As with spoken additions, we prefer to solve multiplications from left-to-right—i.e., starting with the tens and finishing with the units.
Basic method: 46 × 7
- Tens: 40 × 7 = 280
- Units: 6 × 7 = 42
- Addition: 280 + 42 = 322
The method is straightforward. But to be fast, it is important to minimize unnecessary verbalization! When you say numbers to yourself, you are storing this data in the time dimension, so it literally makes you take extra time for the calculation.
However, it is difficult to perform these calculations reliably without any verbalization. You might even feel that you are guessing the answer. The following is a compromise where you verbalize only the numbers shown in quotes:
Same task: 46 × 7
- Tens: 40 × 7 = 280 [“2 80”]
- Units: 6 × 7 = 42 [“42”]
- Addition—add the numbers you just said: 280 + 42 = 322
- note: you might naturally verbalize the answer (“3 22”) while typing it—that’s not a problem because the calculation is already finished!
Notice that you can verbalize these numbers more compactly by saying “3 22” as “three twenty-two” rather than “three hundred and twenty-two”. It’s faster but holds the same information for you.
But what is the purpose of verbalization anyway? Why do most people naturally do it? It is a way for us to feel we have the data stored correctly. But for the addition step, ultimately these numbers need to be stored in visual memory. So the rule to follow is that whenever you verbalize a number, you should see those digits also flash into visual memory—however briefly and ephemeral.
So for this task, I would “see” the following:
- 46 (when listening to the question) but not important to see the 7, as this is just telling me which multiplication facts to access.
- 280 (from the first multiplication fact so I don’t forget it while multiplyng 6 × 7)
- 42 (from the second multiplication fact)
- The 4 would appear aligned with the 8 in 280 so I can see what addition to perform: 28 + 4 = 32
- 32_ during the addition
If you perceive the numbers slightly differently—that’s okay! While I’ve given a high level of detail of my personal process, the important details in general are:
- Start with the tens before the units
- Don’t verbalize anything more than the two multiplication facts (e.g. 280 and 42) and don’t verbalize them more than once.
- The digits you verbalize should also be visualized, even if very briefly and faintly, to ensure they are placed in visual memory.
Improvements
As you practise and get faster, eventually you will find that you can do the addition step (e.g. 280 + 42) before verbalizing the second multiplication fact (e.g. 42). If so, that’s great! The progression to mastery is in three stages:
- Needing to verbalize both 280 and 42
- Needing to verbalize only 280
- Not needing to verbalize anything (except perhaps the answer e.g. 322)
Practise Makes Perfect
TODO link to training tools etc. + goals