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What is Long Multiplication (3-digit × 2-digit)?
Grade Level:
Class 5
Maths, Computing, AI
Definition
What is it?
Long multiplication (3-digit × 2-digit) is a step-by-step method to multiply a three-digit number by a two-digit number. It helps break down big multiplication problems into smaller, easier parts using addition and basic multiplication facts.
Simple Example
Quick Example
Imagine your school buys 12 new cricket bats, and each bat costs ₹245. To find the total cost, you need to multiply 245 by 12. Long multiplication helps you calculate this total amount easily, step-by-step, without needing a calculator.
Worked Example
Step-by-Step
Let's multiply 345 by 23.
Step 1: Multiply 345 by the ones digit of 23, which is 3.
345
x 23
-----
1035 (345 x 3)
---
Step 2: Multiply 345 by the tens digit of 23, which is 2 (or 20). Write a zero in the ones place first.
345
x 23
-----
1035
6900 (345 x 20)
---
Step 3: Add the results from Step 1 and Step 2.
345
x 23
-----
1035
+ 6900
-----
7935
---
Answer: 345 multiplied by 23 is 7935.
Why It Matters
Understanding long multiplication is a basic skill for many fields. In computing, it's how computers perform calculations. In AI, it's part of the logic used for processing data. Even simple tasks like calculating expenses for a small business or managing inventory use this core math concept.
Common Mistakes
MISTAKE: Forgetting to put a zero in the ones place when multiplying by the tens digit. | CORRECTION: Always remember to place a zero in the ones column when you start multiplying by the tens digit of the bottom number.
MISTAKE: Incorrectly carrying over numbers during multiplication or addition steps. | CORRECTION: Double-check your carrying. It's helpful to write down the carried numbers lightly above the next column to avoid confusion.
MISTAKE: Making errors in basic multiplication facts (e.g., 5 x 3 = 18 instead of 15). | CORRECTION: Practice your multiplication tables (1 to 10) regularly. Strong basic facts make long multiplication much easier.
Practice Questions
Try It Yourself
QUESTION: Multiply 125 by 14. | ANSWER: 1750
QUESTION: A train travels 350 km in one day. How many kilometers will it travel in 21 days? | ANSWER: 7350 km
QUESTION: A mobile phone costs ₹1230. If a shop sells 25 such phones, how much money did they earn in total? | ANSWER: ₹30750
MCQ
Quick Quiz
What is the first step when multiplying 456 by 18 using long multiplication?
Multiply 456 by 1
Multiply 456 by 8
Multiply 456 by 10
Add 456 and 18
The Correct Answer Is:
B
The first step in long multiplication is always to multiply the top number by the ones digit of the bottom number. In this case, it's 456 multiplied by 8.
Real World Connection
In the Real World
When a shopkeeper calculates the total cost of 15 shirts, each priced at ₹375, they are doing a 3-digit by 2-digit long multiplication. Similarly, if a delivery app like Swiggy or Zomato needs to estimate the total fuel cost for 20 deliveries, each covering an average of 145 km, they use this skill.
Key Vocabulary
Key Terms
MULTIPLIER: The number by which another number is multiplied (the bottom number in long multiplication) | MULTIPLICAND: The number being multiplied (the top number) | PRODUCT: The result of multiplication | CARRY OVER: Moving a digit from one column to the next when a sum exceeds 9 | PLACE VALUE: The value of a digit based on its position (ones, tens, hundreds)
What's Next
What to Learn Next
Great job mastering long multiplication! Next, you can explore 'Long Multiplication (3-digit × 3-digit)' to tackle even bigger numbers. This will build on the same principles you just learned, making it easy to understand.
