Multiplication of 2-Digit Numbers (Grade 3)
In Class 3, students learn to multiply a 2-digit number by a 1-digit number. This is done using the column method (also called the standard algorithm), where you multiply the ones first, then the tens, and carry over when needed.
This skill is used in everyday situations like finding the total cost of multiple items, calculating distances, and solving word problems.
What is Multiplication of 2-Digit Numbers - Class 3 Maths (Multiplication)?
Multiplying a 2-digit number by a 1-digit number means finding how many times the 2-digit number is added to itself.
Example: 23 × 4 = 23 + 23 + 23 + 23 = 92.
Tens × multiplier + Ones × multiplier = Product
Types and Properties
Steps for column multiplication:
- Write the 2-digit number on top and the 1-digit number below it.
- Multiply the ones digit by the multiplier. Write the ones digit of the result below. Carry the tens digit.
- Multiply the tens digit by the multiplier. Add any carry. Write the result.
Alternative: Split method (expanded form):
- Split the 2-digit number: 34 = 30 + 4
- Multiply each part: 30 × 5 = 150, 4 × 5 = 20
- Add: 150 + 20 = 170
Solved Examples
Example 1: Multiplication Without Carrying
Question: Multiply 23 × 3.
Think:
- Ones: 3 × 3 = 9
- Tens: 2 × 3 = 6
- Product = 69
Answer: 23 × 3 = 69.
Example 2: Multiplication With Carrying
Question: Multiply 47 × 6.
Think:
- Ones: 7 × 6 = 42 → write 2, carry 4
- Tens: 4 × 6 = 24, plus 4 carry = 28
- Product = 282
Answer: 47 × 6 = 282.
Example 3: Using the Split Method
Question: Multiply 35 × 4 using the split method.
Think:
- 35 = 30 + 5
- 30 × 4 = 120
- 5 × 4 = 20
- 120 + 20 = 140
Answer: 35 × 4 = 140.
Example 4: Word Problem - Cost of Items
Question: A notebook costs ₹28. Ria buys 5 notebooks. What is the total cost?
Think:
- Total = 28 × 5
- Ones: 8 × 5 = 40 → write 0, carry 4
- Tens: 2 × 5 = 10, plus 4 = 14
- Total = 140
Answer: The total cost is ₹140.
Example 5: Multiplying by 7
Question: Multiply 56 × 7.
Think:
- Ones: 6 × 7 = 42 → write 2, carry 4
- Tens: 5 × 7 = 35, plus 4 = 39
- Product = 392
Answer: 56 × 7 = 392.
Example 6: Multiplying by 9
Question: Multiply 38 × 9.
Think:
- Ones: 8 × 9 = 72 → write 2, carry 7
- Tens: 3 × 9 = 27, plus 7 = 34
- Product = 342
Answer: 38 × 9 = 342.
Example 7: Word Problem - Distance
Question: An auto-rickshaw travels 15 km each trip. It makes 8 trips in a day. How far does it travel?
Think:
- Total = 15 × 8 = 120 km
Answer: The auto-rickshaw travels 120 km.
Example 8: Multiplying with Zero in the Product
Question: Multiply 50 × 6.
Think:
- Ones: 0 × 6 = 0
- Tens: 5 × 6 = 30
- Product = 300
Answer: 50 × 6 = 300.
Example 9: Checking Multiplication
Question: Dev says 64 × 3 = 182. Check his answer.
Think:
- Ones: 4 × 3 = 12 → write 2, carry 1
- Tens: 6 × 3 = 18, plus 1 = 19
- Product = 192, not 182.
Answer: Dev is wrong. The correct answer is 192.
Key Points to Remember
- To multiply a 2-digit number by a 1-digit number, use the column method.
- Multiply ones first, then tens. Carry over when the product is 10 or more.
- The split method breaks the 2-digit number into tens and ones, multiplies each part, then adds.
- The answer to a 2-digit × 1-digit multiplication can be a 2-digit or 3-digit number.
- Multiplication is repeated addition: 24 × 3 = 24 + 24 + 24.
- Always check your work by re-doing the multiplication or using estimation.
Practice Problems
- Multiply: 32 × 4
- Multiply: 57 × 6
- Multiply: 85 × 3
- A box has 48 mangoes. How many mangoes are in 5 such boxes?
- Multiply 19 × 8 using the split method.
- Find the cost of 7 cricket balls at ₹65 each.
- Multiply: 74 × 9. Check your answer by estimation.
Frequently Asked Questions
Q1. How do you multiply a 2-digit number by a 1-digit number?
Use the column method: multiply the ones digit first, carry over if needed, then multiply the tens digit and add any carry.
Q2. What is the split (expanded form) method?
Break the 2-digit number into tens and ones. Multiply each part by the 1-digit number separately. Then add the results. For example, 34 x 5 = (30 x 5) + (4 x 5) = 150 + 20 = 170.
Q3. When do you carry over in multiplication?
When the product of a digit is 10 or more, write the ones digit in the answer and carry the tens digit to the next column.
Q4. Can the product of a 2-digit number and a 1-digit number be a 3-digit number?
Yes. For example, 25 x 5 = 125, which is a 3-digit number.
Q5. How do you check your multiplication answer?
Re-do the multiplication or use estimation. For 48 x 5, estimate: 50 x 5 = 250, so the answer should be close to 250 (actual: 240).
Q6. What is the largest product of a 2-digit and 1-digit multiplication?
99 x 9 = 891. This is the largest possible product.
Q7. Why is multiplication called repeated addition?
Because 4 x 3 means adding 4 three times: 4 + 4 + 4 = 12. Multiplication is a shortcut for repeated addition.
Q8. Is 2-digit multiplication covered in NCERT Class 3?
Yes. Multiplying 2-digit numbers by 1-digit numbers is part of the Multiplication chapter in NCERT Class 3 Maths.
Related Topics
- Multiplication of 2-Digit by 1-Digit
- Multiplication by 10 and 100
- Multiplication Concept (Grade 3)
- Multiplication Tables of 3 and 4
- Multiplication Tables of 6 and 7
- Multiplication Tables of 8 and 9
- Multiplication Word Problems (Grade 3)
- Properties of Multiplication
- Multiplying by 0 and 1
- Multiplication Tables (2 to 10)
