Can you propose any hack for remembering multiplication tables from $13-19$?

Question

I memorized multiplication tables from $2-12$ when I was in elementary school.

Regarding tables $13-19$:

1. I remember some intermittent elements
2. I find others by multiplication by recombination. E.g., I would calculate $14 \times 4 \Rightarrow 7 \times 8 \Rightarrow 56$, etc.

However, I am not satisfied with this as I miss almost half of them. E.g., I don't remember the result of $17 \times 7$, etc.

The following YouTube videos present some hacks:

1. $17$ times table
2. $18$ times table
3. $19$ times table

However, they aren't homogeneous. I.e., they devised unique techniques for each of the tables.

Can you propose any better hack for remembering multiplication tables from $13-19$?

Answer 1

There is nothing new in this answer. It is just a reminder that you already know a unified method for the multiplication tables from $13$ to $19$. Since you already have multiplication tables from $3$ to $9$ in your mind, you can use them in a two-step approach for multiplication tables from $13$ to $19$.

Here I show the table entries from $17$ to $19$, the other entries can be derived in the same way. We consider \begin{align*} \begin{array}{r|rrr|r} \cdot&17&1\color{blue}{8}&19\\ \hline 1&7&8&9&+\ 10\\ 2&14&16&18&+\ 20\\\ 3&21&24&27&+\ 30\\\ \color{blue}{4}&28&\color{blue}{32}&36&\color{blue}{+\ 40}\\\ 5&35&40&45&+\ 50\\\ 6&42&48&54&+\ 60\\\ 7&49&56&63&+\ 70\\\ 8&56&64&72&+\ 80\\\ 9&63&72&81&+\ 90\\\ 10&70&80&90&+\ 100\\ \end{array} \end{align*} where we list in

• the column with $17$ the multiples of $7$

• the column with $18$ the multiples of $8$

• the column with $19$ the multiples of $9$

• the rightmost column contains the corresponding multiple of $10$ which has to be added.

Example: $18\cdot 4 = (8+10)\cdot 4 = \color{blue}{(8\cdot 4) + 40} = 72$ according to the blue marked entries in the table.