# 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) (a) 137 = 7 + 30 + 100 (b) 36 × 7 = 252 (c) 36 × 30= 1080 (d) 36 × 100 = 3600

(ii) (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) (a) 278 = 8 + 70 + 200 (b) 543 × 8 = 4344 (c) 543 × 70 = 38010 (d) 543 × 200 = 108600 Product = 150954

(ii) (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) → 100 + 7 Multiply by 7 Multiply by 100

(ii) 474 × 240 → 200 + 40 Multiply by 40 Multiply by 200

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 = 4224Step III: Multiply 528 by 70               528 × 70 = 36960Step IV: Multiply 528 by 300              528 × 300 = 158400Step V: Add: 4224, 36960 and 158400            4224 + 36960 + 158400 = 199584 Hence, 528 × 378 = 199584

5. 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.

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

6. Multiply 2437 by 324

Solution:

(i) First Method (a) 324 = 4 + 20 + 300 (b) 2437 × 4 = 9748 (c) 2437 × 20 = 48740 (d) 2437 × 300 = 731100

The product = 789588

(ii) Second Method (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.

 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 = __________

(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 = __________

(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

3. (i) 43392

(ii) 7494272

(iii) 332424

(iv) 127161

(v) 3175168

(vi) 612736

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