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.


I: 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.

× 2 = 8.

Write 8 under O.

Now multiply the tens by 2.

2 × 2 = 4.

Write 4 under T.

Thus, 24 × 2 = 48


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 ones

Step III: Now multiply the digit at the tens place by 2.

2 × 3 = 6 tens

Multiplying 2-Digit Number by 1-Digit Number

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


5. Multiply 34 by 2.

We can multiply a given 2-digit number by a 1-digit number by vertical method.

Multiply the Digit in the Ones Place

Step I: Arrange the numbers in correct place.

Multiply the digit in the ones place by 2.

4 × 2 = 4 × 2 = 8 or 8 ones

Write 8 in the ones column.


Multiply the Digit in the Tens Place

Step II: Multiply the digit in the tens place by 2.

3 tens × 2 = 30 × 2 = 60 or 6 tens.

Write 6 in tens column.


So, 34 × 2 = 68


MULTIPLICATION OF A 2-DIGIT NUMBER BY A 1-DIGIT NUMBER WITHOUT REGROUPING:

6. Let us multiply 24 by 2.

Write the numbers one below the other as shown.

Multiply 2-Digit by 1-Digit

Step I: Multiply the ones digit by 2.

4 ones × 2 = 8 ones

Write 8 in the ones place.


Step II: Multiply the tens digit by 2. 

2 tens × 2 = 4 tens

Write 4 in the tens place.


The product is 48.


Observe the following Example using Three Different Methods:

7. Multiply 13 by 2.

Solution:

First Method: Using Repeated Addition.

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.


II: 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.

× 3 = 18 = one ten + 8 ones

Write 8 under O. carry 1 ten

Now multiply the tens by 3.

6 × 3 = 18

Add 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 ones

Write 5 in the ones column and carry over 1 to the tens column

Step III: Now multiply the digit at the tens place by 3.

3 × 2 = 6 tens

Now, 6 + 1 (carry over) = 7 tens

Multiplying 2-Digit Number by 1-Digit Number with Regrouping

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 ones

Write 4 in the ones column and carry over 2 to the tens column

Step III: Now multiply the digit at the tens place by 4.

4 × 4 = 16 tens

Now, 16 + 2 (carry over) = 18 tens = 1 hundred + 8 tens

Write 8 at the tens place and 1 at the hundred place.

Multiply 2-Digit Number by 1-Digit Number with Regrouping

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


Multiplication with Regrouping Once:

9. Let us multiply 27 by 3.

Write the numbers one below the other as shown.

Multiplication 2-Digit by 1-Digit Number with Regrouping Once

Step I: Multiply the ones digit by 3.

7 ones × 3 = 21 ones

Regroup: 21 ones = 2 tens and 1 one

Write 1 in the ones place.

Carry over 2 tens and write it under T.


Step II: Multiply the tens digit by 3.

2 tens × 3 = 6 tens

Add 6 tens and tens (carried over)

= 6 tens + 2 tens (carried over)

= 8 tens

Write 8 in the tens place.

The product is 81.


Multiplication with Regrouping Twice:

10. Let us multiply 53 by 4.

Write the numbers one below the other as shown.

Multiplication 2-Digit by 1-Digit with Regrouping Twice

Step I: Multiply the ones digit by 4.

3 ones × 4 = 12 ones

Regroup: 12 ones = 1 tens and 2 ones

Write 2 in the ones place.

Carry over 1 ten and write it under T.


Step II: Multiply the tens digit by 4.

5 tens × 4 = 20 tens

Add 20 tens and ten (carried over)

= 20 tens + 1 ten = 21 tens

Regroup: 21 tens = 2 hundreds and 1 ten

Write 1 in the tens place.

Carry over 2 hundreds and write it under H.


Step III: Write 2 in the hundreds place.


The product is 212.


Word Problems on Multiplying a 2-digit Number by a 1-digit Number:

11. Robert can paint 45 pictures in a month. How many pictures can he paint in 3 months?

Multiply the digit in the ones place by 3

Step I: Multiply the digit in the ones place by 3. If the result is a 2-digit number, keep the ones and carry over the tens.

5 × 3 = 15

Keep 5 in the ones column and carry over 1 to the tens column.

Multiply the digit in the tens place by 3

Step II: Multiply the digit in the tens place by 3. Add the carried over number to the result. If it is a 2-digit number, keep the ones and carry over the tens to the hundreds column.

4 × 3 = 12

12 + 1 = 13

Keep 3 at the tens place and carry over 1 to the hundreds column.

Write the carried over digit


Step III: Write the carried over digit in the hundreds column.



Thus, Robert can paint 135 pictures in 3 months.


Worksheet 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 =


Answer:

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


Answer:

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


Answer:

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


Answer:

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 

                 _______

Answer:

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 = _____


Answer:

VI. (i) 105

(ii) 68

(iii) 69

(iv) 81

(v) 76

(vi) 72

(vii) 200

(viii) 192

(ix) 116

(x) 225


VII. Find the following products in your notebook.

(i)

                    T     O

                    2     9

                    ×    7 

                 _______

(ii)

                    T     O

                    6     3

                    ×    4 

                 _______

(iii)

                    T     O

                    3     8

                    ×    7 

                 _______

(iv)

                    T     O

                    6     6

                    ×    4 

                 _______

(v)

                    T     O

                    5     4

                    ×    7 

                 _______

(vi)

                    T     O

                    3     5

                    ×    4 

                 _______

(vii)

                    T     O

                    6     9

                    ×    8 

                 _______

(viii)

                    T     O

                    8     5

                    ×    4 

                 _______

(ix)

                    T     O

                    8     0

                    ×    4 

                 _______

(x)

                    T     O

                    5     8

                    ×    8 

                 _______

(xi)

                    T     O

                    5     1

                    ×    7 

                 _______

(xii)

                    T     O

                    6     3

                    ×    8 

                 _______


Answer:

VIII. (i) 203

(ii) 252

(iii) 266

(iv) 264

(v) 378

(vi) 140

(vii) 552

(viii) 340

(ix) 320

(x) 464

(xi) 357

(xii) 504



VIII. Find the products:

(i) 27 × 4 = __________

(ii) 5 × 10 = __________

(iii) 25 × 9 = __________

(iv) 16 × 4 = __________

(v) 14 × 8 = __________ 

(vi) 37 × 7 = __________

(vii) 63 × 4 = __________

(viii) 2 × 70 = __________

(ix) 53 × 5 = __________


Answer:

VIII. (i) 108

(ii) 50

(iii) 225

(iv) 64

(v) 112

(vi) 259

(vii) 252

(viii) 140

(ix) 265


IX. 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?

Answer:

IX. (i) 90 days

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