Quick Maths Trick for Times Tables of 19, 29, 39, 49
Introduction â A Fast Way to Write Times Tables of numbers ending with 9 such as 19, 29, 39, etc
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.
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 + 1Unit Digit: 10 - nRemaining Digits: a + (n - 1)dWhere, 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
Writing down the Times Table of 29
Writing down the Times Table of 39
Writing down the Times Table of 49
Writing down the Times Table of 59
Writing down the Times Table of 69
Writing down the Times Table of 79
Writing down the Times Table of 89
Writing down the Times Table of 99
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:
Tâ = a + (n â 1)dThis 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
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.