Chapter 4
MULTIPLYING ABOVE & BELOW THE REFERENCE NUMBER
Until now, we have multiplied numbers that were both below the reference number or both above the
reference number. How do we multiply numbers when one number is above the reference number and
the other is below the reference number?
Numbers Above and Below
We will see how this works by multiplying 97 × 125. We will use 100 as our reference number:
Ninety-seven is below the reference number, 100, so we put the circle below. How much below?
Three, so we write 3 in the circle. One hundred and twenty-five is above so we put the circle above.
How much above? Twenty-five, so we write 25 in the circle above.
One hundred and twenty-five is 100 plus 25 so we put a plus sign in front of the 25. Ninety-seven is
100 minus 3 so we put a minus sign in front of the 3.
We now calculate crossways. Either 97 plus 25 or 125 minus 3. One hundred and twenty-five minus 3
is 122. We write 122 after the equals sign. We now multiply 122 by the reference number, 100. One
hundred and twenty-two times 100 is 12,200. (To multiply any number by 100, we simply put two zeros
after the number.) This is similar to what we have done in earlier chapters.
This is how the problem looks so far:
Now we multiply the numbers in the circles. Three times 25 is 75, but that is not really the problem.
We have to multiply 25 by minus 3. The answer is −75.
Now our problem looks like this:
A shortcut for subtraction
Let’s take a break from this problem for a moment to have a look at a shortcut for the subtractions we
are doing.
What is the easiest way to subtract 75? Let me ask another question. What is the easiest way to take 9