Multiplication is one of the important topics that every student has to learn. It is one of the arithmetic operations. Students have to learn to multiply a number by 1 digit number, 2 digit number before learning this topic. Multiplication of a number by a 3 digit number means multiplicand will be a three-digit number irrespective of the multiplier. Find the detailed explanation of two simple methods to solve the multiplying a number by a 3 digit number in the further sections.

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## Multiplication of a Number by a 3-Digit Number

It means 3 digit number will the multiplicand and number is the multiplier. Get the simple tricks and techniques to find the product of a number by a 3-digit number in the below-mentioned sections.

**Method 1: Column Method**

- Write the multiplicand, multiplier in two different columns.
- At first, multiply the unit digit of the second number by the first number (the order of the digits is from left to the right)
- Write the product in the third column.
- Multiply the ten’s digit of the second number by the first number.
- Place x symbol at the unit’s place of the fourth column followed by the product of ten’s digit.
- Again, multiply the hundred’s digit of the bottom number by the top number.
- Place x symbols at the unit’s place, ten’s place of the fifth column and the product.
- Find the sum of the products to get the final result.

**Method 2: Expansion Method**

- Expand both numbers.
- Express the expansion in the place of original numbers.
- Use the distributive property for further expansion.
- Compute the product of each number and then add to get the product.

### Multiplying a Number by 3-Digit Number Examples

**Question 1:**

Solve 456 x 289 using the column method.

**Solution:**

Given that,

456 x 289

Multiply 9 by 456. 9 x 456 = 4104

Multiply 8 by 456. 8 x 456 = 3648

Multiply 2 by 456. 2 x 456 = 912

Place those products in the order mentioned above.

Add the products

4104 + 36480 + 91200 = 131784.

So, 456 x 289 = 131784.

**Question 2:**

Solve 85 x 426 using the expansion method.

**Solution:**

Given that,

85 x 426

Expand the numbers

85 = 80 + 5

426 = 400 + 20 + 6

85 x 426 = (80 + 5) x (400 + 20 + 6)

Using the distributive property

= 80 x (400 + 20 + 6) + 5 x (400 + 20 + 6)

= (80 x 400) + (80 x 20) + (80 x 6) + (5 x 400) + (5 x 20) + (5 x 6)

= 32000 + 1600 + 480 + 2000 + 100 + 35

= 36210

Therefore, 85 x 426 = 36210.

**Question 3:**

Compute 1254 x 125

**Solution:**

Given that,

1254 x 125

Multiply 5 by 1254. 5 x 1254 = 6270

Multiply 2 by 1254. 2 x 1254 = 2508

Multiply 1 by 1254. 1 x 1254 = 1254

Place those products in the order mentioned above.

Add the products

6270 + 25080 + 125400 = 156750

So, 1254 x 125 = 156750.

**Question 4:**

Find 7845 x 364

**Solution:**

Given that,

7845 x 364

364 = 300 + 60 + 4

7845 x 364 = 7845 x (300 + 60 + 4)

= 7845 x 300 + 7845 x 60 + 7845 x 4

= 2353500 + 470700 + 31380

= 2855580

Therefore, 7845 x 364 = 28,55,580

### FAQs on Multiplying by Three Digit Number

**1. How do you multiply 3 digit numbers quickly?**

We must use the column method to multiply the three-digit numbers quickly.

**2. Use the expansion method and multiply 67 by 153?**

67 x 153 = 67 x (100 + 50 + 3)

= 67 x 100 + 67 x 50 + 67 x 3

= 6700 + 3350 + 201

= 10251.

**3. Why a 3 digit multiplication has 3 columns products?**

Because in a three-digit multiplication the second number will be the 3 digit number. So, every 3 digit multiplication has 3 sub-products. By adding those sub-products, we get the final product.