MATHEMATICAL RECREATIONS 187

 

Bx. 1s 27

Upper 14 15 60 15

Exact 7 30 120 240

Lower 3 60 480 T

Lower t-=120 i ol
. : 660

Upper 1 240 255

Lower 0 480 =

27 % 15 = 405 Ans.

This rule follows from § 98, since the remainder corre-
sponding to an exact quotient is 0, that corresponding to a
lower quotient is 1, and the remainder corresponding to an
upper quotient is — 1.

This rule also is tru for numbers written in any radix no-
tation.

Ex. 2. Multiply 27 and 15 by this rule, choosing, when the
quotient is not exact, that one of the two approximate quo-
tients which is even.

Ex. 3. Multiply 359 and 422 by this rule. Check by cast-
ing out the 3’s.

Ex. 4. Multiply 3689 and 2728 by this rule. Check by
casting out the 9’s.

473. Rule 3. The Ternary Rule for Multiplication. The
same as Rule 2 with the following changes:

Divide by 3 instead of by 2 and always choose the quotient
which gives the remainder 0, 1, or — 1.

Triple instead of double.

This rule also is correct for any radix notation.

Ex. 1. 48

Exact 16 21 63 189

Lower 5 63 1701 567
Tpper 2 — —

Ypper' - w25l 1764 756

Uppert 1 567 =

Lower 0 1701 il

 

48 X 21 = 1008 Ans.

Ex. 2. Multiply 979 and 639 by the ternary rule and check
by casting out the elevens.