Here is the problem fully worked out.The above problem can be solved more easily by simply using a single reference number of 100 (try
it), but it is useful to know there is another option.
The next example is definitely easier to solve using two reference numbers.
96 × 67 =
We use reference numbers of 100 and 70.
We multiply 4 times 0.7 to get 2.8 (4 × 7 = 28). We subtract 2.8 from 67 by subtracting 3 and adding
0.2 to get 64.2. Then we multiply our answer of 64.2 by 100 to get 6,420. Multiplying the circled
numbers, 4 times 3, gives us 12.
6,420 + 12 = 6,432 Answer
That was much easier than using 100 as the reference number.
Here is another problem using 200 as our base reference number.
189 × 77 =
We use 200 and 80 as our reference numbers. Eighty is 0.4 of 200.We multiply 11 by 0.4 to get 4.4. (We simply multiply 11 times 4 and divide the answer by 10.) We
write 4.4 below the 11. We now subtract 4.4 from 77. To do this we subtract 5 and add 0.6. Seventy-
seven minus 5 is 72, plus 0.6 is 72.6.
72.6 × 100 = 7,260
We multiply 7,260 by 2 to get 14,520. (We could double 7 to get 14 and 2 times 26 is 52, making a
mental calculation easy.) Our work so far looks like this:
Now we multiply the numbers in the circles.
11 × 3 = 33
Add 33 to 14,520 to get 14,553. Here is the calculation worked out in full.