Multiplication of a Number
by a 3-Digit Number

We know to multiply two digit numbers by two-digit numbers, and three-digit numbers by one-digit or two-digit numbers.

Now, we will learn the multiplication by three-digit numbers.

In multiplication of a number by a 3-digit number are explained here step by step.

Consider the following examples on multiplication of a number by a 3-digit number:

I. Examples to multiply 2-digit numbers by a 3-digit numbers:

1. Find the product of 36 × 137

Solution:

(i)

multiplication by a 3-digit numbers

(a) 137 = 7 + 30 + 100

(b) 36 × 7 = 252

(c) 36 × 30= 1080

(d) 36 × 100 = 3600

(ii)

multiplication by a 3-digit numbers

(a) 137 = 7 ones + 3 tens + 1 hundred

(b) 36 × 7 ones = 252 ones

(c) 36 × 8 tens = 108 tens

(d) 36 × 1 hundred = 36 hundreds


II. Examples to multiply 3-digit numbers by a 3-digit numbers:

2. Multiply 543 by 278

Solution:

(i)

multiplication by a 3-digit numbers

(a) 278 = 8 + 70 + 200

(b) 543 × 8 = 4344

(c) 543 × 70 = 38010

(d) 543 × 200 = 108600

Product = 150954


(ii)

multiplication by a 3-digit numbers

(a) 278 = 8 ones + 7 T + 2 H

(b) 543 × 8 ones = 4344 ones

(c) 543 × 7 T = 3801 tens

(d) 543 × 2 H = 1086 hundreds

Product = 150954


3. Multiply 827 × 107

Solution:

(i)

multiplication by a 3-digit number


→ 100 + 7

Multiply by 7

Multiply by 100


Answer: 88489


(ii) 474 × 240

multiplication by a 3-digit numbers


→ 200 + 40

Multiply by 40

Multiply by 200


Answer: 113760


Multiplying by 3-Digit Number

4. Find the product of 528 and 378.

Step I: Arrange the numbers vertically.

Step II: Multiply 528 by 8

             528 × 8 = 4224

Step III: Multiply 528 by 70

               528 × 70 = 36960

Step IV: Multiply 528 by 300

              528 × 300 = 158400

Step V: Add: 4224, 36960 and 158400

            4224 + 36960 + 158400 = 199584

Multiplying by 3-Digit Number

Hence, 528 × 378 = 199584


5. Multiply 345 by 224.

Multiply 3-Digit by 3-Digit

The product is 77,280.

Step I: Multiply 345 by 4 ones.

345 × 4 = 1380 ones

             = 1380

Step II: Multiply 345 by 2 tens.

345 × 2 = 690 tens

             = 6900

Step III: Multiply 345 by 2 hundreds.

345 × 2 = 690 hundreds

            = 69000

Step IV: Add the products.


III. Example to multiply 4-digit numbers by a 3-digit numbers:


6. Multiply 2437 by 324

Solution:

(i) First Method

multiplication by a 3-digit numbers

(a) 324 = 4 + 20 + 300

(b) 2437 × 4 = 9748

(c) 2437 × 20 = 48740

(d) 2437 × 300 = 731100

The product = 789588


(ii) Second Method

multiplication by a 3-digit numbers

(a) 324 = 4 ones + 2 tens + 3 hundreds

(b) 2437 × 4 ones = 9748 ones

(c) 2437 × 2 T = 4874 tens

(d) 2437 × 3 H = 7311 hundreds

The product = 789588

These are the examples discussed on multiplication of a 2-digit, 3-digit and 4-digit number by a 3-digit number.


7. Multiply 2345 by 142.

Multiply 4-Digit by a 3-Digit Numbers

The product is 3,32,990.

Step I: Multiply 2345 by 2 ones.

2345 × 2 = 4690 ones

               = 4690

Step II: Multiply 2345 by 4 tens.

2345 × 4 = 9380 tens

              = 93800

Step III: Multiply 2345 by 1 hundred.

2345 × 1 = 2345 hundreds

              = 234500

Step IV: Add the products.



Questions and Answers on Multiplication of a Number by a 3-Digit Number:

1. Multiply the given 3-digit numbers by a 3-digit numbers by column method.

(i) 137 × 112 = __________

(ii) 258 × 135 = __________

(iii) 429 × 283 = __________

(iv) 647 × 465 = __________

(v) 874 × 509 = __________

(vi) 173 × 194 = __________


Answers:

(i) 15344

(ii) 34830

(iii) 121407

(iv) 300855

(v) 444866

(vi) 33562



2. Multiply the given 4-digit numbers by a 3-digit numbers by column method.

(i) 1392 × 271 = __________

(ii) 2058 × 380 = __________

(iii) 5483 × 126 = __________

(iv) 4021 × 108 = __________

(v) 3281 × 288 = __________

(vi) 3016 × 160 = __________


Answers:

(i) 377232

(ii) 782040

(iii) 690858

(iv) 434268

(v) 944928

(vi) 482560


3. Multiply the following.

(i) 5424 × 8

(ii) 58549 × 128

(iii) 456 × 729

(iv) 639 × 199

(v) 5024 × 632

(vi) 76592 × 8


Answer:

3. (i) 43392

(ii) 7494272

(iii) 332424

(iv) 127161

(v) 3175168

(vi) 612736

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