

375 



ExAMPLE8.-(l.) Multiply m by a. 



m in ii a, . A tn atn 



, Xa= '. Fora= i5 and 7 X = ---. Ant. 



i ivy 



Multiply '" byo. 



" '' TO 



ili\iiliiii, r tho d. uoiuinator bya, wo have - , which ix tho 



j 



(>r, by tho former part of tho rule, mu 



am -r . am TO 

 wo have . But = , 

 , , cue ax x 



. 

 the denominator. 



\.MiM.r. Multiply n - by />. 



>, 



, * x b = a. For ~ X I = " But since the q 



00 



h tho numerator and denominator, it may bo cm 



it for tho product as brfniv. 



1 t't'i. On tho same principle, a fraction is multiplied into any 

 /; by cancelliny that factor. 



EXERCISE 21. 



1. Multiply - by d . 



c 2m 



2. Multiply a + - d by - * 



y w - - 



l,v 



1 J . 





3. 



4. Multiply a -? by ' ~ 



J 3+d c + y 



5. Multiply _L by -. 



a-rSr 8 



6. Multiply a - , and '- together. 



b' d y 



7. Multiply ^, '- d , -.and -i- together. 



nt v c r -I 



. Multiply 3 "*" b , \ and -- d g together. 



9. Multiply , *iIL-,aDa together. 

 .'/ d + 1 7 



10. Multiply '**, , and a?t together. 



:;-i 2d 



11. Multiply a -J by '"". 



y "'' 



12. Multiply om + d . i, wd l r together. 



ft m 5a 



13. Multiply - by (a - y). 



a-y 



14. Multiply 



3 + m 



by (8-t-m). 



15. Multiply - by y. 



by 



16. Multiply - h - by 6. 



EXERCISE 22. 



1. Multiply -, 4a , and 10a together. 

 25 21 



2. Multiply - by 



8. Multiply 



4. What is 



5. Multiply 



by 

 pro 



tt . 



lid,: + iVo/ 



4. What is the product of 3j: + v x g. 



by 5r. 



. Multiply 3 , * x , and - together. 

 x 3 b 



7. Multiply 



8. Multiply 



by *V 



3x + y abed 



by 



a-b 



0. What is the product of - x- ' x ? x 5. 



b d 4 a 



10. Multiply a - + b by a . 



11. Find the product of a x " x 6*. 



12. Find the product " x 







13. Multiply *~ 4 "" 



-a + * 



1*. Multiply u * bjr JL. 



rb * - 



x 



., 



10. Multiply . v by _ 



- 



LESSONS IN BOTANY. XXXIV 



SECTION XCVIII.-MAGNOLIACiLaS, OB MAUXOLIADS. 



Characteristics: Sepals tl:ree, rarely two, or four, or sir; 

 petals hypogynous at the base of an elongated receptacle, six or 

 more in number, and free; stamens indefinite; ovaries numerous 

 either free or partially cohen-nt ; bi- or pluri-ovalate ; ovules 

 penden; fruit various in character; carpels pedicollod. 



free, or cohort-lit into a spike ; dehiscent or indehisoent, dry or 

 fleshy; nocds having an elongated funicnlus; embryo very small 

 at the ba~o of a fleshy albumen. 



The Magnolias are beautiful trees of South America and 

 tropical Asia, possessing large, often persistent leaves, and mag- 

 nificent flowers. The M<iynolia glauca is a rustic shrub about 

 twenty feet hiyh. havinpr leaves yellow beneath, and very odorous 

 white flowers. The Magnolia Tlwnpsoniana (Fig. 257), a -. 

 of the preceding, is a fine pyramidal tree of about the same height, 

 and differing from the 3Ia<inolia. glmica in the circomstanco of 

 possessing larger leaves, and flowers five inches in diameter. 



SECTION XCIX.-DILLENIACEL5:, OB D1LLEXIADS. 

 Char' - ils free, five ; petals free, five, hypogy- 



nous ; stamens indefinite ; ovaries several, free, or Early frae* 



