Learning the 9 multiplication table

decorate the multiplication table It's not always easy, is it? In this article, we show 4 different methods to know the 9 times table, which is often seen as one of the most difficult to decorate.

Follow along until the end, so you can choose the method you like best and use it when you need it.

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Table of 9 with hands

It is possible to obtain the results of 9 times table using only our fingers. For example, let's get the result of $\bg_white 6 \times 9$ :

Step 1. We number each of the fingers with numbers from 1 to 10;

Step 2. As we are multiplying 9 by 6, so we lower the number 6 finger;

step 3. We verify that the number of fingers to the left of the downed finger is 5 and the number of fingers to the right of the down finger is 4.

Step 4. From these two quantities, we get the result of multiplication: $\bg_white 6 \times 9 \mathbf{54}$ .

See other examples:

get the result of $\bg_white 9 \times 8$ .

Lowering the number 8 finger, we are left with 7 fingers to the left and with 2 fingers to the right of the one who is down.

Then, $\bg_white 9 \times 8 \mathbf{72}$

get the result of $\bg_white 9 \times 10$ .

Lowering the number 10 finger, we are left with 9 fingers to the left and with 0 (none) finger to the right of the bent one.

Then, $\bg_white 9 \times 10 \mathbf{90}$

See how simple and practical it is? But it doesn't stop there, we still have other methods.

Table of 9 using the sum

We can get the results from 9 times table by means of addition (sum) – Multiply the 9 for 2 it is the same as add the number 9 twice, multiply the 9 for 3 it is the same as add the number 9 three times, and so on:

$\dpi{120} \bg_white \begin{matrix} 9 \times 2 && \hspace{-2.3cm}9 + 9 18 \\ 9 \times 3 && \hspace{-1.6cm} 9 + 9 +9 27 \\ 9 \times 4 && \hspace{-0.9cm}9 + 9+9+9 36 \\ 9 \times 5 && \hspace{-0.2cm} 9 + 9+9+9+9 45 \\ \vdots \\ \\ \end{matrix}$

Obs.: This method can be extended to the multiplication tables of other numbers. For example, to find out how much $\dpi{120} \bg_white 8 \times 5$ , just add the 8 five times, that is, $\dpi{120} \bg_white 8 \times 5 8+8+8+8+840$ .

Table of 9 with sequence from 0 to 9 and from 9 to 0

The first digit column in the 9 times table is formed by the integers from 0 to 9, in ascending order (red color), and the column of the second digit is formed by these same numbers in descending order (blue color).

So, in this method, you just need to memorize this pattern:

$\dpi{120} \begin{matrix} 9 \times 1 && {\color{Red} 0} {\color{Blue} 9}\\ 9 \times 2 && {\color{Red} 1} {\color{ Blue} 8}\\ 9 \times 3 && {\color{Red} 2} {\color{Blue} 7}\\ 9 \times 4 && {\color{Red} 3} {\color{Blue} 6}\\ 9 \times 5 && {\color{Red} 4} {\color{Blue} 5}\\ 9 \times 6 && {\color{Red} 5} {\color{Blue} 4}\\ 9 \times 7 && {\color{Red} 6} {\color{Blue} 3}\\ 9 \times 8 && {\color{Red} 7} {\color{Blue} 2}\\ 9 \times 9 && {\color{Red} 8} {\color{ Blue} 1}\\ 9 \times 10 && {\color{Red} 9} {\color{Blue} 0}\\ \end{matrix}$

Table of 9 with a pattern for the first and second digit of each result

We have one more method based on an existing pattern in the results of the 9 times table. Each result of the table of 9 has two digits, where:

first digit: is the number that comes before the one you want to multiply by 9
Second digit: is the result of subtracting 9 from the first digit

Knowing this, it is easy to know any result of this table, see this in the following examples: