Multiplying 4-Digit Numbers: Lesson for Kids

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: Mental Math Strategies for Multiplication: Lesson for Kids

You're on a roll. Keep up the good work!

Take Quiz Watch Next Lesson
 Replay
Your next lesson will play in 10 seconds
  • 0:04 Multiplication in Base 10
  • 2:53 Multiplying 4-Digit…
  • 4:37 Lesson Summary
Save Save Save

Want to watch this again later?

Log in or sign up to add this lesson to a Custom Course.

Log in or Sign up

Timeline
Autoplay
Autoplay
Speed Speed

Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Nick Rogers
Numbers are written using base ten notation. If you understand this, multiplication becomes intuitive and even easy. Dive in to find out the best tricks and techniques to quickly multiply 4-digit numbers.

Multiplication in Base 10

Digits represent powers of 10 - just like the number of fingers we have! In a 4-digit number, they are the thousands, hundreds, tens and ones. For example, the number 1,272 has:

  • One thousand (1)
  • Two hundreds (2)
  • Seven tens (7)
  • Two ones (2)

Multiplying and Collecting Four Digits

Let's work through an example: 1,272 x 1,364.

Broken down into its components, we write it as:

(1,000 + 200 + 70 + 2) * (1,000 + 300 + 60 + 4)

Now, combine the four digits from each number as follows: the product of the thousands gives millions, the product of the hundreds and thousands gives hundreds of thousands and so on. Here are just a few simple multiplications to give us all of the results we need. We'll start with the digit, then mention the source, then look at the result:

Digit Source Result
Millions Thousands * thousands 1 * 1 = 1
Hundreds of thousands Hundreds * thousands (1 * 3) + (2 * 1) = 5
Tens of thousands Tens * thousands (1 * 6) + (7 * 1) = 13
Hundreds * hundreds 3 x 2 = 6
Thousands Hundreds 8 tens (2 * 6) + (7 * 3) = 12 + 21 = 33
Thousands * ones (1 x 4) + (2 * 1) = 6
Hundreds Hundreds * ones (2 * 4) + (2 * 3) = 8 + 6 = 14
Tens * tens 7 * 6 = 42
Tens Tens * ones (7 * 4) + (2 * 6) = 28 + 12 = 40
Ones Ones * ones 2 * 4 = 8

Multiply the terms:

  • Millions: 1 * 1,000,000 = 1,000,000
  • Hundreds of thousands: 5 * 100,000 = 500,000
  • Tens of thousands: (13 + 6) * 10,000 = 190,000
  • Thousands: (33 + 6) * 1,000 = 39,000
  • Hundreds: (14 + 42) * 100 = 5,600
  • Tens: 40 * 10 = 400
  • Ones: 8 * 1 = 8

Now, we add the terms:

1,000,000 + 500,000 + 190,000 + 39,000 + 5,600 + 400 + 8 = 1,735,008

We have multiplied our first 4-digit number!

Multiplying 4-Digit Numbers Quickly

Now that you have a good basis for how multiplication works, let's learn a popular trick that requires less writing.

1. Write down both 4-digit numbers above each other

2. Multiply the first number by each digit of the second

3. Carry any numbers larger than 9, and finally

4. Add the results

multiplication example four digits

To unlock this lesson you must be a Study.com Member.
Create your account

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use Study.com

Become a Study.com member and start learning now.
Become a Member  Back
What teachers are saying about Study.com
Try it risk-free for 30 days

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it risk-free for 30 days!
Create an account
Support