What is Multiplying by a Multiple of 10?

S1-SA1-0120

Grade Level:

Class 4

Maths, Computing, AI

Definition

What is it?

Multiplying by a multiple of 10 means finding the product of a number and a number like 10, 20, 30, 100, 200, 500, and so on. It involves multiplying the non-zero digits first and then adding the total number of zeros from both numbers to the end of the product.

Simple Example

Quick Example

Imagine you are buying 3 packets of biscuits, and each packet costs Rs. 20. To find the total cost, you multiply 3 by 20. You can think of it as 3 x 2 x 10, which is 6 x 10 = Rs. 60.

Worked Example

Step-by-Step

Let's multiply 15 by 300.

Step 1: Identify the non-zero digits in both numbers. Here, they are 15 and 3.
---Step 2: Multiply these non-zero digits: 15 x 3 = 45.
---Step 3: Count the total number of zeros in the original numbers. 15 has 0 zeros. 300 has 2 zeros.
---Step 4: Add the total zeros to the product from Step 2. So, 45 gets 2 zeros added to its end.
---Step 5: The final answer is 4500.

Why It Matters

Understanding this concept helps you calculate faster, which is super useful in daily life and future studies. In computing, algorithms often use similar logic for quick calculations. It's essential for careers in finance, data analysis, and even game development where quick number crunching is needed.

Common Mistakes

MISTAKE: Forgetting to add ALL the zeros from both numbers. For example, for 5 x 20, students might do 5 x 2 = 10, and then add only one zero to get 100. | CORRECTION: Count the total zeros from BOTH numbers. In 5 x 20, 5 has 0 zeros, 20 has 1 zero. Total zeros = 1. So, 5 x 2 = 10, add 1 zero, answer is 100.

MISTAKE: Multiplying the non-zero digits incorrectly. For example, for 12 x 40, doing 12 x 4 = 24. | CORRECTION: Always ensure your basic multiplication of the non-zero digits is correct. 12 x 4 is 48, not 24. Then add the zeros.

MISTAKE: Getting confused when one of the numbers is a multiple of 10 itself, like 10 x 50. Some might think 1 x 5 = 5 and add one zero. | CORRECTION: Treat 10 as having one zero. So, for 10 x 50, multiply non-zero digits (1 x 5 = 5). Count total zeros (1 from 10, 1 from 50 = 2 zeros). Final answer is 500.

Practice Questions

Try It Yourself

QUESTION: A school bus carries 40 students. If there are 8 such buses, how many students are there in total? | ANSWER: 320 students

QUESTION: A shop sells a pack of 12 pencils for Rs. 50. If a customer buys 6 such packs, how much do they pay? | ANSWER: Rs. 300

QUESTION: You are designing a new apartment building. Each floor needs 25 tiles, and there are 20 floors. If each tile costs Rs. 10, what is the total cost of tiles for the entire building? | ANSWER: Rs. 5000

MCQ

Quick Quiz

What is 25 multiplied by 40?

100

1000

10000

100000

The Correct Answer Is:

To multiply 25 by 40, first multiply the non-zero digits: 25 x 4 = 100. Then, count the total zeros in the original numbers (40 has one zero). Add this one zero to 100, which gives 1000.

Real World Connection

In the Real World

When a delivery app like Zepto calculates the total cost for 5 items, each costing Rs. 60, it uses this method (5 x 60 = 300). Similarly, when a cricket analyst calculates the total runs scored by a batsman who hit 7 boundaries (fours) and 5 sixes, they use these quick multiplication tricks (7 x 4 = 28, 5 x 6 = 30).

Key Vocabulary

Key Terms

MULTIPLE OF 10: A number that can be divided by 10 without a remainder (e.g., 20, 50, 100) | PRODUCT: The answer you get when you multiply two or more numbers | NON-ZERO DIGITS: The digits in a number that are not zero (e.g., in 350, 3 and 5 are non-zero digits) | ESTIMATION: Finding an approximate value, often using quick mental calculations like multiplying by multiples of 10.

What's Next

What to Learn Next

Great job mastering multiplication by multiples of 10! Next, you can explore 'Multiplying by Multiples of 100 and 1000' to extend your skills to even larger numbers. This will help you tackle more complex calculations with ease.