Multiplication of 2-Digit by 1-Digit
In Class 3, students learn to multiply a 2-digit number by a 1-digit number. This builds on the multiplication tables and place value knowledge.
There are two main methods: the expanded form method (breaking the 2-digit number into tens and ones) and the column method (standard algorithm). Both give the same answer.
What is Multiplication of 2-Digit by 1-Digit - Class 3 Maths (Multiplication (Grade 3))?
To multiply a 2-digit number by a 1-digit number:
Method 1 — Expanded Form:
- Break the 2-digit number into tens and ones.
- Multiply each part by the 1-digit number.
- Add the results.
Method 2 — Column (Standard) Method:
- Write the numbers in columns.
- Multiply the ones digit first. If the product is 10+, carry the tens digit.
- Multiply the tens digit and add any carry.
Example: 34 × 5 = (30 × 5) + (4 × 5) = 150 + 20 = 170
Solved Examples
Example 1: Expanded Form Method — No Carrying
Question: Multiply 23 × 3.
Think:
- Break 23 into 20 + 3
- 20 × 3 = 60
- 3 × 3 = 9
- 60 + 9 = 69
Answer: 23 × 3 = 69
Example 2: Column Method — No Carrying
Question: Multiply 31 × 2.
Think:
- Ones: 1 × 2 = 2
- Tens: 3 × 2 = 6
Answer: 31 × 2 = 62
Example 3: Column Method — With Carrying
Question: Multiply 46 × 3.
Think:
- Ones: 6 × 3 = 18 → write 8, carry 1
- Tens: 4 × 3 = 12, + 1 (carry) = 13
Answer: 46 × 3 = 138
Example 4: Expanded Form — With Carrying
Question: Multiply 57 × 4.
Think:
- 50 × 4 = 200
- 7 × 4 = 28
- 200 + 28 = 228
Answer: 57 × 4 = 228
Example 5: Word Problem — Chapatis for Students
Question: Each student eats 3 chapatis at lunch. How many chapatis are needed for 45 students?
Think:
- 45 × 3
- 40 × 3 = 120
- 5 × 3 = 15
- 120 + 15 = 135
Answer: 135 chapatis are needed.
Example 6: Word Problem — Cost of Notebooks
Question: A notebook costs ₹28. Priya buys 5 notebooks. How much does she pay?
Think:
- 28 × 5
- Ones: 8 × 5 = 40 → write 0, carry 4
- Tens: 2 × 5 = 10, + 4 = 14
Answer: Priya pays ₹140.
Example 7: Multiplying by 9 Using (10 − 1)
Question: Multiply 36 × 9.
Think:
- 36 × 9 = 36 × (10 − 1) = 360 − 36 = 324
Answer: 36 × 9 = 324
Example 8: Multiplying a Multiple of 10
Question: Multiply 50 × 7.
Think:
- 5 × 7 = 35
- Add one zero → 350
Answer: 50 × 7 = 350
Example 9: Word Problem — Mangoes in Crates
Question: Each crate holds 48 mangoes. Aman has 6 crates. How many mangoes does he have?
Think:
- 48 × 6
- Ones: 8 × 6 = 48 → write 8, carry 4
- Tens: 4 × 6 = 24, + 4 = 28
Answer: Aman has 288 mangoes.
Example 10: Checking with Estimation
Question: Multiply 67 × 4 and check with estimation.
Think:
- Ones: 7 × 4 = 28 → write 8, carry 2
- Tens: 6 × 4 = 24, + 2 = 26
- Answer: 268
- Estimate: 70 × 4 = 280. Answer 268 is close ✓
Answer: 67 × 4 = 268
Real-World Applications
Where is 2-digit by 1-digit multiplication used?
- Shopping: If one apple costs ₹12, then 8 apples cost 12 × 8 = ₹96. This is a common shopping calculation.
- Cooking: A recipe needs 45 g of sugar. To make 3 batches, you need 45 × 3 = 135 g.
- Travel: A bus covers 65 km per hour. In 4 hours, it covers 65 × 4 = 260 km.
- Pocket money: Kavi gets ₹25 per week. In 8 weeks, he gets 25 × 8 = ₹200.
- School supplies: A teacher needs 36 pencils for each section. For 5 sections: 36 × 5 = 180 pencils.
- Time: If Meera reads 15 pages per day, in 7 days she reads 15 × 7 = 105 pages.
This type of multiplication is used countless times in daily life. Once you master the column method and expanded form, you can tackle any such problem quickly and accurately.
Key Points to Remember
- Two methods: expanded form (break into tens and ones) and column method (standard algorithm).
- In the column method, multiply ones first, then tens. Carry when a product is 10 or more.
- The product of a 2-digit number and a 1-digit number can be a 2-digit or 3-digit number.
- Maximum product: 99 × 9 = 891.
- Use estimation to check your answer.
- Multiplying by 9: use the shortcut n × 9 = n × 10 − n.
Practice Problems
- Multiply 35 × 4.
- Multiply 72 × 3.
- Multiply 58 × 6.
- Each row has 24 chairs. How many chairs in 7 rows?
- A pen costs ₹15. What is the cost of 8 pens?
- Multiply 99 × 5.
- Kavi runs 46 metres in one round. How far does he run in 8 rounds?
- Multiply 60 × 9.
Frequently Asked Questions
Q1. Which method is better — expanded form or column method?
Both are correct. The expanded form is easier to understand and good for mental math. The column method is faster for written work and is the standard method used in higher classes.
Q2. What if the product has 3 digits?
That is expected. For example, 56 × 8 = 448 (a 3-digit number). The product of a 2-digit and a 1-digit number can have up to 3 digits.
Q3. How do I handle carrying in the column method?
When the ones product is 10 or more, write the ones digit in the answer and carry the tens digit to the tens column. Add the carry to the tens product.
Q4. Can I multiply in any order?
Yes. 23 × 4 = 4 × 23. But in the column method, always put the 2-digit number on top and the 1-digit number below.
Q5. What is the largest product of a 2-digit number and a 1-digit number?
99 × 9 = 891. This is the largest possible product.
Q6. How do I check my multiplication?
Use estimation (round and multiply), or divide the product by the multiplier — if you get the multiplicand, the answer is correct.
Q7. What if one factor is 0?
Any number multiplied by 0 is 0. For example, 45 × 0 = 0.
Q8. How does this relate to the tables I already know?
The column method applies the multiplication tables digit by digit. For example, in 46 × 3: you use 6 × 3 = 18 and 4 × 3 = 12. Knowing your tables makes this process smooth.
Related Topics
- Multiplication by 10 and 100
- Multiplication Word Problems (Grade 3)
- Multiplication Concept (Grade 3)
- Multiplication Tables of 3 and 4
- Multiplication Tables of 6 and 7
- Multiplication Tables of 8 and 9
- Properties of Multiplication
- Multiplying by 0 and 1
- Multiplication Tables (2 to 10)
- Multiplication of 2-Digit Numbers (Grade 3)
