Chapter 19
DIRECT MULTIPLICATION
Everywhere I teach my methods I am asked, how would you multiply these numbers? Usually I will
show people how to use the methods you have learnt in this book, and the calculation is quite simple.
There are often several ways to use my methods, and I delight in showing different ways to make the
calculation simple.
Occasionally I am given numbers that do not lend themselves to my methods with a reference
number and circles. When this happens I tell people that I use direct multiplication. This is traditional
multiplication, with a difference.
Multiplication with a difference
For instance, if I were asked to multiply 6 times 17, I wouldn’t use my method with the circles as I think
it is not the easiest way to solve this particular problem. I would simply multiply 6 times 10 and add 6
times 7.
6 × 10 = 60
6 × 7 = 42
60 + 42 = 102 Answer
How about 6 times 27?
Six times 20 is 120 (6 × 2 × 10 = 120). Six times 7 is 42. Then, 120 + 42 = 162. The addition is easy:
120 plus 40 is 160, plus 2 is 162.
This is much easier than working with positive and negative numbers.
It is easy to multiply a two-digit number by a one-digit number. For these types of problems, you
have the option of using 60, 70 and 80 as reference numbers. This means that there is no gap in the
numbers up to 100 that are easy to multiply.
Let’s try a few more for practice:
7 × 63 =
You could use two reference numbers for this, so we will try both methods.
Firstly, let’s use direct multiplication.
7 × 60 = 420
7 × 3 = 21
420 + 21 = 441
That wasn’t too hard.
Now let’s use 10 and 70 as reference numbers.