Multiplication of 3-Digit by 1-Digit
Multiplication of a 3-digit number by a 1-digit number builds on the column multiplication skills learned earlier. In Class 4, students move from multiplying 2-digit numbers to handling hundreds, which means working with larger carry-overs and place values.
This skill is essential for solving real-life problems such as calculating the cost of multiple items, finding total distances, and working with measurements.
What is Multiplication of 3-Digit by 1-Digit - Class 4 Maths (Multiplication (Grade 4))?
Multiplying a 3-digit number by a 1-digit number means finding the product when a number between 100 and 999 is multiplied by a number between 1 and 9.
The standard method uses column multiplication (also called the vertical method). We multiply digit by digit from right to left, carrying over when a product exceeds 9.
Multiplication of 3-Digit by 1-Digit Formula
3-Digit Number × 1-Digit Number = Product
The multiplication is done in three steps:
- Step 1: Multiply the ones digit. Write the ones part; carry the tens part.
- Step 2: Multiply the tens digit. Add any carry. Write the ones part; carry the tens part.
- Step 3: Multiply the hundreds digit. Add any carry. Write the result.
Types and Properties
There are different situations when multiplying 3-digit by 1-digit numbers:
- Without regrouping (no carry): When each partial product is less than 10. Example: 213 × 3 = 639
- With regrouping (with carry): When a partial product is 10 or more, we carry over. Example: 456 × 7 = 3,192
- Multiplying by 1: Any number × 1 = the number itself. Example: 847 × 1 = 847
- Multiplying by 0: Any number × 0 = 0. Example: 563 × 0 = 0
Solved Examples
Example 1: Example 1: Without Regrouping
Problem: Multiply 213 × 3
Solution:
Step 1: Ones: 3 × 3 = 9. Write 9.
Step 2: Tens: 1 × 3 = 3. Write 3.
Step 3: Hundreds: 2 × 3 = 6. Write 6.
| 2 | 1 | 3 | |
| × | 3 | ||
| 6 | 3 | 9 |
Answer: 213 × 3 = 639
Example 2: Example 2: With Regrouping in Ones
Problem: Multiply 346 × 4
Solution:
Step 1: Ones: 6 × 4 = 24. Write 4, carry 2.
Step 2: Tens: 4 × 4 = 16, plus carry 2 = 18. Write 8, carry 1.
Step 3: Hundreds: 3 × 4 = 12, plus carry 1 = 13. Write 13.
| 1 | 2 | ||
| 3 | 4 | 6 | |
| × | 4 | ||
| 1 | 3 | 8 | 4 |
Answer: 346 × 4 = 1,384
Example 3: Example 3: Word Problem (Cost Calculation)
Problem: Ria buys 7 notebooks. Each notebook costs ₹145. Find the total cost.
Solution:
Total cost = 145 × 7
Step 1: Ones: 5 × 7 = 35. Write 5, carry 3.
Step 2: Tens: 4 × 7 = 28, plus carry 3 = 31. Write 1, carry 3.
Step 3: Hundreds: 1 × 7 = 7, plus carry 3 = 10. Write 10.
Answer: Total cost = ₹1,015
Example 4: Example 4: With Carry in Every Column
Problem: Multiply 879 × 6
Solution:
Step 1: Ones: 9 × 6 = 54. Write 4, carry 5.
Step 2: Tens: 7 × 6 = 42, plus carry 5 = 47. Write 7, carry 4.
Step 3: Hundreds: 8 × 6 = 48, plus carry 4 = 52. Write 52.
Answer: 879 × 6 = 5,274
Example 5: Example 5: Multiplying with 5
Problem: A school orders 5 packets of pencils. Each packet has 264 pencils. How many pencils in all?
Solution:
Total pencils = 264 × 5
Step 1: Ones: 4 × 5 = 20. Write 0, carry 2.
Step 2: Tens: 6 × 5 = 30, plus carry 2 = 32. Write 2, carry 3.
Step 3: Hundreds: 2 × 5 = 10, plus carry 3 = 13. Write 13.
Answer: Total pencils = 1,320
Example 6: Example 6: Multiplying a Number with Zero in the Middle
Problem: Multiply 508 × 9
Solution:
Step 1: Ones: 8 × 9 = 72. Write 2, carry 7.
Step 2: Tens: 0 × 9 = 0, plus carry 7 = 7. Write 7.
Step 3: Hundreds: 5 × 9 = 45. Write 45.
Answer: 508 × 9 = 4,572
Example 7: Example 7: Distance Word Problem
Problem: Arjun cycles 385 metres every day. How far does he cycle in 6 days?
Solution:
Total distance = 385 × 6
Step 1: 5 × 6 = 30. Write 0, carry 3.
Step 2: 8 × 6 = 48, + 3 = 51. Write 1, carry 5.
Step 3: 3 × 6 = 18, + 5 = 23. Write 23.
Answer: Arjun cycles 2,310 metres in 6 days.
Example 8: Example 8: Verification Using Repeated Addition
Problem: Verify that 125 × 4 = 500 using repeated addition.
Solution:
125 + 125 + 125 + 125
= 250 + 250
= 500
By column multiplication: 125 × 4
5 × 4 = 20 (write 0, carry 2); 2 × 4 = 8, + 2 = 10 (write 0, carry 1); 1 × 4 = 4, + 1 = 5.
Answer: Both methods give 500. Verified.
Example 9: Example 9: Largest 3-Digit Number × 9
Problem: Find the product of the largest 3-digit number and 9.
Solution:
Largest 3-digit number = 999
999 × 9:
Step 1: 9 × 9 = 81. Write 1, carry 8.
Step 2: 9 × 9 = 81, + 8 = 89. Write 9, carry 8.
Step 3: 9 × 9 = 81, + 8 = 89. Write 89.
Answer: 999 × 9 = 8,991
Example 10: Example 10: Pattern Observation
Problem: Find the products: 142 × 2, 142 × 3, 142 × 4. What pattern do you see?
Solution:
142 × 2 = 284
142 × 3 = 426
142 × 4 = 568
The difference between consecutive products is 142 (because we are adding one more group of 142 each time).
284 + 142 = 426 and 426 + 142 = 568.
Answer: Each product increases by 142.
Real-World Applications
Multiplying a 3-digit number by a 1-digit number is used in everyday situations:
- Shopping: Finding the total price when buying several items of the same cost.
- Distance: Calculating total distance covered over several days or trips.
- Packing: Finding total items when each box holds a fixed number.
- Time: Converting weeks to days (e.g., 365 × 2 for two years in days).
Key Points to Remember
- Always multiply from the ones place to the hundreds place (right to left).
- Write only the ones digit of each partial product and carry the tens digit to the next column.
- When a digit is 0, that column's product is 0 plus any carry.
- The product of a 3-digit number and a 1-digit number can be at most a 4-digit number (999 × 9 = 8,991).
- Any number multiplied by 1 gives the number itself; any number multiplied by 0 gives 0.
- Use estimation to check: round the 3-digit number to the nearest hundred and multiply.
Practice Problems
- Find the product: 432 × 6
- Multiply 507 × 8 and write the answer.
- Priya bought 9 packets of colour pencils. Each packet has 136 pencils. How many pencils does she have in total?
- Calculate: 750 × 4
- Dev walks 485 metres to school every day. How many metres does he walk in 5 days (one way)?
- Find the product of 999 and 7.
- A box contains 312 mangoes. Aman has 3 such boxes. How many mangoes does he have?
- Multiply 600 × 8. What do you notice about the product?
Frequently Asked Questions
Q1. What is the maximum number of digits in the product of a 3-digit and a 1-digit number?
The product can have at most 4 digits. The largest product is 999 × 9 = 8,991 (4 digits). The smallest product with a non-zero multiplier is 100 × 1 = 100 (3 digits).
Q2. How do I handle a zero in the middle of the 3-digit number?
Multiply 0 by the 1-digit number to get 0, then add any carry from the previous step. For example, in 305 × 4: ones give 20 (write 0, carry 2); tens give 0 × 4 = 0, plus carry 2 = 2; hundreds give 3 × 4 = 12. Product = 1,220.
Q3. What is regrouping in multiplication?
Regrouping (or carrying) happens when a column product is 10 or more. The ones digit stays in that column and the tens digit is carried to the next column on the left.
Q4. Can I check my answer using repeated addition?
Yes. For example, 213 × 3 can be checked as 213 + 213 + 213 = 639. However, for larger multipliers like 8 or 9, this becomes tedious, so estimation is faster.
Q5. How do I estimate the product before solving?
Round the 3-digit number to the nearest hundred. For example, to estimate 487 × 6, round 487 to 500. Then 500 × 6 = 3,000. The exact answer 2,922 is close to 3,000.
Q6. What is the order of multiplication — does it matter?
No, due to the commutative property, 346 × 4 = 4 × 346. Both give 1,384. However, writing the 3-digit number on top in column multiplication makes the working neater.
Q7. Why is multiplication of 3-digit by 1-digit important?
It is the foundation for multiplying larger numbers (3-digit by 2-digit) and for solving real-world problems involving cost, distance, weight, and quantity calculations.
Q8. What if the carry is more than 9?
A single carry digit from multiplying two single digits can be at most 8 (since 9 × 9 = 81, carry 8). When added to the next column's product, the total carry forward is still at most 8 + 8 = handled normally.
Q9. Is this topic in the NCERT Class 4 textbook?
Yes. NCERT Class 4 Maths (Math Magic) covers multiplication of larger numbers in chapters related to multiplication. The CBSE curriculum expects students to multiply up to 3-digit by 1-digit numbers fluently.
