Multiplication of a Number
by a 3Digit Number
We know to multiply two digit numbers by twodigit numbers, and threedigit numbers by onedigit or twodigit numbers.
Now, we will learn the multiplication by threedigit numbers.
In multiplication of a number by a 3digit number are explained here step by step.
Consider the following examples on multiplication of a number by a 3digit number:
I. Examples to multiply 2digit numbers by a 3digit 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 3digit numbers by a 3digit 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

Answer: 88489
(ii) 474 × 240

→ 200 + 40
Multiply by 40
Multiply by 200

Answer: 113760
Multiplying by 3Digit 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

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 4digit numbers by a 3digit 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 2digit, 3digit and 4digit number by a 3digit 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 3Digit Number:
1. Multiply the given 3digit numbers by a 3digit 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 4digit numbers by a 3digit 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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Related Concept
● Addition
● Word
Problems on Addition
● 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 2Digit Number
● Multiplication
of a Number by a 3Digit Number
● Multiply a Number
● Estimating Products
● Word
Problems on Multiplication
● Multiplication
and Division
● Terms Used in
Division
● Division
of TwoDigit by a OneDigit Numbers
● Division
of FourDigit by a OneDigit Numbers
● Division
by 10 and 100 and 1000
● Dividing Numbers
● Estimating
the Quotient
● Division
by TwoDigit Numbers
● Word
Problems on Division
4th Grade Math Activities
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