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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
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(a) 137 = 7 + 30 + 100 (b) 36 × 7 = 252 (c) 36 × 30= 1080 (d) 36 × 100 = 3600 |
(ii) Second Method
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(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
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(a) 278 = 8 + 70 + 200 (b) 543 × 8 = 4344 (c) 543 × 70 = 38010 (d) 543 × 200 = 108600 Product = 150954 |
(ii) Second Method
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(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:
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Multiply by 7 Multiply by 100 |
Answer: 88489
4. Multiply 474 × 240
Solution:
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→ 200 + 40 Multiply by 40 Multiply by 200 |
Answer: 113760
Multiplying by 3-Digit Number
5. Find the product of 528 and 378.
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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 |
 Hence, 528 × 378 = 199584 |
6. Multiply 345 by 224.
 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.
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Solution: 124 = 100 + 20 + 4 We multiply 625 by 4, 20 and 100 respectively. Finally, we add the results to get the required product. |
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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
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(a) 324 = 4 + 20 + 300 (b) 2437 × 4 = 9748 (c) 2437 × 20 = 48740 (d) 2437 × 300 = 731100 |
The product = 789588
(ii) Second Method
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(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.
 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.
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Solution: 402 = 400 + 0 + 2 We multiply 1519 by 2, 0 and 400 respectively. Finally, we add the results to get the required product. |
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The product is 6,10,638.
11. Find the product of 2129 and 426.
Solution:
426 = 400 + 20 + 6
We multiply 2129 by 6, 20 and 400 respectively.
Finally, we add the results to get the required product.
Therefore, 2129 × 426 = 9,06,954
4-Digit by 3-Digit Multiplication Video:
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:
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(i) |
H |
T |
O |
(ii) |
H |
T |
O |
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8 |
5 |
4 |
8 |
1 |
6 |
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× |
2 |
5 |
4 |
× |
6 |
3 |
4 |
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(iii) |
H |
T |
O |
(iv) |
H |
T |
O |
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3 |
5 |
1 |
6 |
2 |
1 |
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× |
2 |
5 |
3 |
× |
1 |
3 |
6 |
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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:
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(i) |
Th |
H |
T |
O |
(ii) |
Th |
H |
T |
O |
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5 |
2 |
5 |
6 |
4 |
0 |
2 |
6 |
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× |
2 |
6 |
7 |
× |
2 |
4 |
5 |
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(iii) |
Th |
H |
T |
O |
(iv) |
Th |
H |
T |
O |
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2 |
3 |
6 |
8 |
6 |
3 |
2 |
8 |
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× |
3 |
9 |
1 |
× |
1 |
5 |
4 |
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(v) |
Th |
H |
T |
O |
(vi) |
Th |
H |
T |
O |
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3 |
8 |
8 |
4 |
1 |
9 |
2 |
4 |
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× |
2 |
4 |
3 |
× |
3 |
3 |
0 |
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(vii) |
Th |
H |
T |
O |
(viii) |
Th |
H |
T |
O |
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2 |
0 |
1 |
8 |
5 |
3 |
4 |
2 |
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× |
1 |
6 |
4 |
× |
1 |
0 |
3 |
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Answer:
7. (i) 1403352
(ii) 986370
(iii) 925888
(iv) 974512
(v) 943812
(vi) 634920
(vii) 330952
(viii) 550226
Related Concept
● Addition
● Check
for Subtraction and Addition
● Word
Problems Involving Addition and Subtraction
● Estimating
Sums and Differences
● Multiply
a Number by a 2-Digit Number
● Multiplication
of a Number by a 3-Digit Number
● Word
Problems on Multiplication
● 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
● Division
by Two-Digit Numbers
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