Multiplication of 4-Digit Numbers
In Class 5, students advance to multiplying 4-digit numbers by 2-digit and 3-digit numbers. This builds on the multiplication skills learned in earlier classes and prepares students for working with even larger numbers.
Multiplication of 4-digit numbers is used in real life for calculating costs (e.g., ₹2,450 per item for 35 items), finding areas, and solving multi-step word problems. The standard long multiplication algorithm is used, where partial products are added to get the final answer.
What is Multiplication of 4-Digit Numbers - Class 5 Maths (Operations)?
Multiplication is repeated addition. When we multiply a 4-digit number by a 2-digit or 3-digit number, we use the long multiplication method:
- Multiply the 4-digit number by the ones digit of the multiplier.
- Multiply the 4-digit number by the tens digit of the multiplier (shift one place left).
- If there is a hundreds digit, multiply by it too (shift two places left).
- Add all the partial products to get the final answer.
Terminology:
- Multiplicand: The number being multiplied (e.g., 2,345)
- Multiplier: The number you multiply by (e.g., 23)
- Product: The result of multiplication (e.g., 53,935)
Multiplication of 4-Digit Numbers Formula
Product = Multiplicand × Multiplier
Estimation shortcut: Round both numbers to the nearest convenient value, multiply, and check if your exact answer is reasonable.
Solved Examples
Example 1: Example 1: 4-digit × 1-digit
Problem: Calculate 3,256 × 7.
Solution:
3,256
× 7
-------
22,792
Step by step:
- 7 × 6 = 42, write 2 carry 4
- 7 × 5 = 35, + 4 = 39, write 9 carry 3
- 7 × 2 = 14, + 3 = 17, write 7 carry 1
- 7 × 3 = 21, + 1 = 22, write 22
Answer: 3,256 × 7 = 22,792
Example 2: Example 2: 4-digit × 2-digit
Problem: Calculate 1,234 × 26.
Solution:
1,234
× 26
--------
7,404 (1,234 × 6)
+ 24,680 (1,234 × 20)
--------
32,084
Answer: 1,234 × 26 = 32,084
Example 3: Example 3: 4-digit × 2-digit (with carrying)
Problem: Calculate 4,578 × 35.
Solution:
4,578
× 35
--------
22,890 (4,578 × 5)
+ 1,37,340 (4,578 × 30)
---------
1,60,230
Answer: 4,578 × 35 = 1,60,230
Example 4: Example 4: 4-digit × 3-digit
Problem: Calculate 2,105 × 214.
Solution:
2,105
× 214
---------
8,420 (2,105 × 4)
21,050 (2,105 × 10)
+ 4,21,000 (2,105 × 200)
---------
4,50,470
Answer: 2,105 × 214 = 4,50,470
Example 5: Example 5: Multiplying with zeroes
Problem: Calculate 5,040 × 18.
Solution:
5,040
× 18
--------
40,320 (5,040 × 8)
+ 50,400 (5,040 × 10)
--------
90,720
Answer: 5,040 × 18 = 90,720
Example 6: Example 6: Word problem — Cost calculation
Problem: A school ordered 24 computers at ₹3,750 each. What is the total cost?
Solution:
Step 1: Total cost = 3,750 × 24
Step 2:
3,750
× 24
--------
15,000 (3,750 × 4)
+ 75,000 (3,750 × 20)
--------
90,000
Answer: Total cost = ₹90,000
Example 7: Example 7: Word problem — Distance
Problem: A train travels 1,250 km per day. How far does it travel in 15 days?
Solution:
Distance = 1,250 × 15
1,250 × 15 = 1,250 × 10 + 1,250 × 5 = 12,500 + 6,250 = 18,750 km
Example 8: Example 8: Estimating the product
Problem: Estimate the product of 3,876 × 42.
Solution:
Step 1: Round 3,876 to 4,000 and 42 to 40.
Step 2: Estimated product = 4,000 × 40 = 1,60,000
Step 3: Exact product = 3,876 × 42 = 1,62,792 (close to the estimate).
Example 9: Example 9: Word problem — Production
Problem: A factory produces 2,350 toys per day. How many toys does it produce in 28 days?
Solution:
Total = 2,350 × 28
2,350 × 28 = 2,350 × 30 − 2,350 × 2 = 70,500 − 4,700 = 65,800 toys
Key Points to Remember
- In long multiplication, multiply the multiplicand by each digit of the multiplier separately to get partial products.
- Shift each partial product one place to the left for each higher place value of the multiplier digit.
- Add all partial products to get the final answer.
- When multiplying by a number ending in 0, multiply by the non-zero part and append the zero(s).
- Always estimate before calculating to check if your answer is reasonable.
- The product of a 4-digit number and a 2-digit number can have up to 6 digits.
- The product of a 4-digit number and a 3-digit number can have up to 7 digits.
Practice Problems
- Calculate 4,523 × 9.
- Calculate 2,847 × 36.
- Calculate 1,506 × 45.
- A shopkeeper buys 48 bags of rice at ₹1,275 per bag. Find the total cost.
- Calculate 3,200 × 125.
- Meera reads 1,450 words per hour. How many words does she read in 12 hours?
- Estimate the product of 5,678 × 53 by rounding, then calculate the exact answer.
- A truck carries 2,500 kg of goods per trip. How much does it carry in 32 trips?
Frequently Asked Questions
Q1. What is long multiplication?
Long multiplication is a method where you multiply a number by each digit of the multiplier separately (creating partial products) and then add all partial products together. It works for numbers of any size.
Q2. How many digits can the product of a 4-digit and 2-digit number have?
The product can have 5 or 6 digits. The smallest product is 1,000 × 10 = 10,000 (5 digits). The largest is 9,999 × 99 = 9,89,901 (6 digits).
Q3. Why do we shift partial products to the left?
Each digit of the multiplier has a place value. When multiplying by the tens digit, the result is actually 10 times larger, so we shift one place left (which is the same as adding a 0). Similarly for hundreds (shift two places).
Q4. How do I check my multiplication answer?
Use estimation by rounding both numbers and multiplying. If your exact answer is close to the estimate, it is likely correct. You can also verify by dividing the product by one of the factors.
Q5. What is the shortcut for multiplying by 25?
Multiply by 100 and divide by 4. For example, 3,200 × 25 = 3,200 × 100 ÷ 4 = 3,20,000 ÷ 4 = 80,000. This works because 25 = 100 ÷ 4.
Q6. How is multiplication used in daily life?
Multiplication is used for calculating total costs (price × quantity), finding areas (length × breadth), determining distances (speed × time), and many other real-world calculations involving repeated addition.
Q7. What if the multiplier has a zero in the middle (e.g., 302)?
When multiplying by 302, the partial product for the tens digit (0) is 0, so you can skip it. Just multiply by 2 (ones) and by 3 (hundreds, shift two places). Add the two partial products.
Q8. Is there a mental math trick for multiplying 4-digit numbers?
Break the multiplier into convenient parts. For example, to multiply by 15, multiply by 10 and add half of that result. To multiply by 99, multiply by 100 and subtract the original number.
Related Topics
- Multiplication of Large Numbers
- Multiplication of 3-Digit by 2-Digit
- Addition of Large Numbers
- Subtraction of Large Numbers
- Division of Large Numbers
- Order of Operations (BODMAS)
- Word Problems on Four Operations
- Mental Math (Grade 5)
- Division of 4-Digit by 2-Digit Numbers
- Simplification Using BODMAS
- Properties of Operations (Grade 5)
- Unitary Method (Grade 5)
