Multiplication of 3-Digit by 2-Digit
Multiplication of a 3-digit number by a 2-digit number is one of the most important arithmetic skills in Class 4. It combines place value understanding with the step-by-step column method to find products that can go up to five digits.
Once students master this, they can solve complex word problems involving cost, area, weight, and quantity.
What is Multiplication of 3-Digit by 2-Digit - Class 4 Maths (Multiplication (Grade 4))?
Multiplying a 3-digit number by a 2-digit number means finding the total when a number between 100 and 999 is multiplied by a number between 10 and 99.
The standard method involves two partial products:
- Multiply the 3-digit number by the ones digit of the 2-digit number.
- Multiply the 3-digit number by the tens digit of the 2-digit number (shift one place left by writing a 0 in the ones column).
- Add the two partial products to get the final answer.
Multiplication of 3-Digit by 2-Digit Formula
3-Digit × 2-Digit = (3-Digit × Ones Digit) + (3-Digit × Tens Digit × 10)
Types and Properties
Different cases arise depending on whether regrouping is needed:
- Without regrouping: All partial products are single digits. Example: 112 × 21
- With regrouping: Partial products exceed 9, requiring carrying. Example: 456 × 38
- With zeros in the multiplier: When the ones digit is 0 (e.g., × 30, × 40), there is only one meaningful partial product. Example: 245 × 30 = 7,350
- With zeros in the multiplicand: A 0 in the middle of the 3-digit number. Example: 503 × 26
Solved Examples
Example 1: Example 1: Basic Multiplication Without Much Carry
Problem: Multiply 213 × 12
Solution:
Step 1: Multiply 213 × 2 (ones digit)
3 × 2 = 6; 1 × 2 = 2; 2 × 2 = 4 → First partial product = 426
Step 2: Multiply 213 × 1 (tens digit) and shift left
3 × 1 = 3; 1 × 1 = 1; 2 × 1 = 2 → Second partial product = 2130
Step 3: Add: 426 + 2130 = 2,556
| 2 | 1 | 3 | ||
| × | 1 | 2 | ||
| 4 | 2 | 6 | ||
| 2 | 1 | 3 | 0 | |
| 2 | 5 | 5 | 6 |
Answer: 213 × 12 = 2,556
Example 2: Example 2: With Regrouping
Problem: Multiply 347 × 25
Solution:
Step 1: 347 × 5 (ones digit)
7 × 5 = 35 (write 5, carry 3); 4 × 5 = 20 + 3 = 23 (write 3, carry 2); 3 × 5 = 15 + 2 = 17
First partial product = 1,735
Step 2: 347 × 2 (tens digit), shifted left
7 × 2 = 14 (write 4, carry 1); 4 × 2 = 8 + 1 = 9; 3 × 2 = 6
Second partial product = 6,940
Step 3: 1,735 + 6,940 = 8,675
Answer: 347 × 25 = 8,675
Example 3: Example 3: Word Problem (Cost)
Problem: A school buys 36 chairs. Each chair costs ₹475. What is the total cost?
Solution:
Total cost = 475 × 36
Step 1: 475 × 6 = 2,850
(5×6=30, write 0 carry 3; 7×6=42+3=45, write 5 carry 4; 4×6=24+4=28)
Step 2: 475 × 3 (tens), shifted = 14,250
(5×3=15, write 5 carry 1; 7×3=21+1=22, write 2 carry 2; 4×3=12+2=14)
Step 3: 2,850 + 14,250 = 17,100
Answer: Total cost = ₹17,100
Example 4: Example 4: Multiplying by a Multiple of 10
Problem: Multiply 256 × 40
Solution:
Since the ones digit is 0, the first partial product is 0.
Simply compute 256 × 4 = 1,024, then append a 0.
256 × 40 = 10,240
Answer: 256 × 40 = 10,240
Example 5: Example 5: With a Zero in the 3-Digit Number
Problem: Multiply 503 × 18
Solution:
Step 1: 503 × 8 = 4,024
(3×8=24, write 4 carry 2; 0×8=0+2=2; 5×8=40)
Step 2: 503 × 1 (tens), shifted = 5,030
Step 3: 4,024 + 5,030 = 9,054
Answer: 503 × 18 = 9,054
Example 6: Example 6: Estimation Check
Problem: Estimate 489 × 32, then find the exact product.
Solution:
Estimate: 489 ≈ 500 and 32 ≈ 30. Estimated product = 500 × 30 = 15,000
Exact:
489 × 2 = 978
489 × 3 (tens) = 14,670
978 + 14,670 = 15,648
The exact answer 15,648 is close to the estimate 15,000.
Answer: 489 × 32 = 15,648
Example 7: Example 7: Largest Product
Problem: What is the largest possible product of a 3-digit number and a 2-digit number?
Solution:
Largest 3-digit number = 999
Largest 2-digit number = 99
999 × 99 = 999 × (100 − 1) = 99,900 − 999 = 98,901
Answer: The largest product is 98,901 (a 5-digit number).
Example 8: Example 8: Weight Word Problem
Problem: A bag of rice weighs 425 grams. Meera buys 15 such bags. What is the total weight?
Solution:
Total weight = 425 × 15
Step 1: 425 × 5 = 2,125
Step 2: 425 × 1 (tens), shifted = 4,250
Step 3: 2,125 + 4,250 = 6,375
Answer: Total weight = 6,375 grams
Example 9: Example 9: Distributive Property Method
Problem: Find 312 × 24 using the distributive property.
Solution:
312 × 24 = 312 × (20 + 4)
= (312 × 20) + (312 × 4)
= 6,240 + 1,248
= 7,488
Answer: 312 × 24 = 7,488
Example 10: Example 10: Area Word Problem
Problem: A rectangular park is 175 metres long and 24 metres wide. Find its area.
Solution:
Area = Length × Breadth = 175 × 24
175 × 4 = 700
175 × 20 = 3,500
700 + 3,500 = 4,200
Answer: Area of the park = 4,200 sq. metres
Real-World Applications
This type of multiplication appears in many real-life situations:
- Billing: Calculating the total cost of 24 books at ₹350 each.
- Area: Finding the area of rectangular fields and rooms.
- Weight/Capacity: Computing total weight of multiple packages.
- Travel: Finding total distance when a bus covers 185 km daily for 28 days.
Key Points to Remember
- Write the 3-digit number on top and the 2-digit number below in column form.
- First, multiply by the ones digit to get Partial Product 1.
- Next, multiply by the tens digit and place a 0 in the ones column (shift left) to get Partial Product 2.
- Add both partial products for the final answer.
- The product of a 3-digit and a 2-digit number has at most 5 digits.
- Use estimation (round both numbers) to quickly check if your answer is reasonable.
- The distributive property can simplify tricky multiplications: a × (b + c) = a × b + a × c.
Practice Problems
- Multiply 234 × 15 using the column method.
- Find the product of 608 × 23.
- Aman's school ordered 42 sets of textbooks. Each set costs ₹365. Find the total cost.
- Calculate 750 × 48.
- A farmer plants 175 trees in each row. There are 32 rows. How many trees are planted in all?
- Estimate the product of 492 × 37, then find the exact answer.
- Find 999 × 11. Is the answer a 4-digit or 5-digit number?
- Aditi runs 325 metres in each round of the ground. She runs 16 rounds. Find the total distance.
Frequently Asked Questions
Q1. How many digits can the product of a 3-digit and a 2-digit number have?
The product can have 4 or 5 digits. The smallest is 100 × 10 = 1,000 (4 digits) and the largest is 999 × 99 = 98,901 (5 digits).
Q2. Why do we place a 0 when multiplying by the tens digit?
The tens digit represents groups of 10. Writing a 0 in the ones place shifts the partial product one position to the left, correctly accounting for the place value.
Q3. Can I break the 2-digit number to make multiplication easier?
Yes, use the distributive property. For example, 245 × 36 = 245 × 30 + 245 × 6 = 7,350 + 1,470 = 8,820. This is exactly what the column method does.
Q4. How do I check my answer?
Use estimation by rounding both numbers. If 347 × 25 gives 8,675 and the estimate (350 × 25 = 8,750) is close, the answer is likely correct. You can also divide the product by one factor to get the other.
Q5. What is the shortcut for multiplying by 10, 20, 30, etc.?
Multiply by the non-zero digit and append a 0. For example, 256 × 30: compute 256 × 3 = 768, then append 0 to get 7,680.
Q6. Why is column multiplication better than repeated addition?
Repeated addition works but is impractical for large multipliers. Adding 347 twenty-five times would take too long and introduce errors. The column method is systematic and fast.
Q7. What mistakes should I avoid?
Common mistakes include: forgetting to write the 0 placeholder when multiplying by the tens digit, forgetting to add carry-overs, and errors in the final addition of partial products.
Q8. Is this covered in NCERT Class 4 Maths?
Yes. The NCERT Class 4 textbook (Math Magic) includes multiplication of larger numbers. Students are expected to multiply up to 3-digit by 2-digit numbers by the end of Class 4.
Q9. What comes after learning 3-digit by 2-digit multiplication?
Students move on to multiplication word problems involving multi-step operations, and in Class 5 they learn to multiply even larger numbers (4-digit by 2-digit and beyond).
