Multiply a Number by a
2-Digit Numbers
How to multiply a number by a 2-digit numbers?
We shall revise here to multiply 2-digit and 3-digit numbers by a
2-digit number (multiplier) as well as learn another procedure for the
multiplication of 3-digit, 4-digit, etc., numbers by a 2-digit
multiplier.
I. Example to multiply 2-digit numbers by a 2-digit numbers:
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
(b) 4 × 6 tens = 24 tens = 240 ones
(c) 1 ten × 3 ones = 3 tens = 30 ones
(d) 1 ten = 10 × 6 tens = 10 × 60 ones = 600 ones
|
(iii) Third Method
|
|
(a) 14 = (10 + 4)
(b) 63 × 4 = 252
(c) 63 × 10 = 630
|
(iv) Fourth Method
|
|
(a) 14 = 4 ones + 1 ten
(b) 63 × 4 ones = 252 ones
(c) 63 × 1 ten = 63 tens
(Generally the fourth method is adopted)
|
II. Example to multiply 3-digit numbers by a 2-digit numbers:
1. Multiply 456 x 43
Solution:
(i) First Method
|
|
(a) 43 = 3 + 40
(b) 456 × 3 = 1368
(c) 456 × 40 = 18240
|
Therefore, 456 × 43 = 19608
(ii) Second Method
|
|
(a) 43 = 3 ones + 4 tens
(b) 456 × 3 ones = 1368 ones
(c) 456 × 4 tens = 1824 tens
|
Hence, Product = 19608
2. Find the product of 165 and 45.
|
|
→ 40 + 5
Multiply by 5
Multiply by 40
Add the two products
|
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
|
III. Example to multiply 4-digit numbers by a 2-digit numbers:
1. Multiply 3157 x 56
Solution:
(i) First Method
|
|
(a) 56 = 6 + 50
(b) 3157 × 6 = 18942
(c) 3157 × 50 = 157850
|
(ii) Second Method
|
|
(a) 56 = 6 ones + 5 tens
(b) 3157 × 6 ones = 18942 ones
(c) 3157 × 5 tens = 15785 tens
|
Hence, Product = 176792
2. Multiply: 1793 × 25
|
|
→ 20 + 5
Multiply by 5
Multiply by 20
|
Answer: 44825
Questions and Answers on Multiply a Number by a 2-Digit Number:
1. Multiplication of 2-Digit Numbers by 2-Digit Numbers by column method.
(i) 12 × 11 = __________
(ii) 24 × 35 = __________
(iii) 42 × 81 = __________
(iv) 17 × 46 = __________
(v) 44 × 59 = __________
(vi) 73 × 94 = __________
Answers:
(i) 132
(ii) 840
(iii) 3402
(iv) 782
(v) 2596
(vi) 6862
2. Multiplication of 3-Digit Numbers by 2-Digit Numbers by column method.
(i) 139 × 21 = __________
(ii) 256 × 33 = __________
(iii) 507 × 62 = __________
(iv) 780 × 53 = __________
(v) 864 × 74 = __________
(vi) 972 × 80 = __________
Answers:
(i) 2919
(ii) 8448
(iii) 31434
(iv) 41340
(v) 63936
(vi) 77760
3. Multiplication of 4-Digit Numbers by 2-Digit Numbers by column method.
(i) 1457 × 25 = __________
(ii) 1183 × 46 = __________
(iii) 3107 × 77 = __________
(iv) 4662 × 11 = __________
(v) 9381 × 36 = __________
(vi) 6500 × 25 = __________
Answers:
(i) 36425
(ii) 54418
(iii) 239239
(iv) 51282
(v) 337716
(vi) 162500
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● Subtraction
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● Word
Problems Involving Addition and Subtraction
● Estimating
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