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Quick Maths Trick for Times Tables of 19, 29, 39, 49

High School Student reading a maths blog

Multiplication Times Tables of numbers ending in 9, such as 19, 29, 39, ..., 99 and so on, follow a remarkably consistent and elegant structure. Instead of memorizing each product separately, you can observe two predictable patterns.

This trick becomes much easier to understand when you are familiar with Arithmetic Progression (AP). In the multiplication tables of numbers ending in 9 (such as 19, 29, 39, ...), the digits to the left of the unit digit follow a clear Arithmetic Progression. The sequence starts with the non-unit digit of the multiplicand and increases by a constant value each time. Recognizing this AP pattern helps you construct the table systematically instead of multiplying each step separately. If you are not familiar with Arithmetic Progression, refer to the brief explanation provided at the end of this article before exploring the pattern in detail.

The Two Patterns Behind the Trick

Let's take the Times Table of 39 as an example.

39✕1=3939✕2=7839✕3=11739✕4=15639✕5=19539✕6=23439✕7=27339✕8=31239✕9=35139✕10=390

The products are: 39, 78, 117, 156, 195, 234, 273, 312, 351, 390

Pattern I: Unit Digits Decrease Sequentially

The unit digit from each product form this sequence: 9, 8, 7, 6, 5, 4, 3, 2, 1, 0. The unit digit of nth product can be found using 10 - n.

Pattern II: The Remaining Digits Form an Arithmetic Progression

The remaining digits from each product: 3, 7, 11, 15, 19, 23, 27, 31, 35, 39. This is an Arithmetic Progression (AP) with the first term (a) = 3 (from 39) and common difference (d) = a + 1 = 4. These remaining digits of a nth product can be found using a + (n - 1)d.

How to Apply the Pattern

These two patterns give us the formulae to determine the products.

From the multiplicands (such as 19, 29, 39, ..., 99 and so on), we get the first term (a). This is simply the non-unit digit of the multiplicand. For example, the first term (a) will be 1 for 19, 2 for 29, 3 for 39 and so on. 

Common Difference (d): a + 1
Unit Digit: 10 - n
Remaining Digits: a + (n - 1)d

Where, a is the first term, d is the common difference and n is any one of the multipliers from 1 to 10.

See the Pattern in Action

Writing down the Times Table of 19

a = 1 (from 19) d = a + 1 = 2
19
The Pattern
Remaining Digits in AP
(Pattern II)
a + (n - 1)d
Product
Unit Digit
(Pattern I)
10 - n
19 Multiply 1 Equals 19
 
1
19
9
19 Multiply 2 Equals 38
1 Add 2 Equals
3
38
8
19 Multiply 3 Equals 57
3 Add 2 Equals
5
57
7
19 Multiply 4 Equals 76
5 Add 2 Equals
7
76
6
19 Multiply 5 Equals 95
7 Add 2 Equals
9
95
5
19 Multiply 6 Equals 114
9 Add 2 Equals
11
114
4
19 Multiply 7 Equals 133
11 Add 2 Equals
13
133
3
19 Multiply 8 Equals 152
13 Add 2 Equals
15
152
2
19 Multiply 9 Equals 171
15 Add 2 Equals
17
171
1
19 Multiply 10 Equals 190
17 Add 2 Equals
19
190
0

Writing down the Times Table of 29

a = 2 (from 29) d = a + 1 = 3
29
The Pattern
Remaining Digits in AP
(Pattern II)
a + (n - 1)d
Product
Unit Digit
(Pattern I)
10 - n
29 Multiply 1 Equals 29
 
2
29
9
29 Multiply 2 Equals 58
2 Add 3 Equals
5
58
8
29 Multiply 3 Equals 87
5 Add 3 Equals
8
87
7
29 Multiply 4 Equals 116
8 Add 3 Equals
11
116
6
29 Multiply 5 Equals 145
11 Add 3 Equals
14
145
5
29 Multiply 6 Equals 174
14 Add 3 Equals
17
174
4
29 Multiply 7 Equals 203
17 Add 3 Equals
20
203
3
29 Multiply 8 Equals 232
20 Add 3 Equals
23
232
2
29 Multiply 9 Equals 261
23 Add 3 Equals
26
261
1
29 Multiply 10 Equals 290
26 Add 3 Equals
29
290
0

Writing down the Times Table of 39

a = 3 (from 39) d = a + 1 = 4
39
The Pattern
Remaining Digits in AP
(Pattern II)
a + (n - 1)d
Product
Unit Digit
(Pattern I)
10 - n
39 Multiply 1 Equals 39
 
3
39
9
39 Multiply 2 Equals 78
3 Add 4 Equals
7
78
8
39 Multiply 3 Equals 117
7 Add 4 Equals
11
117
7
39 Multiply 4 Equals 156
11 Add 4 Equals
15
156
6
39 Multiply 5 Equals 195
15 Add 4 Equals
19
195
5
39 Multiply 6 Equals 234
19 Add 4 Equals
23
234
4
39 Multiply 7 Equals 273
23 Add 4 Equals
27
273
3
39 Multiply 8 Equals 312
27 Add 4 Equals
31
312
2
39 Multiply 9 Equals 351
31 Add 4 Equals
35
351
1
39 Multiply 10 Equals 390
35 Add 4 Equals
39
390
0

Writing down the Times Table of 49

a = 4 (from 49) d = a + 1 = 5
49
The Pattern
Remaining Digits in AP
(Pattern II)
a + (n - 1)d
Product
Unit Digit
(Pattern I)
10 - n
49 Multiply 1 Equals 49
 
4
49
9
49 Multiply 2 Equals 98
4 Add 5 Equals
9
98
8
49 Multiply 3 Equals 147
9 Add 5 Equals
14
147
7
49 Multiply 4 Equals 196
14 Add 5 Equals
19
196
6
49 Multiply 5 Equals 245
19 Add 5 Equals
24
245
5
49 Multiply 6 Equals 294
24 Add 5 Equals
29
294
4
49 Multiply 7 Equals 343
29 Add 5 Equals
34
343
3
49 Multiply 8 Equals 392
34 Add 5 Equals
39
392
2
49 Multiply 9 Equals 441
39 Add 5 Equals
44
441
1
49 Multiply 10 Equals 490
44 Add 5 Equals
49
490
0

Writing down the Times Table of 59

a = 5 (from 59) d = a + 1 = 6
59
The Pattern
Remaining Digits in AP
(Pattern II)
a + (n - 1)d
Product
Unit Digit
(Pattern I)
10 - n
59 Multiply 1 Equals 59
 
5
59
9
59 Multiply 2 Equals 118
5 Add 6 Equals
11
118
8
59 Multiply 3 Equals 177
11 Add 6 Equals
17
177
7
59 Multiply 4 Equals 236
17 Add 6 Equals
23
236
6
59 Multiply 5 Equals 295
23 Add 6 Equals
29
295
5
59 Multiply 6 Equals 354
29 Add 6 Equals
35
354
4
59 Multiply 7 Equals 413
35 Add 6 Equals
41
413
3
59 Multiply 8 Equals 472
41 Add 6 Equals
47
472
2
59 Multiply 9 Equals 531
47 Add 6 Equals
53
531
1
59 Multiply 10 Equals 590
53 Add 6 Equals
59
590
0

Writing down the Times Table of 69

a = 6 (from 69) d = a + 1 = 7
69
The Pattern
Remaining Digits in AP
(Pattern II)
a + (n - 1)d
Product
Unit Digit
(Pattern I)
10 - n
69 Multiply 1 Equals 69
 
6
69
9
69 Multiply 2 Equals 138
6 Add 7 Equals
13
138
8
69 Multiply 3 Equals 207
13 Add 7 Equals
20
207
7
69 Multiply 4 Equals 276
20 Add 7 Equals
27
276
6
69 Multiply 5 Equals 345
27 Add 7 Equals
34
345
5
69 Multiply 6 Equals 414
34 Add 7 Equals
41
414
4
69 Multiply 7 Equals 483
41 Add 7 Equals
48
483
3
69 Multiply 8 Equals 552
48 Add 7 Equals
55
552
2
69 Multiply 9 Equals 621
55 Add 7 Equals
62
621
1
69 Multiply 10 Equals 690
62 Add 7 Equals
69
690
0

Writing down the Times Table of 79

a = 7 (from 79) d = a + 1 = 8
79
The Pattern
Remaining Digits in AP
(Pattern II)
a + (n - 1)d
Product
Unit Digit
(Pattern I)
10 - n
79 Multiply 1 Equals 79
 
7
79
9
79 Multiply 2 Equals 158
7 Add 8 Equals
15
158
8
79 Multiply 3 Equals 237
15 Add 8 Equals
23
237
7
79 Multiply 4 Equals 316
23 Add 8 Equals
31
316
6
79 Multiply 5 Equals 395
31 Add 8 Equals
39
395
5
79 Multiply 6 Equals 474
39 Add 8 Equals
47
474
4
79 Multiply 7 Equals 553
47 Add 8 Equals
55
553
3
79 Multiply 8 Equals 632
55 Add 8 Equals
63
632
2
79 Multiply 9 Equals 711
63 Add 8 Equals
71
711
1
79 Multiply 10 Equals 790
71 Add 8 Equals
79
790
0

Writing down the Times Table of 89

a = 8 (from 89) d = a + 1 = 9
89
The Pattern
Remaining Digits in AP
(Pattern II)
a + (n - 1)d
Product
Unit Digit
(Pattern I)
10 - n
89 Multiply 1 Equals 89
 
8
89
9
89 Multiply 2 Equals 178
8 Add 9 Equals
17
178
8
89 Multiply 3 Equals 267
17 Add 9 Equals
26
267
7
89 Multiply 4 Equals 356
26 Add 9 Equals
35
356
6
89 Multiply 5 Equals 445
35 Add 9 Equals
44
445
5
89 Multiply 6 Equals 534
44 Add 9 Equals
53
534
4
89 Multiply 7 Equals 623
53 Add 9 Equals
62
623
3
89 Multiply 8 Equals 712
62 Add 9 Equals
71
712
2
89 Multiply 9 Equals 801
71 Add 9 Equals
80
801
1
89 Multiply 10 Equals 890
80 Add 9 Equals
89
890
0

Writing down the Times Table of 99

a = 9 (from 99) d = a + 1 = 10
99
The Pattern
Remaining Digits in AP
(Pattern II)
a + (n - 1)d
Product
Unit Digit
(Pattern I)
10 - n
99 Multiply 1 Equals 99
 
9
99
9
99 Multiply 2 Equals 198
9 Add 10 Equals
19
198
8
99 Multiply 3 Equals 297
19 Add 10 Equals
29
297
7
99 Multiply 4 Equals 396
29 Add 10 Equals
39
396
6
99 Multiply 5 Equals 495
39 Add 10 Equals
49
495
5
99 Multiply 6 Equals 594
49 Add 10 Equals
59
594
4
99 Multiply 7 Equals 693
59 Add 10 Equals
69
693
3
99 Multiply 8 Equals 792
69 Add 10 Equals
79
792
2
99 Multiply 9 Equals 891
79 Add 10 Equals
89
891
1
99 Multiply 10 Equals 990
89 Add 10 Equals
99
990
0

What is Arithmetic Progression (AP)?

Arithmetic Progression (AP) is a sequence of numbers in which the difference between any two consecutive terms is constant. This constant value is called the common difference (d). If the first term is a, then the sequence is formed by repeatedly adding d to each term: 

a, a + d, a + 2d, a + 3d, ...

The nth term of an Arithmetic Progression is given by the formula:

Tₙ = a + (n − 1)d

This Pattern Works for All Numbers Ending in 9

This trick is not limited to numbers from 19 to 99. In fact, the same pattern appears in the multiplication tables of any number that ends with 9 including the single-digit number 9. The unit digits of the products still decrease from 9 to 0, and the remaining digits continue to follow a clear arithmetic progression.

Let's take the Times Table of 479 as an example.

Writing down the Times Table of 479

a = 47 (from 479) d = a + 1 = 48
479
The Pattern
Remaining Digits in AP
(Pattern II)
a + (n - 1)d
Product
Unit Digit
(Pattern I)
10 - n
479 Multiply 1 Equals 479
 
47
479
9
479 Multiply 2 Equals 958
47 Add 48 Equals
95
958
8
479 Multiply 3 Equals 1437
95 Add 48 Equals
143
1437
7
479 Multiply 4 Equals 1916
143 Add 48 Equals
191
1916
6
479 Multiply 5 Equals 2395
191 Add 48 Equals
239
2395
5
479 Multiply 6 Equals 2874
239 Add 48 Equals
287
2874
4
479 Multiply 7 Equals 3353
287 Add 48 Equals
335
3353
3
479 Multiply 8 Equals 3832
335 Add 48 Equals
383
3832
2
479 Multiply 9 Equals 4311
383 Add 48 Equals
431
4311
1
479 Multiply 10 Equals 4790
431 Add 48 Equals
479
4790
0

You can explore this pattern yourself on our Multiplication Times Tables: Reference Chart page. Under Custom option, enter multiplicands up to 999 and generate their tables instantly. Try numbers such as 9, 239, 489, 529, 779, or any number ending in 9, and observe how the same two patterns appear consistently in their times tables.