Chapter 6
MULTIPLICATION USING ANY REFERENCE NUMBER
In Chapters 1 to 4 you learnt how to multiply numbers using an easy method that makes multiplication
fun. It is easy to use when the numbers are near 10 or 100. But what about multiplying numbers that are
around 30 or 60? Can we still use this method? We certainly can.
We chose reference numbers of 10 and 100 because it is easy to multiply by 10 and 100. The method
will work just as well with other reference numbers, but we must choose numbers that are easy to
multiply by.
Multiplication by factors
It is easy to multiply by 20, because 20 is 2 times 10. It is easy to multiply by 10 and it is easy to
multiply by 2. This is called multiplication by factors, because 10 and 2 are factors of 20 (20 = 10 × 2).
So, to multiply any number by 20, you multiply it by 2 and then multiply the answer by 10, or, you
could say, you double the number and add a 0.
For instance, to multiply 7 by 20 you would double it (2 × 7 = 14) then multiply your answer by l0
(14 × 10 = 140). To multiply 32 by 20 you would double 32 (64) then multiply by 10 (640).
Multiplying by 20 is easy because it is easy to multiply by 2 and it is easy to multiply by 10.
So, it is easy to use 20 as a reference number.
Let us try an example:
23 × 21 =
Twenty-three and 21 are just above 20, so we use 20 as our reference number. Both numbers are
above 20 so we put the circles above. How much above are they? Three and 1. We write those numbers
above in the circles. Because the circles are above they are plus numbers.
We add diagonally:
23 + 1 = 24
We multiply the answer, 24, by the reference number, 20. To do this we multiply by 2, then by 10:
24 × 2 = 48
48 × 10 = 480
We could now draw a line through the 24 to show we have finished using it.
The rest is the same as before. We multiply the numbers in the circles:
3 × 1 = 3
480 + 3 = 483
The problem now looks like this: