The AUamont Enterprise - Thursday, March 16,2000
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\S^*Sp*AS0,
letters.Deadline for letters is Tuesday at noon.
Community needs school addition
To the Editor:
As an eighth-grade student at
Voorheesville's High school, I
know firsthand how much this
community needs the proposed
school addition.
Recently o u r school w a s
picked to be one of the top
schools in America for its music
program. How are we to maintain these standards when we
have no room to expand?
Both the stage and hall leading to the band room are used as
storage areas and there is lim-
ited space for i n s t r u m e n t a l
lessons and practice sessions.
S t u d e n t s are often forced to
practice on the stage, in one of
the music teacher's tiny offices,
or in the hallways.
Voorheesville takes pride in
its students' artwork, which is
often displayed in cabinets and
on the walls for all to see. But,
did you know t h a t students in
grades seven through 12 are
sculpting, drawing, and painting
in an old teachers' lunchroom?
That room is extremely small
The Albany County Department of Health will be conducting a
RABIES IMMUNIZATION CLINIC
for
CATS A N D DOGS
at the
BERNE HIGHWAY GARAGE
Helderberg Trail, Route 443, Berne, N.Y.
SATURDAY, MARCH 18, 2000
1.00-2:30 p.m. for CATS
2:30-4:00 p.m. for DOGS
Donation: $5.00 per animal
A Service for Albany County Residents
OPENINGS AVAILABLE
SCHOOL YEAR PROGRAMS • MONTHLY FEE
3's Tuesday and Thursday — 8:30 -11:30 a.m.
4's Monday, Wednesday and Friday — 8:30 -11:30 a.m.
YEAR ROUND PROGRAMS • WEEKLY FEE
Toddlers, 3's and 4's
Minimum 3 days attendance.
Outdoor Activities -» - • Arts n' Crafts
Snacks"/Lunch-™ — • Individual Attention
Prayers and Bible Stories-m - « School Readiness
14 years in Business
Open Door Policy 7 a.m. - 6 p.m.
for an a r t room and could be
dangerous when fumes from
paint and glue are released into
that workspace. Equipment,
supplies, and projects are stored
all over both rooms, making it
hard to move around the room
when everybody is working on
their projects.
When I was younger, swimming lessons were a part of my
summers. I have learned a lot in
the pool at Voorheesville. The
pool has served t h e community
as a place for swimming lessons,
swim teams, and gym classes.
If the addition is not added,
the community will no longer
have a pool. The current pool is
too expensive to maintain and
will be closed whether the addition is added or not. P a r e n t s in
this district will be either forced
to t a k e their children somewhere else to learn to swim or
deprive their children of a great
learning experience.
As p a r t of both t h e D r a m a
Club and the music program, I
often work on t h e stage and in
its surrounding areas. Our present auditorium is very small.
The elementary winter concert
was held at the high school au ditorium this year. Many parents were forced to stand outside
in-the hall because t h e r e was
not enough room for everyone in */
the auditorium. The high school
band and chorus barely fit on
the stage.
The proposed school addition
is a wise investment for t h e fut u r e of our community. The
question is not, "Can we afford
it?" but, "Can we afford not to?"
Matthew Zimmerman
Voorheesville
This is the last issue
for letters to the
editor on the
Voorheesville School
bond vote, since the
vote is March 28.
C a l l for r a t e s 8 6 1 - 5 0 6 7
j a y
mm
.Mimmmm
»
The Enterprise REAL ESTATE
AND HOME GUIDE
Discount:
Advertise in this section at the regular rate of '9.85/ col. inch and get
15% OFF your ad of equal or smaller size in our HOME & GARDEN
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By B r y c e B u t l e r
Math is seldom honored these days for its own sake. So this
week w h e n t h e Guilderland High School is celebrating Pi,
(3.14159...) a t 1:59 p.m. on 03/14 (Tuesday) seems a good opportunity to celebrate an example of the magic that is among the most
available charms of arithmetic.
Setting the nine-times table up vertically immediatly reveals
the magic symmetry:
1x9 =
09
2x9 =
18
3x9 = 27
4x9 = 36
5x9 = 45
6x9 = 54
7x9 =
63
8x9 = 72
9x9 = 81
10x9 = 90
As the numbers rise by one in the ten's column, they go down in
the one's column, so the two columns each use all the digits once,
in reverse order. Every multiple of nine (through 10 times 9) is the
opposite of another.
Naturally, subracting any multiple of nine from another yeilds
an answer divisible by nine (for instance, 63-27 = 36). Because
every one of the multiples is the opposite of another, turning around
any two digits in an addition problem gives an answer higher or
lower than the correct answer by some multiple of nine. (Enterprise reporter Kathy Hill-Brown noticed this when she worked in
a credit union).
For instance, if you're adding:
57
22
34
98
18
the answer is 229.
Now let's say you copy down a ntllmber backwards; say you write
"57" as "75." The new answer is 247, and 247-229 is 18, which is
2x9. This works for addition or subtraction.
It works also for transposed pairs of digits in longer numbers.
For instance, 57302+12997 = 70299. If the first two digits a r e
turned around, you have 75302+12997 = 88299. Subtracting t h e
first answer from the second (88299-70399) givesl8O00, or 9x2000.
You can even transpose two pairs of digits in a long number:
964761-53247 = 431914; 9654761-352874 = 611887; subracting the
first answer from the second (611887-431914) = 179973, which is
19997 x 9.
Now add up the digits of 179973:1 plus 7 is 8, plus 9 is 17, plus
9 is 26, plus 7 is 33 plus 3 is 36. This total (36) is a multiple of 9. Its
two digits (3 plus 6) add up to nine. This is true of any multiple of
v
nine.
For instance, since we're celebrating Pi, take the first 20 digits
of t h a t n u m b e r ( w i t h o u t t h e d e c i m a l ) . T h e y a r e
314159265358979323846. Multiply this by 9, and the answer is
2827433388230813914614. Add these digits together, and the answer is 90, which is almost too neat to be true. I tried it with another long number, generated from some metric figures, and got
135, or 9 times 15.
This property holds for any multiple of 9, as well as 9 itself.
When I deliver The Enterprise to stores, I multiply the number of
unsold papers by $.45, to find what to credit for the bill. Just as
with multiplying by 9, multiplying by 45 gives a string of digits
t h a t add up to 9 or some multiple thereof. Since we stay up very
late Wednesday nights putting the paper together, I am frequently-.,
somewhat zombified when I do this multiplication, so I have taken
to checking it by adding the digits of the answer, and I have found
mistakes t h a t way.
Like 9 itself, 45 is an interesting number. It is 5 times 9, and so,
of course, half of 10 times 9, or 90. This would be true for any
number. But here again, 9 is special. Returning again to the column of the 9 times table, you can see that 4.5 is not only mid-way
between 0 and 9, it is half-way between any of the two pairs of
numbers in the 9 times table, so:
09
0 plus 4.5=4.5, plus 4.5=9
18
1 plus 3.5=4.5, plus 3.5=8
27
2 plus 2.5 = 4.5, plus 2.5 = 7
36
3 plus 1.5 = 4.5, plus 1.5 = 6
45
4 plus .5 = 4.5, plus .5 = 5.
2
3
4
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The magical 9-times table
L
4.5
- . 5 - 9x5-.5
4.5
9x 1
5
6
!
!
7
8
(
I
!
1
i
i
4.5 -
Because the numbers in the second half of the list are the same,
the rest (54, 63, 72, 81, and 90, are the same in reverse.
Neat, huh?
On the 9-times table, either column (123456789) adds up to 45
— half of 90.This is because the average of each column is 5, and 9
times 5 is 45.
Adding up all the two-column numbers gives 495 — 45 with a 9
stuck in the middle, sort of like the group was taking a bow at the
end of the show.
This is all I know. Math students are welcome to come up with
more, and students of algebra are invited to come up with reasons
why all this neat stuff works for nines, and not for other numbers.
The Enterprise
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