\fdO'^ - Old Forge Coal Mines

ALGEBRA. 107
l^ + U- 6c- 3d
— lla + 2d-^-\-4:d
3a + 6d— 10c + d
Adding each term of the subtrahend (with the sign
changed) to its corresponding term in the minuend, the difference,
or result, is 3a-{- Qd — lOc -\- d. Ans.
(203) The numerical values of the following, when a
= 16, ^ = 10, and ;r = 5, are:
{ab'x + %abx) 4^ = (16 X 10' X 5 + 2 X 16 X 10 X 5)
{a)
X 4 X 16. It must be remembered that when no sign is
expressed between symbols or quantities, the sign of multiplication
is understood.
(16 X 100 X 5 -H 2 X 16 X 10 X 5) X 64 = (8,000 + 1,600)
X 64 = 9,600 X 64 = 614,400. Ans.
{b) 2^4^ -li^ + ^lHf:.. a-2^/64- b '
"
'
X
16 - 10
10-5 ,^ 100 , , 96-100 + 6 2 1 .
-^- = 16-— +1 = _^_ = _^_ Ans.
{c) {b - \^) {x' - b') {a' - b") = (10 - VT6) (5' - 10')
(16' - 10') = (10 - 4) (125 - 100) (256 - 100) = 6 X 25 X
156 = 23,400. Ans.
(204) (a) Dividing both numerator and denominator
by 15 m —— xy', '-fj- = .
•' "^ '
75 ;« x'y
Ans.
5 xjy
.,. x'-l (x-\-l){x-l) ,
-—7—-—-- = -^^— ^, ^
H—/ , ^.
^'
lo)
4;ir(;r+l) 4^'(;ir+l)
when the numerator is
factored.
Canceling {x -]- 1)
X — 1
inator (Art. 484), the result is — — .
j
from both the numerator and denom-
Ans.
'
'
(c) ;
,.: ;
, ,,! when factored becomes
^ '
{a' — b^) {a' — ab-\- b)
{a + b){a^-ab-^b^){a^ + ab + b*)
{^a-b){d' + ab-\- b') {a^-ab + bj
^ ^^^''
.