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# 3 Digit by 1 Digit Multiplication

In mathematics, multiplication is one of the important and basic arithmetic operations in number representation. Number has a complete unit or entity but has a no fractional part. For a three digit number, the right most digit is the units place, the number at the center is the tens place and the number at the left most is the hundreds place.
The notation a * b, means that "a is multiplied by b"

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## Multiplication 3 Digit by 1 Digit

There are 2 method for multiplying 3 digit by 1 digit number:

Method 1:

3 digit number is written in expanded form. Then the 1 digit number is multiplied to each number.

For example: Multiply 456 by 7.

Expanded form: 456 = 400 + 50 + 6

• We multiply 7 with 6.

7 x 6 = 42

• Next multiply 7 with 50.

7 x 50 = 7 x 5 and a zero added to the right. = 350

• Next we multiply 7 with 400. This is multiply 7 and 4 and place two zeros in the right of the product. 7 x 400 = 2800

456 x 7 = (400 + 50 + 6) x 7 =

400 x 7 = 2800

50 x 7 = 350

6 x 7 = 42 Now we need to add these and so we get, + 3192

Method 2:

Steps:
Step 1:
Multiplication starts always at the right most place i.e the unit’s digit.
Step 2: We multiply the unit’s digit with the 1 digit number.
Step 3: If the product is a 1 digit number we place it below them.
Step 4: If the product is a two digit number, we place the units place below and the tens digit is carried over.
Step 5: Repeat step 1 with the tens digit and add the carrier over if any.
Step 6: This procedure is repeated with the digit in hundreds place also.

Multiply 945 by 3

945

X 3

The unit’s digit of 945 is 5.

3 x 5 is 15. We place the 5 as the units place below the 3 and carry the 1.

945

X 3

5 Carry over 1

The ten’s digit of 945 is 4. 4 x 3 = 12. Carry over is 1. 12 +1 = 13. We place 3 next to 5 on the left.

945

X 3

35 Carry over 1

The hundred’s digit of 945 is 9. 3 x 9 =27. Carry over is 1. 27 +1 = 28. We place 28 to the left of 25.

945

X 3

2835

The product of 945 with 3 is 2835

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