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) First Method

multiplication by a 3-digit numbers

(a) 137 = 7 + 30 + 100

(b) 36 × 7 = 252

(c) 36 × 30= 1080

(d) 36 × 100 = 3600


(ii) Second Method

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) First Method

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) Second Method

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:

multiplication by a 3-digit number


→ 100 + 7

Multiply by 7

Multiply by 100


Answer: 88489


4. Multiply 474 × 240

Solution:

multiplication by a 3-digit numbers


→ 200 + 40

Multiply by 40

Multiply by 200


Answer: 113760


Multiplying by 3-Digit Number

5. 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


6. 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.


7. Multiply 625 by 124.

Solution:

124 = 100 + 20 + 4

We multiply 625 by 4, 20 and 100 respectively.

Finally, we add the results to get the required product.

3-Digit by 3-Digit Multiplication

Therefore, the product of 625 and 124 = 77,500.


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


8. 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.


9. 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.


10. Multiply 1519 and 402.

Solution:

402 = 400 + 0 + 2

We multiply 1519 by 2, 0 and 400 respectively.

Finally, we add the results to get the required product.

4-Digit by 3-Digit Multiplication

The product is 6,10,638.


11. Find the product of 2129 and 426.

426 = 400 + 20 + 6

We multiply 2129 by 6, 20 and 400 respectively.

Finally, we add the results to get the required product.

Multiply by 3-Digit Numbers

Therefore, 2129 × 426 = 9,06,954


Worksheet 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 3-digit by 3-digit numbers:

(i) 354 by 435

(ii) 508 by 434

(iii) 458 by 392

(iv) 601 by 124


Answer:

2. (i) 153990

(ii) 220472

(iii) 179536

(iv) 74524


3. Find the following products:

(i)

H

T

O

(ii)

H

T

O

8

5

4

8

1

6

×

2

5

4

×

6

3

4



 

 

  

  

  

  

 

  



(iii)

H

T

O

(iv)

H

T

O

3

5

1

6

2

1

×

2

5

3

×

1

3

6



 

 

  

  

  

  

 

  



Answer:

3. (i) 216916

(ii) 517344

(iii) 88803

(iv) 84456


4. 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:

4. (i) 377232

(ii) 782040

(iii) 690858

(iv) 434268

(v) 944928

(vi) 482560


5. Multiply the following.

(i) 5424 × 8

(ii) 58549 × 128

(iii) 456 × 729

(iv) 639 × 199

(v) 5024 × 632

(vi) 76592 × 8


Answer:

5. (i) 43392

(ii) 7494272

(iii) 332424

(iv) 127161

(v) 3175168

(vi) 612736


6. Multiply 4-digit by 3-digit numbers:

(v) 4,032 by 196

(vi) 5,012 by 132

(vii) 5,647 by 243

(viii) 3,012 by 213


Answer:

6. (v) 790272

(vi) 661584

(vii) 1372221

(viii) 641556


7. Find the following products:

(i)

Th

H

T

O

(ii)

Th

H

T

O

5

2

5

6

4

0

2

6

×

2

6

7

×

2

4

5



 

 

  

  

  

  

 

  



(iii)

Th

H

T

O

(iv)

Th

H

T

O

2

3

6

8

6

3

2

8

×

3

9

1

×

1

5

4



 

 

  

  

  

  

 

  



(v)

Th

H

T

O

(vi)

Th

H

T

O

3

8

8

4

1

9

2

4

×

2

4

3

×

3

3

0



(vii)

Th

H

T

O

(viii)

Th

H

T

O

2

0

1

8

5

3

4

2

×

1

6

4

×

1

0

3

 

 

  

  

  

  

 

  



Answer:

7. (i) 1403352

(ii) 986370

(iii) 925888

(iv) 974512

(v) 943812

(vi) 634920

(vii) 330952

(viii) 550226

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Subtraction

Check for Subtraction and Addition

Word Problems Involving Addition and Subtraction

Estimating Sums and Differences

Find the Missing Digits

Multiplication

Multiply a Number by a 2-Digit Number

Multiplication of a Number by a 3-Digit Number

Multiply a Number

Estimating Products

Word Problems on Multiplication

Multiplication and Division

Terms Used in Division

Division of Two-Digit by a One-Digit Numbers

Division of Four-Digit by a One-Digit Numbers

Division by 10 and 100 and 1000

Dividing Numbers

Estimating the Quotient

Division by Two-Digit Numbers

Word Problems on Division





4th Grade Math Activities

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