By now, you can recall single-digit multiplication facts from mem0ry (e.g. 4 × 7 = 28), and you can calculate the multiplication of any 2-digit number by any 1-digit number by splitting the 2-digit number (e.g. 34 × 7 = 210 + 28).
What next?
The next most effective thing is to memorize some of the 2-digit × 1 digit multiplications as facts. This allows you to:
- solve these multiplications instantly without needing a calculation; and
- multiply larger number more easily, such as 2-digits × 2 digits.
But there are 648 of these, so we certainly won’t memorize all of them(!) We’ll only memorize at the ones that appear most often in mental math. For example, it’s helpful to know that 16 × 4 = 64, but not worthwhile to learn that 73 × 7 = 511.
Most Useful Advanced Multiplication Facts
- According to Benford’s Law, we encounter more numbers beginning with 1 (or 2) than with larger digits like 7, 8 or 9. Therefore we will need to multiply by numbers like 13, 16 and 24 more often then numbers like 73, 86 or 92. So we should focus on multiplication facts of smaller 2-digit numbers.
- Multiplications of smaller numbers often have 2-digit answers, such as 16 × 4 = 64. These are slightly easier to memorize than 3-digit answers like 73 × 7 = 511.
- Numbers with many factors—such as 15, 16, 18 and 24—appear more often in life than prime numbers like 17 or 73. Therefore it is more helpful to learn multiplication facts of these numbers with many factors.
- Percentage increases are often equivalent to multiplying by a number between 10 and 19, for example a 40% increase on $640 is equivalent to 640 × 1.4 or 64 × 14. Knowing the 14× table can help with this.
By considering these criteria, I’ve developed lists of multiplication facts that are most worthwhile to learn.
[TODO details and info]