Division Facts
Division facts are basic division sentences that you should know by heart, just like you know your multiplication tables. Every multiplication fact has two matching division facts.
For example, if you know that 3 × 4 = 12, then you also know: 12 ÷ 3 = 4 and 12 ÷ 4 = 3. These are the division facts for 3, 4, and 12.
Learning all the division facts for divisors 1 through 10 helps you solve bigger division problems, fractions, and word problems quickly and accurately.
What is Division Facts - Class 3 Maths (Division (Grade 3))?
A division fact is a division sentence where the dividend, divisor, and quotient are all known whole numbers. Division facts use divisors from 1 to 10 and have no remainder.
Dividend ÷ Divisor = Quotient
Example: 24 ÷ 6 = 4
The three parts of every division fact are:
- Dividend — the total number being divided. In 24 ÷ 6 = 4, the dividend is 24.
- Divisor — the number you divide by. In 24 ÷ 6 = 4, the divisor is 6.
- Quotient — the answer you get after dividing. In 24 ÷ 6 = 4, the quotient is 4.
Division means splitting a number into equal groups. When you say 24 ÷ 6 = 4, it means 24 objects split into 6 equal groups gives 4 in each group.
Division Facts Formula
Multiplication and division are inverse operations:
If a × b = c, then c ÷ a = b and c ÷ b = a
Example: Since 5 × 7 = 35, we know that 35 ÷ 5 = 7 and 35 ÷ 7 = 5.
This means you do not need to memorise division facts separately. If you know your multiplication tables well, you can work out any division fact.
Special rules of division (remember these):
- Rule 1 — Any number ÷ 1 = the same number. Splitting 8 into 1 group gives 8. So 8 ÷ 1 = 8.
- Rule 2 — Any number ÷ itself = 1. Splitting 9 into 9 equal groups gives 1 each. So 9 ÷ 9 = 1.
- Rule 3 — 0 ÷ any number = 0. If there are 0 sweets, nobody gets any. So 0 ÷ 5 = 0.
- Rule 4 — We never divide by 0. It is not possible to split things into 0 groups. Division by zero is undefined.
Types and Properties
Division fact families group related multiplication and division facts together. Each family uses the same three numbers.
Here are some examples of complete fact families:
| Numbers | Multiplication Facts | Division Facts |
|---|---|---|
| 3, 6, 18 | 3 × 6 = 18 6 × 3 = 18 | 18 ÷ 3 = 6 18 ÷ 6 = 3 |
| 4, 7, 28 | 4 × 7 = 28 7 × 4 = 28 | 28 ÷ 4 = 7 28 ÷ 7 = 4 |
| 5, 8, 40 | 5 × 8 = 40 8 × 5 = 40 | 40 ÷ 5 = 8 40 ÷ 8 = 5 |
| 6, 9, 54 | 6 × 9 = 54 9 × 6 = 54 | 54 ÷ 6 = 9 54 ÷ 9 = 6 |
| 7, 8, 56 | 7 × 8 = 56 8 × 7 = 56 | 56 ÷ 7 = 8 56 ÷ 8 = 7 |
Common division facts chart (divisors 1 to 10):
| ÷ | Quotient 1 | Quotient 2 | Quotient 3 | Quotient 4 | Quotient 5 |
|---|---|---|---|---|---|
| ÷ 2 | 2÷2=1 | 4÷2=2 | 6÷2=3 | 8÷2=4 | 10÷2=5 |
| ÷ 3 | 3÷3=1 | 6÷3=2 | 9÷3=3 | 12÷3=4 | 15÷3=5 |
| ÷ 4 | 4÷4=1 | 8÷4=2 | 12÷4=3 | 16÷4=4 | 20÷4=5 |
| ÷ 5 | 5÷5=1 | 10÷5=2 | 15÷5=3 | 20÷5=4 | 25÷5=5 |
| ÷ 6 | 6÷6=1 | 12÷6=2 | 18÷6=3 | 24÷6=4 | 30÷6=5 |
| ÷ 7 | 7÷7=1 | 14÷7=2 | 21÷7=3 | 28÷7=4 | 35÷7=5 |
| ÷ 8 | 8÷8=1 | 16÷8=2 | 24÷8=3 | 32÷8=4 | 40÷8=5 |
| ÷ 9 | 9÷9=1 | 18÷9=2 | 27÷9=3 | 36÷9=4 | 45÷9=5 |
| ÷ 10 | 10÷10=1 | 20÷10=2 | 30÷10=3 | 40÷10=4 | 50÷10=5 |
This chart shows quotients 1 through 5 only. The pattern continues up to quotient 10 for each divisor.
Solved Examples
Example 1: Writing Division Facts from Multiplication
Question: Write two division facts from 4 × 6 = 24.
Think:
- The three numbers are 4, 6, and 24.
- The product (24) becomes the dividend in division.
- Division fact 1: 24 ÷ 4 = 6
- Division fact 2: 24 ÷ 6 = 4
Answer: The two division facts are 24 ÷ 4 = 6 and 24 ÷ 6 = 4.
Example 2: Using the Multiplication Table Backwards
Question: Find 42 ÷ 7.
Think:
- Ask yourself: 7 × ? = 42
- Go through the 7-times table: 7 × 1 = 7, 7 × 2 = 14, 7 × 3 = 21, 7 × 4 = 28, 7 × 5 = 35, 7 × 6 = 42.
- So 7 × 6 = 42, which means 42 ÷ 7 = 6.
Answer: 42 ÷ 7 = 6.
Check: 6 × 7 = 42. Correct!
Example 3: Division by 1
Question: Find 9 ÷ 1.
Think:
- Rule: Any number divided by 1 gives the same number.
- If you put 9 objects in 1 group, that group has 9.
- So 9 ÷ 1 = 9.
Answer: 9 ÷ 1 = 9.
Example 4: Division by Itself
Question: Find 8 ÷ 8.
Think:
- Rule: Any number divided by itself gives 1.
- If you share 8 sweets equally among 8 friends, each friend gets exactly 1 sweet.
- So 8 ÷ 8 = 1.
Answer: 8 ÷ 8 = 1.
Example 5: Sharing Equally — Mangoes in Baskets
Question: Ria has 36 mangoes. She puts them equally into 9 baskets. How many mangoes are in each basket?
Think:
- Total mangoes = 36. Number of baskets = 9.
- We need to divide equally: 36 ÷ 9 = ?
- Ask: 9 × ? = 36. From the 9-times table, 9 × 4 = 36.
Answer: Each basket has 4 mangoes.
Check: 4 × 9 = 36. Correct!
Example 6: Grouping — Cricket Balls
Question: Dev has 30 cricket balls. He puts them in bags of 5 each. How many bags does he need?
Think:
- Total balls = 30. Each bag holds 5 balls.
- We are making groups: 30 ÷ 5 = ?
- Ask: 5 × ? = 30. From the 5-times table, 5 × 6 = 30.
Answer: Dev needs 6 bags.
Check: 6 × 5 = 30. Correct!
Example 7: Finding the Missing Divisor
Question: Fill in the blank: 56 ÷ ___ = 8.
Think:
- We need to find the divisor.
- Rearrange: ? × 8 = 56.
- From the 8-times table: 7 × 8 = 56.
- So the missing divisor is 7.
Answer: 56 ÷ 7 = 8.
Check: 7 × 8 = 56 and 56 ÷ 7 = 8. Correct!
Example 8: Complete Fact Family
Question: Write the complete fact family for the numbers 3, 8, and 24.
Think:
- Multiplication facts: 3 × 8 = 24 and 8 × 3 = 24.
- Division facts: 24 ÷ 3 = 8 and 24 ÷ 8 = 3.
- All four facts use the same three numbers: 3, 8, and 24.
Answer: The fact family is:
- 3 × 8 = 24
- 8 × 3 = 24
- 24 ÷ 3 = 8
- 24 ÷ 8 = 3
Example 9: Zero Divided by a Number
Question: Find 0 ÷ 6.
Think:
- Rule: Zero divided by any number is 0.
- If you have 0 sweets and share them among 6 children, each child gets 0 sweets.
- So 0 ÷ 6 = 0.
Answer: 0 ÷ 6 = 0.
Remember: 0 ÷ (any number) = 0, but (any number) ÷ 0 is NOT allowed.
Example 10: Money — Buying Notebooks
Question: Priya has ₹72. She wants to buy notebooks that cost ₹8 each. How many notebooks can she buy?
Think:
- Total money = ₹72. Cost of one notebook = ₹8.
- Number of notebooks = 72 ÷ 8 = ?
- Ask: 8 × ? = 72. From the 8-times table, 8 × 9 = 72.
Answer: Priya can buy 9 notebooks.
Check: 9 × ₹8 = ₹72. All the money is used. Correct!
Real-World Applications
Where do we use division facts in everyday life?
- Sharing equally: Dividing mangoes, sweets, or stickers equally among friends. If Aman has 20 toffees and 4 friends, each gets 20 ÷ 4 = 5 toffees.
- Making teams: A class of 40 students making groups of 8 for a project. 40 ÷ 8 = 5 groups.
- Shopping with money: Finding how many items you can buy with a given amount. ₹45 ÷ ₹9 per eraser = 5 erasers.
- Time: Splitting 60 minutes into equal activity blocks. 60 ÷ 10 = 6 blocks of 10 minutes each.
- Measurement: Cutting a 24 cm ribbon into 6 equal pieces. Each piece = 24 ÷ 6 = 4 cm.
- Cooking: Dividing 18 chapatis equally on 3 plates. 18 ÷ 3 = 6 chapatis per plate.
Knowing division facts by heart builds the foundation for fractions, long division, and problem-solving in higher classes.
Key Points to Remember
- A division fact is a basic division with no remainder, using divisors from 1 to 10.
- Every multiplication fact gives two division facts. If 6 × 7 = 42, then 42 ÷ 6 = 7 and 42 ÷ 7 = 6.
- A fact family has 2 multiplication facts and 2 division facts using the same three numbers.
- Any number ÷ 1 = the same number. Example: 7 ÷ 1 = 7.
- Any number ÷ itself = 1. Example: 10 ÷ 10 = 1.
- 0 ÷ any number = 0. Example: 0 ÷ 3 = 0.
- We can never divide by 0. It is undefined.
- To recall a division fact, think of the multiplication table: divisor × ? = dividend.
- Always check your answer: quotient × divisor should equal the dividend.
Practice Problems
- Write two division facts from 7 × 9 = 63.
- Find 48 ÷ 6.
- Find 81 ÷ 9.
- Aman has 45 marbles. He divides them equally among 5 friends. How many marbles does each friend get?
- Fill in the blank: 32 ÷ ___ = 4.
- Write the complete fact family for the numbers 4, 9, and 36.
- Meera has ₹56. She buys bangles that cost ₹7 each. How many bangles can she buy?
- Find 0 ÷ 8.
Frequently Asked Questions
Q1. What are division facts?
Division facts are basic division sentences using divisors from 1 to 10 that give a whole number answer with no remainder. For example, 18 ÷ 3 = 6 and 40 ÷ 8 = 5 are division facts.
Q2. How are multiplication and division facts related?
They are inverse (opposite) operations. Every multiplication fact gives two division facts. Since 5 × 8 = 40, we know 40 ÷ 5 = 8 and 40 ÷ 8 = 5. Learning multiplication tables makes division facts automatic.
Q3. What is a fact family in division?
A fact family is a set of 4 related number sentences — 2 multiplication and 2 division — that use the same three numbers. For 3, 7, and 21 the family is: 3 × 7 = 21, 7 × 3 = 21, 21 ÷ 3 = 7, and 21 ÷ 7 = 3.
Q4. What happens when you divide a number by 1?
The answer is the number itself. Dividing by 1 means putting everything in one group. For example, 6 ÷ 1 = 6 and 100 ÷ 1 = 100.
Q5. What happens when you divide a number by itself?
The answer is always 1. If you share 7 things equally among 7 people, each person gets exactly 1. So 7 ÷ 7 = 1.
Q6. Can we divide zero by a number?
Yes. Zero divided by any non-zero number is always 0. If you have 0 sweets to share among 4 friends, each friend gets 0 sweets. So 0 ÷ 4 = 0.
Q7. Why can we not divide by zero?
Dividing by zero has no meaning in mathematics. You cannot split something into zero groups. There is no number that works as an answer. So division by zero is not allowed.
Q8. How can I memorise division facts quickly?
Start by learning your multiplication tables thoroughly. Then practise saying them in reverse: instead of 8 × 6 = 48, say 48 ÷ 8 = 6. Use flash cards, write fact families, and practise a few facts every day.
Q9. What if the division does not come out exactly?
Then there is a remainder. For example, 17 ÷ 5 = 3 remainder 2 because 5 × 3 = 15, and 17 − 15 = 2. Division facts only cover exact divisions where the remainder is zero.
Q10. Is this topic covered in the NCERT Class 3 textbook?
Yes. The NCERT Class 3 Maths textbook covers basic division facts through sharing, grouping activities, and the connection between multiplication tables and division.
