Division by 10
Division by 10 is one of the simplest and most useful division skills in Class 3 Maths. When you divide a number by 10, you are finding out how many groups of 10 are in that number.
Dividing by 10 follows a quick pattern: just remove the zero at the end of the number. This shortcut works because our number system is based on tens (the decimal system).
For example, 80 ÷ 10 = 8. The zero at the end of 80 is removed, and the answer is 8. This idea connects to place value — each digit moves one place to the right when you divide by 10.
What is Division by 10 - Class 3 Maths (Division (Grade 3))?
Division by 10 means splitting a number into groups of 10 and finding how many such groups exist.
Rule: To divide a number ending in 0 by 10, remove the last zero.
When a number ends in zero, dividing by 10 gives a whole number. For example:
- 30 ÷ 10 = 3
- 150 ÷ 10 = 15
- 700 ÷ 10 = 70
The place value of each digit shifts one place to the right. The hundreds digit becomes the tens digit, and the tens digit becomes the ones digit.
Division by 10 Formula
Number ÷ 10 = Remove the last zero
(when the number ends in 0)
This is the reverse of multiplying by 10, where you add a zero at the end.
| Number | ÷ 10 | Answer |
|---|---|---|
| 10 | ÷ 10 | 1 |
| 40 | ÷ 10 | 4 |
| 90 | ÷ 10 | 9 |
| 120 | ÷ 10 | 12 |
| 350 | ÷ 10 | 35 |
| 500 | ÷ 10 | 50 |
| 1000 | ÷ 10 | 100 |
Types and Properties
Types of Division by 10 Problems
1. Exact Division (No Remainder)
When a number ends in 0, it divides exactly by 10.
- 60 ÷ 10 = 6 (no remainder)
- 200 ÷ 10 = 20 (no remainder)
2. Division with a Remainder
When a number does NOT end in 0, there is a remainder.
- 23 ÷ 10 = 2 remainder 3
- 47 ÷ 10 = 4 remainder 7
- 85 ÷ 10 = 8 remainder 5
The ones digit becomes the remainder, and the remaining digits form the quotient.
3. Word Problems
Division by 10 appears in real-life situations such as:
- Packing items into boxes of 10
- Sharing equally among 10 people
- Converting paise to rupees (100 paise = ₹1, so 10 paise = ₹0.10)
Solved Examples
Example 1: Example 1: Simple Division by 10
Question: Find 70 ÷ 10.
Think:
- 70 ends in 0
- Remove the last zero
- 70 ÷ 10 = 7
Answer: 7
Example 2: Example 2: Three-Digit Number
Question: Find 240 ÷ 10.
Think:
- 240 ends in 0
- Remove the last zero → 24
Answer: 240 ÷ 10 = 24
Example 3: Example 3: Division with Remainder
Question: Find 53 ÷ 10.
Think:
- 53 does not end in 0
- How many tens in 53? → 5 tens and 3 ones
- Quotient = 5, Remainder = 3
Answer: 53 ÷ 10 = 5 remainder 3
Example 4: Example 4: Word Problem – Packing Pencils
Question: Aman has 80 pencils. He puts them in boxes of 10. How many boxes does he need?
Think:
- Total pencils = 80
- Each box holds 10 pencils
- 80 ÷ 10 = 8
Answer: Aman needs 8 boxes.
Example 5: Example 5: Larger Number
Question: Find 600 ÷ 10.
Think:
- 600 ends in 0
- Remove the last zero → 60
Answer: 600 ÷ 10 = 60
Example 6: Example 6: Word Problem – Sharing Mangoes
Question: Priya has 90 mangoes. She wants to share them equally among 10 friends. How many mangoes does each friend get?
Think:
- Total mangoes = 90
- Number of friends = 10
- 90 ÷ 10 = 9
Answer: Each friend gets 9 mangoes.
Example 7: Example 7: Place Value Shift
Question: In 350, what happens to each digit when we divide by 10?
Think:
| Hundreds | Tens | Ones | |
|---|---|---|---|
| 350 | 3 | 5 | 0 |
| 350 ÷ 10 = 35 | — | 3 | 5 |
Each digit moved one place to the right.
Answer: 350 ÷ 10 = 35
Example 8: Example 8: Remainder Word Problem
Question: Meera has 46 stickers. She wants to make packets of 10. How many full packets can she make? How many stickers are left?
Think:
- 46 ÷ 10 → Quotient = 4, Remainder = 6
- She can make 4 full packets
- 6 stickers are left over
Answer: 4 full packets and 6 stickers left.
Example 9: Example 9: Connecting Multiplication and Division
Question: If 10 × 7 = 70, what is 70 ÷ 10?
Think:
- Multiplication and division are opposite operations
- 10 × 7 = 70, so 70 ÷ 10 = 7
Answer: 70 ÷ 10 = 7
Example 10: Example 10: Money Problem
Question: Rahul earned ₹150 by selling 10 packets of chips. What was the price of each packet?
Think:
- Total money = ₹150
- Number of packets = 10
- ₹150 ÷ 10 = ₹15
Answer: Each packet costs ₹15.
Real-World Applications
Where Do We Use Division by 10?
- Packing and grouping: Putting items into packets of 10 (eggs in trays, pencils in boxes).
- Money calculations: Splitting ₹100 among 10 people gives ₹10 each.
- Place value understanding: Division by 10 helps understand how digits shift in our number system.
- Measurement: Converting millimetres to centimetres (10 mm = 1 cm, so mm ÷ 10 = cm).
- Quick mental maths: Dividing by 10 is one of the fastest calculations you can do in your head.
Key Points to Remember
- To divide a number ending in 0 by 10, remove the last zero.
- When a number does not end in 0, the ones digit becomes the remainder.
- Division by 10 shifts every digit one place to the right in the place value chart.
- Division by 10 is the reverse of multiplication by 10.
- If 10 × a = b, then b ÷ 10 = a.
- Division by 10 is useful in money, measurement, and everyday grouping problems.
Practice Problems
- Find 50 ÷ 10.
- Find 110 ÷ 10.
- Find 400 ÷ 10.
- Aditi has 60 beads. She makes necklaces with 10 beads each. How many necklaces can she make?
- Find the quotient and remainder: 37 ÷ 10.
- Dev earned ₹200 in 10 days. How much did he earn each day?
- Find 1000 ÷ 10.
- Kavi has 75 marbles. He puts 10 marbles in each bag. How many full bags can he fill? How many marbles are left?
Frequently Asked Questions
Q1. What is the rule for dividing by 10?
When a number ends in 0, remove the last zero to get the answer. For example, 90 ÷ 10 = 9. If the number does not end in 0, the ones digit becomes the remainder.
Q2. What is 100 ÷ 10?
100 ÷ 10 = 10. Remove the last zero from 100 to get 10.
Q3. Can we divide a number that does not end in 0 by 10?
Yes, but there will be a remainder. For example, 34 ÷ 10 = 3 remainder 4. The tens digit is the quotient and the ones digit is the remainder.
Q4. How is dividing by 10 related to multiplying by 10?
They are opposite (inverse) operations. Multiplying by 10 adds a zero at the end, while dividing by 10 removes the last zero. If 10 × 6 = 60, then 60 ÷ 10 = 6.
Q5. What happens to place value when we divide by 10?
Each digit moves one place to the right. The hundreds digit becomes the tens digit, the tens digit becomes the ones digit, and the ones digit (if 0) disappears.
Q6. What is 0 ÷ 10?
0 ÷ 10 = 0. Zero divided by any number is always zero.
Q7. Is dividing by 10 the same as dividing by 2 and then by 5?
Yes, because 2 × 5 = 10. Dividing by 10 gives the same result as dividing first by 2 and then by 5, or first by 5 and then by 2.
Q8. How can I check my answer after dividing by 10?
Multiply the quotient by 10 and add the remainder. If you get back the original number, your answer is correct. For example, 83 ÷ 10 = 8 R 3. Check: 8 × 10 + 3 = 83.
Q9. Where do we use division by 10 in daily life?
Division by 10 is used when sharing items among 10 people, packing things in groups of 10, converting units (like mm to cm), and making quick mental calculations with money.
