This is something to play with and experiment with. We just used the same formula three different
ways to get the same answer. The last method (using a fraction as a multiplication factor) can be used to
make many multiplication problems easier.
Let’s try 96 times 321. We could use 100 and 325 as reference numbers.
We multiply 4 by 3¼ to get 13 (4 × 3 = 12, plus a quarter of 4 gives another 1, making 13). Write 13
in a circle below the 4, under 96.
Subtract crossways.
321 − 13 = 308
Multiply 308 by the base reference number of 100 to get 30,800. Then multiply the numbers in the
circles.
4 × 4 = 16
Then:
30,800 + 16 = 30,816 Answer
That can easily be done in your head, and is most impressive.Using decimal fractions as reference numbers
Here is another variation for using two reference numbers. The second reference number can be
expressed as a decimal fraction of the first. Let’s try it with 58 times 98. We will use reference numbers
of 100 and 60, expressed as 0.6 of 100.
(100 × 0.6) 98 × 58 =
The circles go below in each case. Write 2 inside both circles. Multiply 2 times the multiplication
factor of 0.6. The answer is 1.2. All we do is multiply 6 times 2 to get 12, and divide by 10.
Our work looks like this:
Subtract 1.2 from 58 to get 56.8. Multiply by 100 to get 5,680. Multiply the numbers in the circles: 2
times 2 is 4.
5,680 + 4 = 5,684 Answer