Are you confused about the Expansion method of multiplication? This page gives you clear information about the expansion method of multiplication. This will include the Definition of the Expansion method, Steps to follow for the expansion method of multiplication. You can also find examples on the Expansion Method of Multiplication of a 2 digit number by 1 digit number, Expansion method of multiplication of a three-digit number by 1 digit number, Expansion method of multiplication of a three-digit number by 2 digit number.

In the Expansion Method of Multiplication, you will give each digit a value based on its place value within the number. For Example Expanded form of 654=600+50+4.

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## Expanded Method Multiplication Steps | How to Multiply using Expansion?

The steps to be followed for the Expansion Method of Multiplication are as follows

- Write the problem in expanded form.
- Multiply the digits in the one’s column by the bottom digit and write your answer.
- Multiply the bottom digit by tens column on top and write the answer.
- Add the Products.

Here we will solve some examples of multiplication of 2 digit numbers and 3 digit numbers by 1 digit numbers.

**Example 1:**

Multiply 62, 5?

**Solution:**

1. Write the expanded form of a number and then multiply by 5.

(60+2)*5

2. Multiply 5 with 2 and 5 with 60 and then add the products.

60*5+2*5

=300+10

=310.

Multiplication of 62,5 is 310.

**Example 2:**

Multiply 125, 5?

**Solution:**

1. Write the expanded form of 125 and then multiply with 5

(100+20+5)*5

2. Multiply 5 with 100,20,5 and then add the products.

=100*5+20*5+5*5

=500+100+25

=625

Multiplication of 125,5 is 625.

Multiplying a combination of numbers by 1 digit number will result in several products being added together.

2 digit by 1 digit =2 products added together.

3 digit by 1 digit =3 products added together.

4 digit by 1 digit = 4 products added together.

**Example 3:**

Find the multiplication of 1254, 6?

**Solution:**

1.The expanded form of 1254 is 1000+200+50+4.

2.We can write this as follows:

1000 200 50 4

*6

——–——–——–——–

——–——–——–——–

3. Multiply 6 with 4,50,200,1000′ and then add the products.

1000*6+200*6+50*6+4*6

=6000+1200+300+24

=7524

Multiplication of 1254,6 is 7524.

### Multiplication of Three-Digit Number by a Two-Digit Number

Follow the steps for multiplication of a three-digit number by a two-digit number.

- Write the three-digit number and two-digit number in expanded form.
- Multiply the one’s digit on the bottom by one’s column.
- Multiply the one’s digit on the bottom by tens column.
- Multiply the one’s digit on the bottom by hundreds column.
- Multiply the tens digit on the bottom by one’s column.
- Multiply the tens digit on the bottom by the tens column.
- Multiply the tens digit on the bottom by the hundred’s column.
- Add the products.

### Examples of Multiplication of Three-Digit Number by Two-Digit Number

**Example 1:**

Find the Multiplication of 363 by 26

**Solution:**

1.Expansion form of 363 is 300+60+3

2.Expansion form of 26 is 20+6.

We can write this as follows:

300 60 3

*20 6

——–——–——–——–

——–——–——–——–

3. Multiply the one’s digit on the bottom by the one’s digit on top. i.e.6*3=18.

4. Multiply the one’s digit on the bottom by the tens digit on top. i.e.6*60=360.

5. Multiply the one’s digit on the bottom by the Hundred’s digit on top. i.e.6*300=1800.

6. Multiply the tens digit on the bottom by the ones digit on top. i.e.20*3=60.

7.Multiply the tens digit on the bottom by the tens digit on top. i.e.20*60=1200.

8. Multiply the tens digit on the bottom by the hundred’s digit on top. i.e. 20*300=6000.

9. Add the products. i.e.12+360+1800+60+1200+6000=9438.

Multiplication of 363,26 is 9,438.

Multiplying a combination of numbers by a 1 digit number will result in several products being added together

3 digit by 1 digit= 3 products added

3 digit by 2 digit= 6 products added

3 digit by 3 digit= 9 products added.