Chapter 10
MULTIPLICATION USING TWO REFERENCE NUMBERS
The general rule for using a reference number for multiplication is that you choose a reference number
that is close to both numbers being multiplied. If possible, you try to keep both numbers either above or
below the reference number so you end up with an addition.
What do you do if the numbers aren’t close together? What do you do if it is impossible to choose a
reference number that is anywhere close to both numbers?
Here is an example of how our method works using two reference numbers:
8 × 37 =
Firstly, we choose two reference numbers. The first reference number should be an easy number to
use as a multiplier, such as 10 or 100. In this case we choose 10 as our reference number for 8.
The second reference number should be a multiple of the first reference number. That is, it should be
double the first reference number, or three times, four times or even sixteen times the first reference
number. In this case I would choose 40 as the second reference number as it equals 4 times 10.
We then write the reference numbers in brackets to the side of the problem, with the easy multiplier
written first and the second number written as a multiple of the first. So, we would write 10 and 40 as
(10 × 4), the 10 being the main reference number and the 4 being a multiple of the main reference.
The problem is written like this:
(10 × 4) 8 × 37 =
Both numbers are below their reference numbers so we draw the circles below.
What do we write in the circles? How much below the reference numbers are the numbers we are
multiplying? Two and 3, so we write 2 and 3 in the circles.
Here is the difference. We now multiply the 2 below the 8 by the multiplication factor, 4, in the
brackets. Two times 4 is 8. Draw another circle below the 8 (under the 2) and write −8 in it.
The calculation now looks like this:
Now subtract 8 from 37.
37 − 8 = 29
Write 29 after the equals sign.