You can use any combination of reference numbers. The general rules are:
1 Make the main reference number an easy number to multiply by; for example, 10, 20 or 50.
2 The second reference number must be a multiple of the main reference number; for example,
double the main reference number, or three times, ten times or fourteen times the main reference
number.
There is no end to the possibilities. Play and experiment with the methods and you will find you are
performing like a genius. Each time you use these strategies you develop your mathematical skills.
Would we use two reference numbers to calculate problems such as 8 × 17 or 7 × 26? No, I think the
easy way to calculate 8 × 17 is to multiply 8 by 10 and then 8 by 7.
8 × 10 = 80
8 × 7 = 56
80 + 56 = 136
How about 7 × 26? I would say 20 times 7 is 140. To multiply by 20 we multiply by 2 and by 10.
Two times 7 is 14, times 10 is 140. Then 7 times 6 is 42. The answer is 140 plus 42, which is 182.
Experiment for yourself to see which method you find easiest. You will find you can easily do the
calculations entirely in your head.
Playing with two reference numbers
Let’s multiply 13 times 76. We would use reference numbers of 10 and 70. We wouldn’t normally use
80 as a reference number because we would have a subtraction at the end. Let’s try a few methods to see
how they work.
Firstly, using 10 and 70.
We multiply the 3 above the 13 by the multiplication factor of 7 in the brackets. Three times 7 is 21;
write 21 in a circle above the 3.
Now we add crossways.
76 + 21 = 97
Multiply 97 by the base reference number of 10 to get 970. Now multiply 3 times 6 to get 18. Add
this to 970 to get 988.
Here is the full calculation:
Now let’s try using reference numbers of 10 and 80.