Multiplying 2 -Digit By 2 -Digit Numbers
Multiplying 2 -Digit By 2 -Digit Numbers
Let’s go through the steps of multiplying two-digit numbers using the vertical method with detailed examples.
Example 1: Multiply 34 by 26
Step 1: Write the numbers vertically
Write the numbers one below the other, aligning the digits by place value.
34
× 26
Step 2: Multiply the bottom number’s ones digit by the top number
Start by multiplying the digit in the ones place of the bottom number (6) by each digit in the top number (34).
- Multiply 6 (ones place) by 4 (ones place of 34):
6×4=24
Write down 4 under the line, and carry over the 2 to the next column. - Multiply 6 by 3 (tens place of 34) and add the carried-over 2:
6×3=18
18+2=20
Write 20 under the line.
So the first partial product is 204.
34
× 26
------
204 (This is 34 × 6)
Step 3: Multiply the bottom number’s tens digit by the top number
Now multiply the tens digit of the bottom number (2) by each digit of the top number (34). Since we’re working with the tens place, we need to add a zero in the ones place before writing the result.
- Multiply 2 by 4 (ones place of 34):
2×4=8
Write 8 in the tens place, starting from the left. - Multiply 2 by 3 (tens place of 34):
2×3=6
Write 6 next to the 8.
So the second partial product is 680.
34
× 26
------
204 (34 × 6)
+ 6800 (34 × 20, shifted by one place to the left)
------
Step 4: Add the partial products
Finally, add the two partial products together.
204
+ 680
------
884
Final Answer
So, 34 multiplied by 26 equals 884.
Example 2: Multiply 53 by 47
Step 1: Write the numbers vertically
53
× 47
Step 2: Multiply the ones digit of the bottom number by the top number
- Multiply 7 by 3:
7×3=21
Write down 1, carry over 2. - Multiply 7 by 5, then add the carried-over 2:
7×5=35
35+2=37
Write down 37.
So the first partial product is 371.
53
× 47
------
371 (53 × 7)
Step 3: Multiply the tens digit of the bottom number by the top number
- Multiply 4 by 3:
4×3=12
Write 2 in the tens place, carry over 1. - Multiply 4 by 5, then add the carried-over 1:
4×5=20
20+1=21
Write down 21, starting from the left, and add a zero in the ones place.
So the second partial product is 2120.
53
× 47
------
371 (53 × 7)
+2120 (53 × 40, shifted one place left)
------
Step 4: Add the partial products
371
+ 2120
------
2491
Final Answer
So, 53 multiplied by 47 equals 2,491.
Example 3: Multiply 82 by 29
Step 1: Write the numbers vertically
82
× 29
Step 2: Multiply the ones digit of the bottom number by the top number
- Multiply 9 by 2:
9×2=18
Write down 8, carry over 1. - Multiply 9 by 8, then add the carried-over 1:
9×8=72
72+1=73
Write down 73.
So the first partial product is 738.
82
× 29
------
738 (82 × 9)
Step 3: Multiply the tens digit of the bottom number by the top number
- Multiply 2 by 2:
2×2=4
Write down 4. - Multiply 2 by 8:
2×8=16
Write down 16 starting from the left and add a zero in the ones place.
So the second partial product is 1640.
82
× 29
------
738 (82 × 9)
+1640 (82 × 20, shifted one place left)
------
Step 4: Add the partial products
738
+ 1640
------
2378
Final Answer
So, 82 multiplied by 29 equals 2,378.
Let’s tackle some more complex two-digit multiplication examples. These will involve slightly larger numbers but will follow the same vertical multiplication method.
Example 4: Multiply 96 by 78
Step 1: Write the numbers vertically
96
× 78
Step 2: Multiply the ones digit of the bottom number by the top number
- Multiply 8 by 6:
8×6=48
Write down 8, carry over 4. - Multiply 8 by 9, then add the carried-over 4:
8×9=72
72+4=76
Write down 76.
So the first partial product is 768.
96
× 78
------
768 (96 × 8)
Step 3: Multiply the tens digit of the bottom number by the top number
- Multiply 7 by 6:
7×6=42
Write down 2, carry over 4. - Multiply 7 by 9, then add the carried-over 4:
7×9=63
63+4=67
Write down 67, adding a zero in the ones place since this is the tens digit.
So the second partial product is 6720.
96
× 78
------
768 (96 × 8)
+6720 (96 × 70, shifted one place left)
------
Step 4: Add the partial products
768
+ 6720
------
7488
Final Answer
So, 96 multiplied by 78 equals 7,488.
Example 5: Multiply 84 by 93
Step 1: Write the numbers vertically
84
× 93
Step 2: Multiply the ones digit of the bottom number by the top number
- Multiply 3 by 4:
3×4=12
Write down 2, carry over 1. - Multiply 3 by 8, then add the carried-over 1:
3×8=24
24+1=25
Write down 25.
So the first partial product is 252.
84
× 93
------
252 (84 × 3)
Step 3: Multiply the tens digit of the bottom number by the top number
- Multiply 9 by 4:
9×4=36
Write down 6, carry over 3. - Multiply 9 by 8, then add the carried-over 3:
9×8=72
72+3=75
Write down 75, adding a zero in the ones place since this is the tens digit.
So the second partial product is 7560.
84
× 93
------
252 (84 × 3)
+7560 (84 × 90, shifted one place left)
------
Step 4: Add the partial products
252
+ 7560
------
7812
Final Answer
So, 84 multiplied by 93 equals 7,812.
Example 6: Multiply 67 by 89
Step 6: Write the numbers vertically
67
× 89
Step 2: Multiply the ones digit of the bottom number by the top number
- Multiply 9 by 7:
9×7=63
Write down 3, carry over 6. - Multiply 9 by 6, then add the carried-over 6:
9×6=54
54+6=60
Write down 60.
So the first partial product is 603.
67
× 89
------
603 (67 × 9)
Step 3: Multiply the tens digit of the bottom number by the top number
- Multiply 8 by 7:
8×7=56
Write down 6, carry over 5. - Multiply 8 by 6, then add the carried-over 5:
8×6=48
48+5=53
Write down 53, adding a zero in the ones place since this is the tens digit.
So the second partial product is 5360.
67
× 89
------
603 (67 × 9)
+5360 (67 × 80, shifted one place left)
------
Step 4: Add the partial products
603
+ 5360
------
5963
Final Answer
So, 67 multiplied by 89 equals 5,963.
Example 7: Multiply 75 by 64
Step 1: Write the numbers vertically
75
× 64
Step 2: Multiply the ones digit of the bottom number by the top number
- Multiply 4 by 5:
4×5=20
Write down 0, carry over 2. - Multiply 4 by 7, then add the carried-over 2:
4×7=28
28+2=30
Write down 30.
So the first partial product is 300.
75
× 64
------
300 (75 × 4)
Step 3: Multiply the tens digit of the bottom number by the top number
- Multiply 6 by 5:
6×5=30
Write down 0, carry over 3. - Multiply 6 by 7, then add the carried-over 3:
6×7=42
42+3=45
Write down 45, adding a zero in the ones place since this is the tens digit.
So the second partial product is 4500.
75
× 64
------
300 (75 × 4)
+4500 (75 × 60, shifted one place left)
------
Step 4: Add the partial products
300
+ 4500
------
4800
Final Answer
So, 75 multiplied by 64 equals 4,800.
Example 8: Multiply 91 by 58
Step 1: Write the numbers vertically
91
× 58
Step 2: Multiply the ones digit of the bottom number by the top number
- Multiply 8 by 1:
8×1=8
Write down 8. - Multiply 8 by 9:
8×9=72
Write down 72.
So the first partial product is 728.
91
× 58
------
728 (91 × 8)
Step 3: Multiply the tens digit of the bottom number by the top number
- Multiply 5 by 1:
5×1=5
Write down 5. - Multiply 5 by 9:
5×9=45
Write down 45, adding a zero in the ones place since this is the tens digit.
So the second partial product is 4550.
91
× 58
------
728 (91 × 8)
+4550 (91 × 50, shifted one place left)
------
Step 4: Add the partial products
728
+ 4550
------
5278
Final Answer
So, 91 multiplied by 58 equals 5,278.
Example 9: Multiply 83 by 76
Step 1: Write the numbers vertically
83
× 76
Step 2: Multiply the ones digit of the bottom number by the top number
- Multiply 6 by 3:
6×3=18
Write down 8, carry over 1. - Multiply 6 by 8, then add the carried-over 1:
6×8=48
48+1=49
Write down 49.
So the first partial product is 498.
83
× 76
------
498 (83 × 6)
Step 3: Multiply the tens digit of the bottom number by the top number
- Multiply 7 by 3:
7×3=21
Write down 1, carry over 2. - Multiply 7 by 8, then add the carried-over 2:
7×8=56
56+2=58
Write down 58, adding a zero in the ones place since this is the tens digit.
So the second partial product is 5810.
83
× 76
------
498 (83 × 6)
+5810 (83 × 70, shifted one place left)
------
Step 4: Add the partial products
498
+ 5810
------
6308
Final Answer
So, 83 multiplied by 76 equals 6,308.
Example 10: Multiply 47 by 93
Step 1: Write the numbers vertically
47
× 93
Step 2: Multiply the ones digit of the bottom number by the top number
- Multiply 3 by 7:
3×7=21
Write down 1, carry over 2. - Multiply 3 by 4, then add the carried-over 2:
3×4=12
12+2=14
Write down 14.
So the first partial product is 141.
47
× 93
------
141 (47 × 3)
Step 3: Multiply the tens digit of the bottom number by the top number
- Multiply 9 by 7:
9×7=63
Write down 3, carry over 6. - Multiply 9 by 4, then add the carried-over 6:
9×4=36
36+6=42
Write down 42, adding a zero in the ones place since this is the tens digit.
So the second partial product is 4230.
47
× 93
------
141 (47 × 3)
+4230 (47 × 90, shifted one place left)
------
Step 4: Add the partial products
141
+ 4230
------
4371
Final Answer
So, 47 multiplied by 93 equals 4,371.
Example 11: Multiply 68 by 74
Step 1: Write the numbers vertically
68
× 74
Step 2: Multiply the ones digit of the bottom number by the top number
- Multiply 4 by 8:
4×8=32
Write down 2, carry over 3. - Multiply 4 by 6, then add the carried-over 3:
4×6=24
24+3=27
Write down 27.
So the first partial product is 272.
68
× 74
------
272 (68 × 4)
Step 3: Multiply the tens digit of the bottom number by the top number
- Multiply 7 by 8:
7×8=56
Write down 6, carry over 5. - Multiply 7 by 6, then add the carried-over 5:
7×6=42
42+5=47
Write down 47, adding a zero in the ones place since this is the tens digit.
So the second partial product is 4760.
68
× 74
------
272 (68 × 4)
+4760 (68 × 70, shifted one place left)
------
Step 4: Add the partial products
272
+ 4760
------
5032
Final Answer
So, 68 multiplied by 74 equals 5,032.
Example 12: Multiply 59 by 86
Step 1: Write the numbers vertically
59
× 86
Step 2: Multiply the ones digit of the bottom number by the top number
- Multiply 6 by 9:
6×9=54
Write down 4, carry over 5. - Multiply 6 by 5, then add the carried-over 5:
6×5=30
30+5=35
Write down 35.
So the first partial product is 354.
59
× 86
------
354 (59 × 6)
Step 3: Multiply the tens digit of the bottom number by the top number
- Multiply 8 by 9:
8×9=72
Write down 2, carry over 7. - Multiply 8 by 5, then add the carried-over 7:
8×5=40
40+7=47
Write down 47, adding a zero in the ones place since this is the tens digit.
So the second partial product is 4720.
59
× 86
------
354 (59 × 6)
+4720 (59 × 80, shifted one place left)
------
Step 4: Add the partial products
354
+ 4720
------
5074
Final Answer
So, 59 multiplied by 86 equals 5,074.
Example 13: Multiply 91 by 77
Step 1: Write the numbers vertically
91
× 77
Step 2: Multiply the ones digit of the bottom number by the top number
- Multiply 7 by 1:
7×1=7
Write down 7. - Multiply 7 by 9:
7×9=63
Write down 63.
So the first partial product is 637.
91
× 77
------
637 (91 × 7)
Step 3: Multiply the tens digit of the bottom number by the top number
- Multiply 7 by 1:
7×1=7
Write down 7. - Multiply 7 by 9:
7×9=63
Write down 63, adding a zero in the ones place since this is the tens digit.
So the second partial product is 6370.
91
× 77
------
637 (91 × 7)
+6370 (91 × 70, shifted one place left)
------
Step 4: Add the partial products
637
+ 6370
------
7007
Final Answer
So, 91 multiplied by 77 equals 7,007.
Example 14: Multiply 94 by 82
Step 1: Write the numbers vertically
94
× 82
Step 2: Multiply the ones digit of the bottom number by the top number
- Multiply 2 by 4:
2×4=8
Write down 8. - Multiply 2 by 9:
2×9=18
Write down 18.
So the first partial product is 188.
94
× 82
------
188 (94 × 2)
Step 3: Multiply the tens digit of the bottom number by the top number
- Multiply 8 by 4:
8×4=32
Write down 2, carry over 3. - Multiply 8 by 9, then add the carried-over 3:
8×9=72
72+3=75
Write down 75, adding a zero in the ones place since this is the tens digit.
So the second partial product is 7520.
94
× 82
------
188 (94 × 2)
+7520 (94 × 80, shifted one place left)
------
Step 4: Add the partial products
188
+ 7520
------
7708
Final Answer
So, 94 multiplied by 82 equals 7,708.
Example 15: Multiply 63 by 95
Step 1: Write the numbers vertically
63
× 95
Step 2: Multiply the ones digit of the bottom number by the top number
- Multiply 5 by 3:
5×3=15
Write down 5, carry over 1. - Multiply 5 by 6, then add the carried-over 1:
5×6=30
30+1=31
Write down 31.
So the first partial product is 315.
63
× 95
------
315 (63 × 5)
Step 3: Multiply the tens digit of the bottom number by the top number
- Multiply 9 by 3:
9×3=27
Write down 7, carry over 2. - Multiply 9 by 6, then add the carried-over 2:
9×6=54
54+2=56
Write down 56, adding a zero in the ones place since this is the tens digit.
So the second partial product is 5670.
63
× 95
------
315 (63 × 5)
+5670 (63 × 90, shifted one place left)
------
Step 4: Add the partial products
315
+ 5670
------
5985
Final Answer
So, 63 multiplied by 95 equals 5,985.
Example 16: Multiply 79 by 68
Step 1: Write the numbers vertically
79
× 68
Step 2: Multiply the ones digit of the bottom number by the top number
- Multiply 8 by 9:
8×9=72
Write down 2, carry over 7. - Multiply 8 by 7, then add the carried-over 7:
8×7=56
56+7=63
Write down 63.
So the first partial product is 632.
79
× 68
------
632 (79 × 8)
Step 3: Multiply the tens digit of the bottom number by the top number
- Multiply 6 by 9:
6×9=54
Write down 4, carry over 5. - Multiply 6 by 7, then add the carried-over 5:
6×7=42
42+5=47
Write down 47, adding a zero in the ones place since this is the tens digit.
So the second partial product is 4740.
79
× 68
------
632 (79 × 8)
+4740 (79 × 60, shifted one place left)
------
Step 4: Add the partial products
632
+ 4740
------
5372
Final Answer
So, 79 multiplied by 68 equals 5,372.
Example 17: Multiply 84 by 93
Step 1: Write the numbers vertically
84
× 93
Step 2: Multiply the ones digit of the bottom number by the top number
- Multiply 3 by 4:
3×4=12
Write down 2, carry over 1. - Multiply 3 by 8, then add the carried-over 1:
3×8=24
24+1=25
Write down 25.
So the first partial product is 252.
84
× 93
------
252 (84 × 3)
Step 3: Multiply the tens digit of the bottom number by the top number
- Multiply 9 by 4:
9×4=36
Write down 6, carry over 3. - Multiply 9 by 8, then add the carried-over 3:
9×8=72
72+3=75
Write down 75, adding a zero in the ones place since this is the tens digit.
So the second partial product is 7560.
84
× 93
------
252 (84 × 3)
+7560 (84 × 90, shifted one place left)
------
Step 4: Add the partial products
252
+ 7560
------
7812
Final Answer
So, 84 multiplied by 93 equals 7,812.
Example 18: Multiply 52 by 77
Step 1: Write the numbers vertically
52
× 77
Step 2: Multiply the ones digit of the bottom number by the top number
- Multiply 7 by 2:
7×2=14
Write down 4, carry over 1. - Multiply 7 by 5, then add the carried-over 1:
7×5=35
35+1=36
Write down 36.
So the first partial product is 364.
52
× 77
------
364 (52 × 7)
Step 3: Multiply the tens digit of the bottom number by the top number
- Multiply 7 by 2:
7×2=14
Write down 4, carry over 1. - Multiply 7 by 5, then add the carried-over 1:
7×5=35
35+1=36
Write down 36, adding a zero in the ones place since this is the tens digit.
So the second partial product is 3640.
52
× 77
------
364 (52 × 7)
+3640 (52 × 70, shifted one place left)
------
Step 4: Add the partial products
364
+ 3640
------
4004
Final Answer
So, 52 multiplied by 77 equals 4,004.
Example 19: Multiply 69 by 84
Step 1: Write the numbers vertically
69
× 84
Step 2: Multiply the ones digit of the bottom number by the top number
- Multiply 4 by 9:
4×9=36
Write down 6, carry over 3. - Multiply 4 by 6, then add the carried-over 3:
4×6=24
24+3=27
Write down 27.
So the first partial product is 276
69
× 84
------
276 (69 × 4)
Step 3: Multiply the tens digit of the bottom number by the top number
- Multiply 8 by 9:
8×9=72
Write down 2, carry over 7. - Multiply 8 by 6, then add the carried-over 7:
8×6=48
48+7=55
Write down 55, adding a zero in the ones place since this is the tens digit.
So the second partial product is 5520.
69
× 84
------
276 (69 × 4)
+5520 (69 × 80, shifted one place left)
------
Step 4: Add the partial products
276
+ 5520
------
5796
Final Answer
So, 69 multiplied by 84 equals 5,796.
Example 20: Multiply 73 by 59
Step 1: Write the numbers vertically
73
× 59
Step 2: Multiply the ones digit of the bottom number by the top number
- Multiply 9 by 3:
9×3=27
Write down 7, carry over 2. - Multiply 9 by 7, then add the carried-over 2:
9×7=63
63+2=65
Write down 65.
So the first partial product is 657.
73
× 59
------
657 (73 × 9)
Step 3: Multiply the tens digit of the bottom number by the top number
- Multiply 5 by 3:
5×3=15
Write down 5, carry over 1. - Multiply 5 by 7, then add the carried-over 1:
5×7=35
35+1=36
Write down 36, adding a zero in the ones place since this is the tens digit.
So the second partial product is 3650.
73
× 59
------
657 (73 × 9)
+3650 (73 × 50, shifted one place left)
------
Step 4: Add the partial products
657
+ 3650
------
4307
Final Answer
So, 73 multiplied by 59 equals 4,307.
Example 21: Multiply 47 by 68
Step 1: Write the numbers vertically
47
× 68
Step 2: Multiply the ones digit of the bottom number by the top number
- Multiply 8 by 7:
8×7=5
Write down 6, carry over 5. - Multiply 8 by 4, then add the carried-over 5:
8×4=32
32+5=37
Write down 37.
So the first partial product is 376.
47
× 68
------
376 (47 × 8)
Step 3: Multiply the tens digit of the bottom number by the top number
- Multiply 6 by 7:
6×7=42
Write down 2, carry over 4. - Multiply 6 by 4, then add the carried-over 4:
6×4=24
24+4=28
Write down 28, adding a zero in the ones place since this is the tens digit.
So the second partial product is 2820.
47
× 68
------
376 (47 × 8)
+2820 (47 × 60, shifted one place left)
------
Step 4: Add the partial products
376
+2820
------
3196
Final Answer
So, 47 multiplied by 68 equals 3,196.
Example 22: Multiply 55 by 76
Step 1: Write the numbers vertically
55
× 76
Step 2: Multiply the ones digit of the bottom number by the top number
- Multiply 6 by 5:
6×5=30
Write down 0, carry over 3. - Multiply 6 by 5, then add the carried-over 3:
6×5=30
30+3=33
Write down 33.
So the first partial product is 330.
55
× 76
------
330 (55 × 6)
Step 3: Multiply the tens digit of the bottom number by the top number
- Multiply 7 by 5:
7×5=35
Write down 5, carry over 3. - Multiply 7 by 5, then add the carried-over 3:
7×5=35
35+3=38
Write down 38, adding a zero in the ones place since this is the tens digit.
So the second partial product is 3850.
55
× 76
------
330 (55 × 6)
+3850 (55 × 70, shifted one place left)
------
Step 4: Add the partial products
330
+3850
------
4180
Final Answer
So, 55 multiplied by 76 equals 4,180.
Example 23: Multiply 68 by 52
Step 1: Write the numbers vertically
68
× 52
Step 2: Multiply the ones digit of the bottom number by the top number
- Multiply 2 by 8:
2×8=16
Write down 6, carry over 1. - Multiply 2 by 6, then add the carried-over 1:
2×6=12
12+1=13
Write down 13.
So the first partial product is 136.
68
× 52
------
136 (68 × 2)
Step 3: Multiply the tens digit of the bottom number by the top number
- Multiply 5 by 8:
5×8=40
Write down 0, carry over 4. - Multiply 5 by 6, then add the carried-over 4:
5×6=30
30+4=34
Write down 34, adding a zero in the ones place since this is the tens digit.
So the second partial product is 3400.
68
× 52
------
136 (68 × 2)
+3400 (68 × 50, shifted one place left)
------
Step 4: Add the partial products
136
+3400
------
3536
Final Answer
So, 68 multiplied by 52 equals 3,536.
Example 24: Multiply 82 by 47
Step 1: Write the numbers vertically
82
× 47
Step 2: Multiply the ones digit of the bottom number by the top number
- Multiply 7 by 2:
7×2=14
Write down 4, carry over 1. - Multiply 7 by 8, then add the carried-over 1:
7×8=56
56+1=57
Write down 57.
So the first partial product is 574.
82
× 47
------
574 (82 × 7)
Step 3: Multiply the tens digit of the bottom number by the top number
- Multiply 4 by 2:
4×2=8
Write down 8. - Multiply 4 by 8:
4×8=32
Write down 32, adding a zero in the ones place since this is the tens digit.
So the second partial product is 3280.
82
× 47
------
574 (82 × 7)
+3280 (82 × 40, shifted one place left)
------
Step 4: Add the partial products
574
+3280
------
3854
Final Answer
So, 82 multiplied by 47 equals 3,854.
Example 25: Multiply 97 by 34
Step 1: Write the numbers vertically
97
× 34
Step 2: Multiply the ones digit of the bottom number by the top number
- Multiply 4 by 7:
4×7=28
Write down 8, carry over 2. - Multiply 4 by 9, then add the carried-over 2:
4×9=36
36+2=38
Write down 38.
So the first partial product is 388.
97
× 34
------
388 (97 × 4)
Step 3: Multiply the tens digit of the bottom number by the top number
- Multiply 3 by 7:
3×7=21
Write down 1, carry over 2. - Multiply 3 by 9, then add the carried-over 2:
3×9=27
27+2=29
Write down 29, adding a zero in the ones place since this is the tens digit.
So the second partial product is 2910.
97
× 34
------
388 (97 × 4)
+2910 (97 × 30, shifted one place left)
------
Step 4: Add the partial products
388
+2910
------
3298
Final Answer
So, 97 multiplied by 34 equals 3,298.
Example 26: Multiply 56 by 83
Step 1: Write the numbers vertically
56
× 83
Step 2: Multiply the ones digit of the bottom number by the top number
- Multiply 3 by 6:
3×6=18
Write down 8, carry over 1. - Multiply 3 by 5, then add the carried-over 1:
3×5=15
15+1=16
Write down 16.
So the first partial product is 168.
56
× 83
------
168 (56 × 3)
Step 3: Multiply the tens digit of the bottom number by the top number
- Multiply 8 by 6:
8×6=48
Write down 8, carry over 4. - Multiply 8 by 5, then add the carried-over 4:
8×5=40
40+4=44
Write down 44, adding a zero in the ones place since this is the tens digit.
So the second partial product is 4480.
56
× 83
------
168 (56 × 3)
+4480 (56 × 80, shifted one place left)
------
Step 4: Add the partial products
168
+4480
------
4648
Final Answer
So, 56 multiplied by 83 equals 4,648.
Example 27: Multiply 74 by 29
Step 1: Write the numbers vertically
74
× 29
Step 2: Multiply the ones digit of the bottom number by the top number
- Multiply 9 by 4:
9×4=36
Write down 6, carry over 3. - Multiply 9 by 7, then add the carried-over 3:
9×7=63
63+3=66
Write down 66.
So the first partial product is 666.
74
× 29
------
666 (74 × 9)
Step 3: Multiply the tens digit of the bottom number by the top number
- Multiply 2 by 4:
2×4=8
Write down 8. - Multiply 2 by 7:
2×7=14
Write down 14, adding a zero in the ones place since this is the tens digit.
So the second partial product is 1480.
74
× 29
------
666 (74 × 9)
+1480 (74 × 20, shifted one place left)
------
Step 4: Add the partial products
666
+1480
------
2146
Final Answer
So, 74 multiplied by 29 equals 2,146.
Example 28: Multiply 83 by 47
Step 1: Write the numbers vertically
83
× 47
Step 2: Multiply the ones digit of the bottom number by the top number
- Multiply 7 by 3:
7×3=21
Write down 1, carry over 2. - Multiply 7 by 8, then add the carried-over 2:
7×8=56
56+2=58
Write down 58.
So the first partial product is 581.
83
× 47
------
581 (83 × 7)
Step 3: Multiply the tens digit of the bottom number by the top number
- Multiply 4 by 3:
4×3=12
Write down 2, carry over 1. - Multiply 4 by 8, then add the carried-over 1:
4×8=32
32+1=33
Write down 33, adding a zero in the ones place since this is the tens digit.
So the second partial product is 3320.
83
× 47
------
581 (83 × 7)
+3320 (83 × 40, shifted one place left)
------
Step 4: Add the partial products
581
+3320
------
3901
Final Answer
So, 83 multiplied by 47 equals 3,901.
Example 29: Multiply 91 by 36
Step 1: Write the numbers vertically
91
× 36
Step 2: Multiply the ones digit of the bottom number by the top number
- Multiply 6 by 1:
6×1=6
Write down 6. - Multiply 6 by 9:
6×9=54
Write down 54.
So the first partial product is 546.
91
× 36
------
546 (91 × 6)
Step 3: Multiply the tens digit of the bottom number by the top number
- Multiply 3 by 1:
3×1=3
Write down 3. - Multiply 3 by 9:
3×9=27
Write down 27, adding a zero in the ones place since this is the tens digit.
So the second partial product is 2730.
91
× 36
------
546 (91 × 6)
+2730 (91 × 30, shifted one place left)
------
Step 4: Add the partial products
546
+2730
------
3276
Final Answer
So, 91 multiplied by 36 equals 3,276.
Example 30: Multiply 64 by 57
Step 1: Write the numbers vertically
64
× 57
Step 2: Multiply the ones digit of the bottom number by the top number
- Multiply 7 by 4:
7×4=28
Write down 8, carry over 2. - Multiply 7 by 6, then add the carried-over 2:
7×6=42
42+2=44
Write down 44.
So the first partial product is 448.
64
× 57
------
448 (64 × 7)
Step 3: Multiply the tens digit of the bottom number by the top number
- Multiply 5 by 4:
5×4=20
Write down 0, carry over 2. - Multiply 5 by 6, then add the carried-over 2:
5×6=30
30+2=32
Write down 32, adding a zero in the ones place since this is the tens digit.
So the second partial product is 3200.
64
× 57
------
448 (64 × 7)
+3200 (64 × 50, shifted one place left)
------
Step 4: Add the partial products
448
+3200
------
3648
Final Answer
So, 64 multiplied by 57 equals 3,648.
These examples continue to show the systematic process of vertical multiplication, where each digit of the bottom number is multiplied by the entire top number, and then the resulting partial products are added together to get the final answer.