The citizen. [volume] (Berea, Ky.) 1899-1958, 1905-07-13
Berea Teachers
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Nlqbe<% LEwIs, BEREA, Ky.


week Of general interest. One is, as
to the importance of Decimals and
the other concerns the old question
Of inverting the diyisor in division Of
fractions.
AS to the first, would say that
there is no more important topic in
Arithmetic. In actual business deci-
mails are rapidly superseding COM
mon fractions because of their great
er simplicity.
They should be studied after quite
a thorough understanding Of com
mon fractions has been attained. Be
sure in your teaching to emphasize
the following points: First, that
there are no new principles involved,
and that decimals are only a special
case in which the denominator is ten
or some power OF ten. Give much
practice in writing equivalent ex-
pressions such as 3 $40, .27 -
27-l00, .003 ~ $1,000, and 2-5-
a, S-25 - .32, etc. Second, that
point is placed between the unit and
the tenths periods and that from
there ON to the right one unit in every
period is equal to ten nnits in the
next period to the right just as in
whole numbers. Drill until pupils
know just as thoroughly that three
standing in the second period to the
right Of the decimal point is three
hundredths as that three standing in
the second period to the left Of the
decimal point is three tens. Spend
much time ON writing decimals. Do
not quit until your pupils read and
write them as readily as whole num-
bers.
You will have no trouble with ad-
dition and subtraction il you have
done good work up to that point.
When you come to multiplication
you will have no trouble to teach
the process. To teach the reason
may be more difficult. Remember
that when the multiplier is unity
the product will be of the same or
der as the multiplicand, and that as
you decrease the multiplier you will al
so decrease the product, so that the
product will contain the number of
decimal places occurring in the null
tiplicand plus the number in the
multiplier. Have work frequently
done in both common and decimal
fractions e. g. Sxs - rs K .S75.
In division keep in the mind of
the pupil the fact that when the par
tial dividend used is of the same Or
der as the divisor, the figure in the
quotient will be in the unit period.
In division of common fractions |
would always teach inverting the di-
visor from the first as it will be used
by every pupil sooner or later and is
just as easily explained as the pro-
cess of reducing to common denomi-
nator.
From the beginning of oral arith-
metic work the child should know
that one whole thing is four fourths,
seven seventies, thirteen thirteenths,
ETC., and that is contained four
times in one whole unit, II seven
times, etc. That is, they must
know thoroughly the relation exist
ing between the unit fraction II
and the fractional unit II. With
this knowledge you come to the place
where you wish to find how many
times is contained in 4. You lead
the child's mnid in this way: How
often is contained in one unit
-Four times How often will be
contained in one unit, them as
often, that is of 4 times or As
times, because Is three times as
large as I. Theu il 7 is contained
in one unit As times it will be con-
tanned in four units 4 4-3 times
or 1873 times. just as simple is the
problem How often is 81 contain
ed in 3-l9. You reason again that
since II is contained Z times in one
unit, 81 will be contained l-5 of Z
times or 10 times in one unit, and
il it is contained rs times in one
unit it will be contained 2-l3 Of rs
times in 2-l3 of a unit, or l485
times.
In this way child soon sees that
the divisor inverted gives an express
ion for the number of times the di-
visor is contained in unity, and that
in any other number, fractional or
or integral it will be contained that
number of times as often as in one
unit.
Later on, all that need be put on
the board is the equation indicating
the operation, which may be briefly
explained thus; Since 81 is con-
tanned 10 times in one unit it will
be contained 2-13 of 7-5 times or
1865 times in 2-l3 OF one unit.