# Multiplying 2-Digit Number by 1-Digit Number

Here we will learn multiplying 2-digit number by 1-digit number. In two different ways we will learn to multiply a two-digit number by a one-digit number.

Examples of multiplying 2-digit number by 1-digit number without Regrouping:

We will have a quick review of multiplication of 2-digit number by 1-digit number without regrouping:

1. Multiply 24 by 2.

 T     O               2     4            ×        2               4     8 First multiply the ones by 2.4 × 2 = 8.Write 8 under O.Now multiply the tens by 2.3 × 3 = 9.Write 9 under T.

2. Multiply 34 and 2

Solution:

 Step I: Arrange the numbers vertically.Step II: First multiply the digit at the ones place by 2.2 × 4 = 8 onesStep III: Now multiply the digit at the tens place by 2. 2 × 3 = 6 tens Thus, 34 × 2 = 68

3. Multiply 20 by 3 by using expanded form

Solution:

20         →                           2 tens + 0 ones

×    3         →                                       ×      3

6 tens + 0 ones

= 60 + 0

= 60

Therefore, 20 × 3 = 60

4. Multiply 50 by 1 by using short form

Solution:

50                      →                50

×    1                      →             ×   1

0                                           50

(i) First digit of one’s place is multiplied by 1, i.e., 0 × 1 = 0

(ii) Then digit at ten’s place is multiplied by 1, i.e., 5 tens × 1 = 5 tens

Hence, 50 × 1 = 50

Observe the following Example using Three Different Methods:

5. Multiply 13 by 2.

Solution:

13 x 2 = 13 + 13 = 26

Therefore, 13 x 2 = 26.

Second Method: Using Expanded Form

Consider 13 as 10 + 3.

13 × 2 = (10 + 3) × 2

= 10 × 2 + 3 × 2

= 20 + 6

= 26.

Third Method: Short Form

Write the numbers according to place value shown on the right.

Step I:

Multiply the ones:

3 ones × 2 = 6 ones

Write 6 under ones column.

Step II:

Multiply the tens:

1 ten × 2 = 2 tens

Write 2 under tens column.

Thus, the product of 13 and 2 is 26.

Examples of multiplying 2-digit number by 1-digit number with Regrouping:

1. Multiply 66 by 3

 T     O               1               6     6            ×        3        1     4     8 First multiply the ones by 3.6 × 3 = 18 = one ten + 8 onesWrite 8 under O. carry 1 tenNow multiply the tens by 3.6 × 3 = 18Add 1 to the product.18 + 1 = 19

2. Multiply 25 by 3

 Step I: Arrange the numbers vertically.Step II: First multiply the digit at the ones place by 3.3 × 5 = 15 = 1 ten + 5 onesWrite 5 in the ones column and carry over 1 to the tens columnStep III: Now multiply the digit at the tens place by 3.3 × 2 = 6 tens Now, 6 + 1 (carry over) = 7 tens Thus, 25 × 3 = 75

3. Multiply 46 by 4

 Step I: Arrange the numbers vertically.Step II: Multiply the digit at the ones place by 4.6 × 4 = 24 = 2 tens + 4 onesWrite 4 in the ones column and carry over 2 to the tens columnStep III: Now multiply the digit at the tens place by 4.4 × 4 = 16 tensNow, 16 + 2 (carry over) = 18 tens = 1 hundred + 8 tens Write 8 at the tens place and 1 at the hundred place. Thus, 46 × 4 = 184

4. Multiply 20 by 3 by using expanded form

Solution:

20         →                           2 tens + 0 ones

×    3         →                                       ×      3

6 tens + 0 ones

= 60 + 0

= 60

Therefore, 20 × 3 = 60

5. Multiply 26 by 7 by using expanded form

Solution:

26          →       20 + 6          →           2 tens + 6 ones

×      7          →         ×   7           →                          ×     7

(2 × 7) tens + (6 × 7) ones

2 tens + 6 ones

×                  7 ones

14 tens + 42 ones

= 14 tens + (40 + 2) ones

= 14 tens + 4 tens + 2 ones

= 18 tens + 2 ones

= 180 + 2

= 182

Therefore, 26 × 7 = 182

6. Multiply 48 by 6 by using short form

Solution:

48

×         6

24 ← 48

= 28 tens 8 ones

= 288

Hence, 48 × 6 = 288

(i) 48 × 6 is written in column from.

(ii) 8 ones are multiplied by 6, i.e., 6 × 8 = 48 ones = 4 tens + 8 ones

8 is written is one’s column and 4 tens is gained.

(iii) Gained 4 is carried to the ten’s column.

(iv) Now 4 tens is multiplied by 6, i.e., 4 tens × 6 = 24 tens

(v) Carried 4 tens is added to 24 tens, i.e., 4 tens + 24 tens = 28 tens

7. Find the product of 58 × 5.

Solution:

58

×   5

25 ← 40

= 25 + 4 ← 0

= 29          0

= 290

(i) 8 ones × 5 = 40 = 4 tens + 0 one

(ii) 5 tens × 5 = 25 tens

(iii) 25 tens + 4 tens = 29 tens

Hence, 58 × 5 = 290

8. Multiply 37 by 8

Solution:

3  7

×          8

5   6

+   2   4   0

2   9    6

(i) 7 ones × 8 = 56 ones = 5 tens 6 ones

56 is placed in such way that 5 comes under tens and 6 under ones

(ii) 3 tens × 8 = 24 tens = 240 ones

= 2 hundreds, 4 tens and 0 ones

240 is placed below 56 in such way that 2 comes under hundreds, 4 under tens and 0 under ones.

Hence, 37 × 8 = 296

Questions and Answers on Multiplying 2-Digit Number by 1-Digit Number:

Multiplication of 2-Digit Number by 1-Digit Number Without Regrouping:

I. Find the product:

(i) 23 × 3 =

(ii) 44 × 2 =

(iii) 33 × 2 =

(iv) 22 × 4 =

(v) 32 × 3 =

(vi) 40 × 2 =

(vii) 43 × 2 =

(viii)  12 × 3 =

(ix) 23 × 2 =

(x) 11 × 9 =

(xi) 21 × 4 =

(xii) 13 × 3 =

I. (i) 69

(ii) 88

(iii) 66

(iv) 44

(v) 96

(vi) 80

(vii) 86

(viii) 36

(ix) 46

(x) 99

(xi) 84

(xii) 39

Multiplication of 2-Digit Number by 1-Digit Number With Regrouping:

II. Find the product:

(i) 46 × 2

(ii) 19 × 4

(iii) 27 × 3

(iv) 18 × 5

II. (i) 92

(ii) 76

(iii) 81

(iv) 90

III. Multiply the following:

(i) 78 × 4

(ii)  63 × 6

(iii) 51 × 6

(iv) 39 × 8

(v) 72 × 9

(vi) 45 × 7

(vii) 17 × 4

(viii) 88 × 8

III. (i) 312

(ii)  398

(iii) 306

(iv) 312

(v) 648

(vi) 315

(vii) 68

(viii) 704

IV. Solve the following:

(i) 37 × 6

(ii) 72 × 4

(iii) 56 × 7

(iv) 84 × 2

(v) 45 × 9

IV. (i) 37 × 6

(ii) 72 × 4

(iii) 56 × 7

(iv) 84 × 2

(v) 45 × 9

V. Multiply the following :

 (i)                    T     O                    3     1                    ×    2                  _______ (ii)                    T     O                    4     7                    ×    1                  _______
 (iii)                    T     O                    1     1                    ×    3                  _______ (iv)                    T     O                    2     2                    ×    2                  _______
 (v)                    T     O                    2     3                    ×    2                  _______ (vi)                    T     O                    2     6                    ×    3                  _______
 (vii)                    T     O                    4     9                    ×    2                  _______ (viii)                    T     O                    2     3                    ×    4                  _______
 (ix)                    T     O                    1     6                    ×    6                  _______ (x)                    T     O                    1     9                    ×    5                  _______
 (xi)                    T     O                    5     2                    ×    5                  _______ (xii)                    T     O                    2     3                    ×    6                  _______
 (xiii)                    T     O                    6     4                    ×    9                  _______ (xiv)                    T     O                    3     2                    ×    7                  _______
 (xv)                    T     O                    7     5                    ×    8                  _______

III. (i) 62

(ii) 47

(iii) 33

(iv) 44

(v) 46

(vi) 78

(vii) 98

(viii) 92

(ix) 96

(x) 95

(xi) 260

(xii) 138

(xiii) 576

(xiv) 224

(xv) 600

VI. Multiply the following:

(i) 21 × 5 = _____

(ii) 34 × 2 = _____

(iii) 23 × 3 = _____

(iv) 27 × 3 = _____

(v) 38 × 2 = _____

(vi) 18 × 4 = _____

(vii) 25 × 8 = _____

(viii) 32 × 6 = _____

(ix) 29 × 4 = _____

(x) 45 × 5 = _____

VI. (i) 105

(ii) 68

(iii) 69

(iv) 81

(v) 76

(vi) 72

(vii) 200

(viii) 192

(ix) 116

(x) 225

V. Word Problem on Multiplying 2-Digit Number by 1-Digit Number:

(i) A month has 30 days. How many days be there in 3 such months?

V. (i) 90 days

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