Try using the reference numbers 9 and 11 to multiply 7 by 8.
Let’s try 9 first.
The numbers are below 9 so we draw the circles below. How much below 9? Two and 1. Write 2 and
1 in the circles. Subtract crossways.
7 − 1 = 6
Multiply 6 by the reference number, 9.
6 × 9 = 54
This is our subtotal.
Now multiply the numbers in the circles and add the result to 54.
2 × 1 = 2
54 + 2 = 56 Answer
This is obviously impractical but it proves it can be done.
Let’s try 11 as a reference number.
Seven is 4 below 11 and 8 is 3 below. We write 4 and 3 in the circles.
Subtract crossways.
7 − 3 = 4
Multiply by the reference number.
11 × 4 = 44
Multiply the numbers in the circles and add the result to 44.
4 × 3 = 12
44 + 12 = 56 Answer
This method will also work if we use 8 or 17 as reference numbers. It obviously makes more sense to
use 10 as a reference number for the calculation as we can immediately call out the answer, 56. Still, it