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. 4 × 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 |
 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.
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.
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.
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. 6 × 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 |
 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
Multiplication with Regrouping Once:
9. Let us multiply 27 by 3.
Write the numbers one below the other as shown.
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 2 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.
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 1 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?
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.
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.
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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