# Multiplying 4-Digit Numbers: Lesson for Kids

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• 0:04 Multiplication in Base 10
• 2:53 Multiplying 4-Digit…
• 4:37 Lesson Summary
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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

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