a 2 a+b - b Ex. 7. Add and together. 2aa +262 Ans. 2-62 a ta Ex. 8. Add 2, and together. at 40x Ans. aa 302 2 2x --3 Ex. 9. Add 20+ and 3x + together. 3 4 10x -17 Ans. 5x + 12 72 Es. 10. Add 4.0, ģ and 2+together. 44% Ans. 4x4-2+ 45 20 50 Ex. 11. Add 52 and ---4x together. 7 9 17 Ans. + 63 Ex. 12. It is required to find the sum of 2a, X2 and Ans. 2a +2+ a2 a a To subtract one fractional quantity from another. RULE. 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. с a -( -(-) с с с -( v2 +)=+ 9 axb 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 y y -b (Art. 128); to the fractional quantity it 5 ax ; to the mixed 5 5 3a +b 3a +b quantity 5x Y 3a+b -5x + ; and to the mixed quantity - 30+ Y 2 2 2-1 it becomes =3a с 2 =3a+ с 3x 520 Ex. 1. Subtract from 5 Here 30 X 7=21x) 25x - 212 numerators, 53 X5=25x 35 4.2 5X7=35 com, denom. is the differ 35 ence required. becomes -( :) " -(-3a+:-) с с 3b 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 15bc required. Or, by prefixing the negative sign to the quantity 20-40 2a-4 42-2a it becomes ; then it only 50 50 50 4xremains to add and together, as in ad50 36 dition, and the result will be the same as above. aX (-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 ad X2 2a +-2.1 ence required is 2ab-2ab+ al 22 ad X2 a - (2aba * )=–2ab+ a atx a 15 10x-_-9 38-5 Ex. 4. From subtract 7 Here (10x –9) X 7=70x—637 numerators. (3x ---5) X 15=45x—75 15X7=105 common denominator. 70x - 63 450-75 Therefore, 105 105 70-63-45%-+-75 25x+12 is the fraction requi105 105 red. 4ah Ex. 5. From subtract Ans. a+b a?-62 1 1 20 Ex. 6. From subtract Ans. at a? - 22. 4x+2 23 -- 3 4x2 +3 Ex. 7. From subtract Ans. 3 3х 3x a+ a-6 a Ex. 8. From 3x+; subtract x . с b cx-t-bx - ab Ans. 2x+ bc 2.0 +7 30? ta? Ex. 9. Subtract from 8 36 24x2 +8a2-6bx - 216 Ans. 246 2x - 3 -2 Ex. 10. Subtract 4x from 50+ 5 3 11-19 Ans. ** 15 a tox Ex. 11. Subtract from atala a(at) 4% Ans. a a ?? a Ex. 12. Required the difference of 3r and 3a +12x 3х — за Ans. 5 5 50-2 4x +5 Ex. 13. From 2x -+- subtract 3x 7 6 168 +23 Ans. 42 3 VI. MULTIPLICATION AND DIVISION OF ALGE BRAIC FRACTIONS. To multiply fractional quantities logether. RULE. 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= a 200 a с ac and 7 * 1 1 a a |