Chapter
NUMBERS ABOVE THE REFERENCE NUMBER
What if you want to multiply numbers above the reference number; above 10 or 100? Does the method
still work? Let’s find out.
Multiplying Numbers in The Teens
Here is how we multiply numbers in the teens. We will use 13 × 15 as an example and use 10 as our
reference number.
Both 13 and 15 are above the reference number, 10, so we draw the circles above the numbers,
instead of below as we have been doing. How much above 10 are they? Three and 5, so we write 3 and
5 in the circles above 13 and 15. Thirteen is 10 plus 3, so we write a plus sign in front of the 3; 15 is
plus 5, so we write a plus sign in front of the 5.
As before, we now go crossways. Thirteen plus 5 or 15 plus 3 is 18. We write 18 after the equals sign.We then multiply the 18 by the reference number, 10, and get 180. (To multiply a number by 10 we
add a 0 to the end of the number.) One hundred and eighty is our subtotal, so we write 180 after the
equals sign.
For the last step, we multiply the numbers in the circles. Three times 5 equals 15. Add 15 to 180 and
we get our answer of 195. This is how we write the problem in full:
If the number we are multiplying is above the reference number we put the circle above. If the
number is below the reference number we put the circle below.
If the circled number is above we add diagonally. If the circled number is below we subtract
diagonally.
The numbers in the circles above are plus numbers and the numbers in the circles below are minus
numbers.