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What is Short Multiplication (1-digit × multi-digit)?
Grade Level:
Class 3
Maths, Computing, AI
Definition
What is it?
Short multiplication is a simple way to multiply a multi-digit number (like 23 or 145) by a single-digit number (like 2 or 7). It helps us find the total quickly by multiplying each digit of the larger number separately and adding any 'carry-over' values.
Simple Example
Quick Example
Imagine you buy 3 packets of biscuits, and each packet costs ₹18. To find the total cost, you can use short multiplication: 18 x 3. You'll multiply 3 by 8 (the ones digit) and then 3 by 1 (the tens digit), remembering to carry over any extra.
Worked Example
Step-by-Step
Let's multiply 45 by 6.
Step 1: Write the numbers one below the other, aligning the ones digits.
45
x 6
-----
Step 2: Multiply the ones digit of the top number (5) by the single-digit number (6).
5 x 6 = 30. Write down 0 in the ones place and carry over 3 to the tens place.
4(3)5
x 6
-----
0
Step 3: Multiply the tens digit of the top number (4) by the single-digit number (6).
4 x 6 = 24.
Step 4: Add the carried-over number (3) to this result.
24 + 3 = 27. Write down 27 in front of the 0.
45
x 6
-----
270
Answer: So, 45 multiplied by 6 is 270.
Why It Matters
Understanding short multiplication is fundamental for many areas, from managing your pocket money to advanced computing. In AI and data science, algorithms often perform massive calculations that are built on basic arithmetic like this. It's a core skill for careers in finance, engineering, and even game development.
Common Mistakes
MISTAKE: Forgetting to add the carried-over number. For example, in 25 x 3, students might do 5x3=15 (write 5, carry 1), then 2x3=6, and write 65 as the answer. | CORRECTION: Always remember to add the carried-over digit to the product of the next place value.
MISTAKE: Carrying over the wrong digit. For example, if 5 x 6 = 30, writing down 3 and carrying over 0. | CORRECTION: Always write the ones digit of the product in the current place value and carry over the tens digit to the next place value.
MISTAKE: Not aligning numbers correctly, especially when writing the problem down. This can lead to multiplying the wrong place values. | CORRECTION: Always align the ones digits directly below each other to ensure you multiply the correct place values.
Practice Questions
Try It Yourself
QUESTION: Multiply 34 by 2. | ANSWER: 68
QUESTION: A school bus carries 52 students. If there are 4 such buses, how many students are there in total? | ANSWER: 208 students
QUESTION: A grocer sells 125 kg of rice every day. How much rice does he sell in 7 days? | ANSWER: 875 kg
MCQ
Quick Quiz
What is the correct result of 78 multiplied by 5?
350
390
358
398
The Correct Answer Is:
B
First, 8 x 5 = 40. Write 0, carry over 4. Next, 7 x 5 = 35. Add the carried-over 4: 35 + 4 = 39. Combine to get 390.
Real World Connection
In the Real World
When a shopkeeper calculates the cost of 6 packets of chips, each costing ₹25, they are using short multiplication. Even apps like Swiggy or Zomato use similar calculations behind the scenes to sum up your order when you select multiple items of the same type.
Key Vocabulary
Key Terms
MULTIPLY: To combine equal groups to find a total | PRODUCT: The answer to a multiplication problem | CARRY OVER: To move a digit from one place value column to the next higher place value column during calculation | PLACE VALUE: The value of a digit based on its position in a number (e.g., ones, tens, hundreds)
What's Next
What to Learn Next
Once you master short multiplication, you can move on to 'Long Multiplication' where you multiply multi-digit numbers by other multi-digit numbers. It builds on the same ideas of multiplying by place value and carrying over, but with more steps.
