Multiplication of 2-Digit by 2-Digit
In Class 4, you learn to multiply a 2-digit number by another 2-digit number. This produces a product that can be 3 or 4 digits long.
The standard method is column multiplication (long multiplication), where you multiply by the ones digit first, then by the tens digit, and finally add the two partial products.
This skill is essential for calculating areas, finding total costs of multiple items, and solving real-life multiplication problems.
What is Multiplication of 2-Digit by 2-Digit - Class 4 Maths (Multiplication)?
Column multiplication (long multiplication) for 2-digit by 2-digit:
- Step 1: Multiply the top number by the ones digit of the bottom number. Write this as the first partial product.
- Step 2: Multiply the top number by the tens digit of the bottom number. Write this as the second partial product, shifted one place to the left (or add a 0 at the end).
- Step 3: Add the two partial products to get the final answer.
Product = (Top number x Ones digit) + (Top number x Tens digit x 10)
Types and Properties
Worked example: 43 x 27
| 4 3 | ||||
| x | 2 7 | |||
| 3 0 1 (43 x 7) | ||||
| 8 6 0 (43 x 20) | ||||
| 1 1 6 1 | ||||
Breakdown:
- 43 x 7 = 301 (first partial product)
- 43 x 20 = 860 (second partial product)
- 301 + 860 = 1,161
Special cases:
- Multiplying by a number ending in 0: 35 x 40 = 35 x 4 x 10 = 140 x 10 = 1,400
- Multiplying by 11: 45 x 11 = 45 x 10 + 45 x 1 = 450 + 45 = 495
Solved Examples
Example 1: Example 1: Basic 2-digit by 2-digit
Problem: Multiply 23 x 14.
Solution:
Step 1: 23 x 4 = 92
Step 2: 23 x 10 = 230
Step 3: 92 + 230 = 322
Answer: 23 x 14 = 322
Example 2: Example 2: With carrying
Problem: Multiply 56 x 38.
Solution:
Step 1: 56 x 8: 6x8=48 (write 8, carry 4); 5x8=40+4=44. Partial product = 448
Step 2: 56 x 30: 6x3=18 (write 8, carry 1); 5x3=15+1=16. Then x10 = 1,680
Step 3: 448 + 1,680 = 2,128
Answer: 56 x 38 = 2,128
Example 3: Example 3: Multiplying with zeros
Problem: Multiply 45 x 20.
Solution:
Step 1: 45 x 2 = 90
Step 2: Append one zero (since we are multiplying by 20, not 2).
Answer: 45 x 20 = 900
Example 4: Example 4: Product close to 1,000
Problem: Multiply 32 x 31.
Solution:
Step 1: 32 x 1 = 32
Step 2: 32 x 30 = 960
Step 3: 32 + 960 = 992
Answer: 32 x 31 = 992
Example 5: Example 5: Word problem - cost of items
Problem: A notebook costs ₹45. Ria's school ordered 36 notebooks. What is the total cost?
Solution:
Step 1: 45 x 6 = 270
Step 2: 45 x 30 = 1,350
Step 3: 270 + 1,350 = 1,620
Answer: Total cost = ₹1,620
Example 6: Example 6: Word problem - area of a rectangle
Problem: A rectangular garden is 54 m long and 28 m wide. Find the area.
Solution:
Step 1: Area = length x breadth = 54 x 28
Step 2: 54 x 8 = 432
Step 3: 54 x 20 = 1,080
Step 4: 432 + 1,080 = 1,512
Answer: Area = 1,512 sq m
Example 7: Example 7: Large product
Problem: Multiply 87 x 96.
Solution:
Step 1: 87 x 6 = 522
Step 2: 87 x 90 = 7,830
Step 3: 522 + 7,830 = 8,352
Answer: 87 x 96 = 8,352
Example 8: Example 8: Word problem - seating arrangement
Problem: A hall has 48 rows with 52 chairs in each row. How many chairs in total?
Solution:
Step 1: 48 x 2 = 96
Step 2: 48 x 50 = 2,400
Step 3: 96 + 2,400 = 2,496
Answer: Total chairs = 2,496
Example 9: Example 9: Checking with estimation
Problem: Multiply 63 x 47. Verify with estimation.
Solution:
Calculation:
63 x 7 = 441. 63 x 40 = 2,520. Total = 441 + 2,520 = 2,961
Estimation check: 60 x 50 = 3,000. Our answer 2,961 is close to 3,000.
Answer: 63 x 47 = 2,961 (verified)
Example 10: Example 10: Word problem - bus capacity
Problem: An Orchids school bus carries 72 students. If 15 buses make a field trip, how many students go on the trip?
Solution:
Step 1: 72 x 5 = 360
Step 2: 72 x 10 = 720
Step 3: 360 + 720 = 1,080
Answer: 1,080 students go on the trip.
Key Points to Remember
- Multiply the top number by the ones digit of the bottom number (first partial product).
- Multiply the top number by the tens digit of the bottom number and add a zero (second partial product).
- Add both partial products for the final answer.
- The product of two 2-digit numbers is always between 100 (10 x 10) and 9,801 (99 x 99).
- When multiplying by a number ending in 0 (like 40, 50), multiply by the non-zero digit first, then append the zero.
- Use estimation to check: round both numbers to the nearest 10, multiply, and compare.
- Commutative property: 43 x 27 = 27 x 43 (same answer either way).
Practice Problems
- Multiply 24 x 13.
- Multiply 56 x 42.
- Multiply 78 x 65.
- Multiply 35 x 20.
- A book has 64 pages. Kavi reads 12 such books. How many pages in total?
- Each student plants 25 saplings. If 34 students participate, how many saplings are planted?
- Find the area of a rectangle with length 46 cm and breadth 28 cm.
- Estimate 67 x 43. Then calculate the exact answer.
Frequently Asked Questions
Q1. How do you multiply a 2-digit number by a 2-digit number?
Use column (long) multiplication: (1) Multiply by the ones digit to get the first partial product. (2) Multiply by the tens digit and add a zero to get the second partial product. (3) Add both partial products.
Q2. What is a partial product?
A partial product is the result of multiplying the top number by just one digit of the bottom number. In 45 x 23, the partial products are 45 x 3 = 135 and 45 x 20 = 900.
Q3. Why do we add a zero in the second partial product?
Because the tens digit represents tens, not ones. When you multiply by the tens digit (e.g., the 2 in 23), you are really multiplying by 20 (not 2). Adding a zero accounts for this.
Q4. What is the largest product of two 2-digit numbers?
99 x 99 = 9,801. This is a 4-digit number. The smallest product is 10 x 10 = 100 (a 3-digit number).
Q5. Can I multiply in any order?
Yes. Multiplication is commutative: 45 x 32 = 32 x 45. Sometimes one order is easier to calculate. Choose the order that has simpler partial products.
Q6. How do I check my multiplication answer?
Use estimation: round both numbers to the nearest 10 and multiply. If 56 x 38 = 2,128, estimate: 60 x 40 = 2,400. Since 2,128 is reasonably close, the answer is likely correct.
Q7. What is the shortcut for multiplying by 11?
Multiply by 10 and add the number itself. Example: 45 x 11 = 45 x 10 + 45 = 450 + 45 = 495.
Q8. Is 2-digit by 2-digit multiplication in NCERT Class 4?
Yes. NCERT Class 4 Maths covers multiplication of 2-digit by 2-digit numbers in the multiplication chapter, including word problems and estimation.
Q9. What if I get the partial products wrong?
The final answer will be wrong. Always double-check each partial product separately. Use multiplication tables you know well, and carry digits carefully.
