MULTIPLICATION BY FIVE

The rule for multiplying by 5 is like those for 6 and for 7, but simpler. Instead of adding in the “number” as we do for 6, or doubling it as we do for 7, we use the “number” only to look at. We look at it and see whether it is odd or even. It it is odd we add in the 5, as before:

Half the neighbor, plus 5 if the number is odd.

Suppose we wish to multiply 426 by 5:

0 4 2 6  /  0  x  5   look at 6, it is even; there is no 5 to add;                      there is no neighbor

0 4 2 6  / 30  x  5  look at 2, it is even, use half of 6

0 4 2 6  / 130 x  5  look at 4, it is even; use half of 2

0 4 2 6  / 2130 x 5 look at zero, it is even, use half of 4

Now if we had an odd digit in the multiplicand we would add 5:

0 4 3 6   /  0    x  5   as above

0 4 3 6  /   80  x  5   the 3 is odd; say 5 plus 3

0 4 3 6  / 2180  x 5 

This is easy to do. There is very little figuring involved. It seems rather odd at first, though, because of the little mental twist that you have to do: you use the neighbor, rather than the digit at the place where you are working. Actually it is good practice in keeping one’s place.  Later on, in multiplying one long number by another long number, we shall find that a certain amount of concentration is needed to remember where we are in the number we are multiplying. This multiplication method for 5 is a little preliminary practice.