups; division breaks the total back into groups. They undo each other.
Q2. What is a fact family?
A fact family is a set of related facts using the same three numbers — two multiplication facts and two division facts. For example: 3 × 5 = 15, 5 × 3 = 15, 15 ÷ 3 = 5, 15 ÷ 5 = 3.
Q3. How does knowing multiplication help with division?
If you know 8 × 7 = 56, you instantly know 56 ÷ 8 = 7 and 56 ÷ 7 = 8. You do not need to do repeated subtraction.
Q4. Can I check a division answer using multiplication?
Yes. Multiply the quotient by the divisor. If you get the dividend, your answer is correct. For 42 ÷ 6 = 7: check 7 × 6 = 42.
Q5. What if both factors in a fact family are the same?
Then there are only 2 unique facts instead of 4. For example, 6 × 6 = 36 and 36 ÷ 6 = 6.
Q6. Does this work with remainders?
The fact family relationship works for exact division. With remainders, the check formula is: Dividend = Divisor × Quotient + Remainder.
Q7. Why should I learn fact families?
Fact families connect multiplication and division. They help you divide faster, find missing numbers, and verify your calculations.
Q8. Is this relationship covered in NCERT Class 3?
Yes. NCERT Class 3 Maths explains the link between multiplication and division, and uses fact families to help students divide using tables.
