3 × 7 = 21
420 + 21 = 441
The calculations were almost identical in this case, but I think the direct method was easier.
How about 6 × 84?
6 × 80 = 480
6 × 4 = 24
480 + 24 = 504
Now using two reference numbers we have:Subtracting 36 from 84 we get 480. Four times 6 is 24, then 480 + 24 = 504.
Happily, we get the same answer. This time the direct method was definitely easier, although, again,
the calculations ended up being very similar.
Let’s try one more: 8 × 27.
By direct multiplication we have:
8 × 20 = 160
8 × 7 = 56
160 + 56 = 216
Now using two reference numbers we have:
This time the calculation was easier using two reference numbers.
Is it difficult to use direct multiplication when we have a reference number of 60, 70 or 80? Let’s try
it for 67 times 67. We will use 70 as our reference number.
We subtract 3 from 67 to get 64. Then we multiply 64 by our reference number, 70. Seventy is 7
times 10, so we multiply by 7 and then by 10.
Seven times 60 is 420 (6 × 7 = 42, then by 10 is 420).
Seven times 4 is 28. Then, 420 + 28 = 448, so 7 times 64 is 448, and 70 times 64 is 4,480.
Multiply the numbers in the circles: 3 × 3 = 9. Then:
4,480 + 9 = 4,489 Answer
Even if you go back to using your calculator for such problems, you have at least proven to yourself
that you can do them yourself. You have acquired a new mathematical skill.