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.

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

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:

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.

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

1. Multiply 66 by 3

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

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.

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 =

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 :

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

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?

Answer:

V. (i) 90 days

2nd Grade Math Practice

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