Education > Complete treatise on practical arithmetic and book-keeping

59
REDUCTION OF VULOAR FRACTIONS.
Note S. Any number is divisible
y 3, if the sum of its digits be so:
bus 417 is divisible by 3; because
which is the sum of 4, 1, and
.U so.
Examples.
45 __15— 3
120“40 .8
126 __ '
411
534
672
Note 5. When any number which is expressed by several others with
e sign of addition or subtraction between them, is to be divided by
ty number; then all the parts of it must be divided by this number.
Note 6. But if the given number be expressed by others with the sign
.multiplication between them, only one of them must be divided: So
7x3x8x10 3x4x10 _1x4x10_1x2x10_2Q
1x6
Note 4. If there be any ciphers
at the end of each, cut off as many
as are common to both.
Examples.
200 20 10
340 34~17
1200
18000“
Thus-
■i+c!—§=2+3—4=5—4=1.
2
7x2x6
1x2
-20.
1x1 1
> in both the numerator
And in this case, when the same number is
d denominator, it may be left out of them.
N. B. But instead of writing down the whole fraction anew after every
vision in the abbreviation, as is here done in this last example in five
BFerent values One after another in the whole length of the line, the
Driest method, and which is constantly practised by those who best
ow the value and use of this part of the abbreviation, is thus: whal¬
er numbers are abbreviated, or which cancel one another, draw a small
through them with the pen, and place the quotients of the numbers
ove them or below them, according as they are in the numerator or
ii nominator. So the foregoing fraction being here again written down
or draw a small line through the two
, because they cancel each other, as
ing equal; then dash the 3 and the 6, 2
d write the quotient 2 below the 6; next
sh the 8 and a 9, writing the quotient 4 /v^vqvio
ove the 8 : lastly, dash the 4 and the o- "—r .-I =20.
r 2, writing the quotient 2 above the 4: ]j xplxp
re being then no more figures to divide g'
multiply together the numbers 2 and
, which are not dashed, and the product
is the value of the fraction required.—And in this manner let the pu-
be exercised in many examples in this rule till he is perfect in it, be-