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- b Ex. 7. Add and
2aa +262 Ans.
2-62 a ta Ex. 8. Add 2, and
aa 302 2
2x --3 Ex. 9. Add 20+ and 3x +
10x -17 Ans. 5x +
12 72 Es. 10. Add 4.0, ģ and 2+together.
44% Ans. 4x4-2+
50 Ex. 11. Add 52 and ---4x together. 7 9
17 Ans. +
63 Ex. 12. It is required to find the sum of 2a,
Ans. 2a +2+
To subtract one fractional quantity from another.
155. Reduce the fractions to a common denominator, if necessary, and then subtract the numerators from each other, and under the difference write the common denominator, and it will give the difference of the fractions required.
Or, enclose the fractional quantity to be subtracted in a parenthesis; then, prefixing the negative sign, and performing the operation, observing the same remarks and rules as in addition, the result will be the difference required.
The reason of this is evident; because, adding a negative quantity is equivalent to subtracting a positive one (Art. 63): thus, prefixing the negative
a-b sign to the fractional quantity
it becomes -b b
'; to the fractional quan+
a ? ta tity
it becomes y
-b (Art. 128); to the fractional quantity
; to the mixed 5
5 3a +b
3a +b quantity 5x
Y 3a+b -5x + ; and to the mixed quantity - 30+
2-1 it becomes
с 2 =3a+ с
3x 520 Ex. 1. Subtract from
5 Here 30 X 7=21x)
25x - 212 numerators, 53 X5=25x
4.2 5X7=35 com, denom.
is the differ
35 ence required.
2a-428 1-Y Ex. 2. Subtract from
50 Here (2a --4x) x 3b=6ab-12bx
numerators. (-y) x 5c= 50. - 5cy S
50 X 36=15bc common denominator.
5cx — 5cy Whence,
15bc 12bx--6ab_5cx-5cy +126x —Gab
is the difference 15bc
Or, by prefixing the negative sign to the quantity 20-40
42-2a it becomes
; then it only 50
50 4xremains to add
together, as in ad50
36 dition, and the result will be the same as above.
(-X Ex. 3. From 2ab +
subtract 2ab a to
at Here prefixing the negative sign to the quantity 2ab
we have - 2abatæ
hence the difference of the proposed fracat tions is equivalent to the sum of 2ab + and
at - 2ab to
; but the sum of the fractional parts a
at 2a2 +- 2x2 and is
: Therefore the differatoa
2a +-2.1 ence required is 2ab-2ab+
al 22 ad X2
- (2aba * )=–2ab+
38-5 Ex. 4. From
7 Here (10x –9) X 7=70x—637
numerators. (3x ---5) X 15=45x—75
15X7=105 common denominator.
70x - 63 450-75 Therefore,
105 70-63-45%-+-75 25x+12
is the fraction requi105
4ah Ex. 5. From subtract
a?-62 1 1
20 Ex. 6. From subtract
a? - 22. 4x+2
23 -- 3
4x2 +3 Ex. 7. From subtract Ans. 3
Ex. 8. From 3x+; subtract x
cx-t-bx - ab Ans. 2x+
bc 2.0 +7 30? ta? Ex. 9. Subtract from
36 24x2 +8a2-6bx - 216 Ans.
246 2x - 3
-2 Ex. 10. Subtract 4x
from 50+ 5
11-19 Ans. **
15 a tox Ex. 11. Subtract
4% Ans. a
Ex. 12. Required the difference of 3r and 3a +12x
3х — за
4x +5 Ex. 13. From 2x -+- subtract 3x
168 +23 Ans.
3 VI. MULTIPLICATION AND DIVISION OF ALGE
To multiply fractional quantities logether.
156. Multiply their numerators together for a new numerator, and their denominators together for a new denominator; reduce the resulting fraction to its lowest terms, and it will be the product of the fractions required.
It has been already observed, (Art. 119), that when a fraction is to be multiplied by a whole quantity, the numerator is multiplied by that quantity, and the denominator is retained :
100 Thus, 6 xc="C, and ** 5=%"; or, which is =
X5 b b
b the same, making an improper fraction of the integral quantity, and then proceeding according to the
2x 5 10. rule, we have xi b b'
b. Hence, if a fraction be multiplied by its denominator, the product is the numerator; thus, g xb=
and 7 *