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What is Long Multiplication (2-digit × 2-digit)?
Grade Level:
Class 4
Maths, Computing, AI
Definition
What is it?
Long multiplication for 2-digit numbers is a step-by-step method to multiply two numbers, each having two digits. It breaks down a big multiplication problem into smaller, easier-to-solve parts using addition and single-digit multiplication. This helps you find the total product accurately.
Simple Example
Quick Example
Imagine a cricket match where a batsman scores 45 runs in each of 23 matches. To find the total runs he scored, you could add 45 twenty-three times, but that would take too long! Long multiplication helps you quickly calculate 45 x 23 to find the total runs.
Worked Example
Step-by-Step
Let's multiply 34 x 26:
1. Multiply the top number (34) by the ones digit of the bottom number (6).
34
x 26
----
204 (Because 6 x 4 = 24, write 4, carry 2. Then 6 x 3 = 18, plus 2 = 20. So, 6 x 34 = 204)
---
2. Now, multiply the top number (34) by the tens digit of the bottom number (2). Remember, this '2' is actually 20, so we put a zero as a placeholder in the ones column first.
34
x 26
----
204
680 (Because 2 x 4 = 8, and 2 x 3 = 6. Since we are multiplying by 20, it's 680)
---
3. Add the two results (204 and 680) together.
204
+ 680
-----
884
---
ANSWER: So, 34 x 26 = 884.
Why It Matters
Understanding long multiplication is key for basic computing and helps build logic for advanced algorithms. It's used by software developers to create programs that handle large calculations, by data analysts to process numerical information, and even in AI to train models that recognize patterns in numbers, like calculating the cost of many items in a grocery app.
Common Mistakes
MISTAKE: Forgetting to put a zero placeholder when multiplying by the tens digit. | CORRECTION: Always add a zero in the ones place on the second line of multiplication because you are multiplying by a 'tens' value (e.g., 20, 30).
MISTAKE: Not carrying over digits correctly during the multiplication steps. | CORRECTION: When a product is a 2-digit number (e.g., 6 x 7 = 42), write the ones digit (2) and carry over the tens digit (4) to add to the next multiplication result.
MISTAKE: Making errors while adding the final two product lines. | CORRECTION: Double-check your addition carefully. Line up the numbers correctly by their place values (ones under ones, tens under tens) to avoid addition mistakes.
Practice Questions
Try It Yourself
QUESTION: Multiply 18 x 12 | ANSWER: 216
QUESTION: A bus travels 65 km every day. How many km does it travel in 31 days? | ANSWER: 2015 km
QUESTION: A school has 4 sections in Class 4. Each section has 32 students. If each student pays ₹25 for a field trip, what is the total amount collected from Class 4? | ANSWER: ₹3200 (Hint: First find total students, then total amount)
MCQ
Quick Quiz
When multiplying 54 x 32, what is the first number you write on the second line of multiplication (after the first line for 54 x 2)?
108
162
1620
54
The Correct Answer Is:
C
The first line is 54 x 2 = 108. For the second line, you multiply 54 by 3 (which is actually 30). So 54 x 3 = 162, and adding the zero placeholder makes it 1620.
Real World Connection
In the Real World
Imagine a shopkeeper in a local market calculating the total cost of 25 shirts, each priced at ₹199. They use long multiplication, perhaps mentally or with a calculator, to quickly find the total amount (25 x 199). This skill is crucial for managing money, billing customers, and keeping accounts, whether it's for a small 'kirana' store or a big e-commerce platform like Flipkart during festival sales.
Key Vocabulary
Key Terms
PRODUCT: The result of multiplication | MULTIPLIER: The number by which another number is multiplied | MULTIPLICAND: The number being multiplied | PLACEHOLDER ZERO: A zero used to hold a place value when multiplying by tens, hundreds, etc. | CARRY OVER: Moving a digit to the next place value column when the product of two digits is too large for one column.
What's Next
What to Learn Next
Great job mastering 2-digit long multiplication! Next, you can explore 'Long Multiplication (3-digit × 2-digit)' and then 'Long Multiplication (3-digit × 3-digit)'. These concepts build on the same steps but involve more digits, preparing you for even larger calculations.
