How to multiply a number by a 2digit numbers?
We shall revise here to multiply 2digit and 3digit numbers by a 2digit number (multiplier) as well as learn another procedure for the multiplication of 3digit, 4digit, etc., numbers by a 2digit multiplier.
I. Example to multiply 2digit numbers by a 2digit numbers:
1. Multiply 63 by 14
Solution:
(i) First Method
63 x 14
= (60 + 3) × (10 + 4) 63 = 60 + 3 14 = 10 + 4
= (60 + 3) × 10 + (60 + 3) × 4
= (600 + 30) + (240 + 12)
= 630 + 252
= 882
or, 63 × 14 = (60 + 3) (10 + 4)
= (60 + 3) x 4 + (60 + 3) x l0
= (240 +12) + (600 + 30)
= 252 + 630
= 882
(ii) Second Method
(a) 4 × 3 ones = 12 ones 
(iii) Third Method
(iv) Fourth Method
(a) 14 = 4 ones + 1 ten 
2. Multiply 42 by 27
Step I: Write 42 and 27 as shown.
4 
2  
× 
2 
7 



Step II: Multiply 42 by 7 and write the partial product as shown.
4 
2  
× 

7 
2 
9 
4 
Step III: Now, since 2 a at tens place we have to multiply 42 by 20.
Now, Multiply 42 by 20.
4 
2  
× 
2 
7 
2 
9 
4 
← 42 × 7 
8 
4 
0 
← 42 × 20 
Step IV: Add the two partial products.
4 
2  
× 
2 
7 
2 
9 
4  
+ 
8 
4 
0 
1 
1 
3 
4 
Hence, 42 × 27 = 1,134
The above procedure can be summarised as:
II. Example to multiply 3digit numbers by a 2digit numbers:
1. Multiply 456 x 43
Solution:
(i) First Method
(ii) Second Method
Hence, Product = 19608
2. Find the product of 165 and 45.
Answer: 7290
3. Multiply 687 and 23.
Solution:
Step I: Arrange the numbers vertically. Step II: Multiply 687 by 3 ones 687 × 3 = 2061 Step III: Multiply 687 by 2 tens 687 × 20 = 13740 Step IV: Add 2061 and 13740 2061 + 13740 = 15801 
Hence, 687 × 23 = 15801 
4. Multiply 624 and 22.
Solution:
We multiply 624 by 2 and 624 by 20 respectively.
Finally add the results to get the required product.
Therefore, 624 × 22 = 13,728
III. Example to multiply 4digit numbers by a 2digit numbers:
1. Multiply 3157 x 56
Solution:
(i) First Method
(ii) Second Method
Hence, Product = 176792
2. Multiply: 1793 × 25
Answer: 44,825
We can find the product of two numbers by lattice multiplication algorithm mathematics lab as follows:
Let us find 12413 × 37
Take a white chart paper and prepare a box.
Write 12413 on the top and 37 on the side as shown.
Multiply 3 by 3 and write the product 9 as 09 under the column headed by 3.
Similarly, multiply 1 by 3, 4 by 3, 2 by 3 and 1 by 3 and write the products under respective columns.
The multiply each of the digits 3, 1, 4, 2 and 1 by 7 and write the products under the respective columns.
Starting from the sower most row and the last column add.
The first sum is 1. Next 9 + 2 + 7 = 18
Carry 1 and so on.
Now the product is 0459281.
Hence, 12413 × 37459281 = 459281.
Worksheet on Multiply a Number by a 2Digit Number:
1. Multiplication of 2Digit Numbers by 2Digit Numbers by column method.
(i) 12 × 11 = __________
(ii) 24 × 35 = __________
(iii) 42 × 81 = __________
(iv) 17 × 46 = __________
(v) 44 × 59 = __________
(vi) 73 × 94 = __________
Answers:
1. (i) 132
(ii) 840
(iii) 3402
(iv) 782
(v) 2596
(vi) 6862
2. Multiply (2digit by 2digit) each of the following:
(i) 
6 7 × 1 3 _________ 
(ii) 
2 5 × 1 4 _________ 
Answer:
2. (i) 871
(ii) 350
3. Multiplication of 3Digit Numbers by 2Digit Numbers by column method.
(i) 139 × 21 = __________
(ii) 256 × 33 = __________
(iii) 507 × 62 = __________
(iv) 780 × 53 = __________
(v) 864 × 74 = __________
(vi) 972 × 80 = __________
Answers:
3. (i) 2919
(ii) 8448
(iii) 31434
(iv) 41340
(v) 63936
(vi) 77760
4. Multiply 3digit by 2digit number:
(i) 
4 2 3 × 2 7 _____________ 
(ii) 
2 8 9 × 3 3 _____________ 
(iii) 
4 6 4 × 2 3 _____________ 
(iv) 
8 5 0 × 2 2 _____________ 
(v) 
1 7 6 × 3 5 _____________ 
(vi) 
8 8 9 × 4 3 _____________ 
Answer:
4. (i) 11421
(ii) 9537
(iii) 10672
(iv) 18700
(v) 6160
(vi) 38227
5. Multiplication of 4Digit Numbers by 2Digit Numbers by column method.
(i) 1457 × 25 = __________
(ii) 1183 × 46 = __________
(iii) 3107 × 77 = __________
(iv) 4662 × 11 = __________
(v) 9381 × 36 = __________
(vi) 6500 × 25 = __________
Answers:
5. (i) 36425
(ii) 54418
(iii) 239239
(iv) 51282
(v) 337716
(vi) 162500
6. Multiply by 2digit numbers:
(i) 27 by 29
(ii) 28 by 49
(iii) 129 by 42
(iv) 205 by 63
(v) 625 by 73
(vi) 125 by 42
(vii) 405 by 14
(viii) 325 by 25
Answer:
6. (i) 783
(ii) 1372
(iii) 5418
(iv) 12915
(v) 45625
(vi) 5250
(vii) 5670
(viii) 8125
Related Concept
● Addition
● Check for Subtraction and Addition
● Word Problems Involving Addition and Subtraction
● Estimating Sums and Differences
● Multiply a Number by a 2Digit Number
● Multiplication of a Number by a 3Digit Number
● Word Problems on Multiplication
● Division of TwoDigit by a OneDigit Numbers
● Division of FourDigit by a OneDigit Numbers
● Division by 10 and 100 and 1000
● Division by TwoDigit Numbers
4th Grade Math Activities
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