FRACTIONS 



2292 



FRACTIONS 



8 X648 

 2V6X2 _6 

 7 X2~14 



3X9 27 

 236X8^19 

 4X8 32 



ii x2 JL 



15X2 30 



4V&X6~2G 

 8^X10^ 82 

 12V4XlO m 125 

 4 X? j _28_14 

 3#X7 22 11 

 16X3 48 

 9%X3~29 



^ 

 94X20-15 



To reduce a complex fraction to a simple frac- 

 tion: (1) Multiply both terms by a number that 

 will rid numerator and denominator of fraction. 

 The simplest such number is the least common 

 denominator of these fractions. 



(2) Divide numerator by denominator; as, 



(3) Divide numerator and denominator by the 

 same number; as, 



5 - 



r* 



=% 



A more complicated form of complex frac- 

 tions is seen in such expressions as /J . This 



is simplified by multiplying both terms by 



2^+%X6 15+4 1Q . 

 the same number: g^*:^^ 



The third method is not generally applicable, 



as the divisor is not always apparent. The 



first method is generally the most satisfactory. 



Problems. (1) 6 Ib. 8 oz. is what part of 



20 Ib.? The part=^=i%o. 



(2) Three ladies divided a bolt of ribbon (10 

 yd.) in this way: Mrs. R. took 3% yd., Mrs. 

 M. took 4^ yd. and Mrs. Y. took 1% yd. For 

 what part of the bolt should each one pay? 



Mrs. R's part = -^=i%o=% 

 Mrs. M's part= TT = %O 

 Mrs. Y's part=^|=74o 



(3) When a working day is 7} hr., and the 

 wages are $4.50, how much does a man lose 



who is off duty 1% hr.? Loss=^| of $4.50=% 

 of $4.50=$.90. 



(4) A piece of fine lace 21% inches long is 

 marked to sell for $17. What part of the strip 

 is 15 inches? How much would it cost? 



(7) 6 months and 12 days is what part of a 

 year? ^=s %0 = %5 . 



(8) 9 months and 20 days is what part of a 

 year? 



(9) If the interest on $8000 is $480 for a 

 year, what should it be for 9 months and 20 

 days? 



A Fraction as an Expressed Division. (1) 

 Divide $2 equally among three men. What 

 does each receive? Answer, $%. This fraction 

 $% shows that $2 is divided into 3 equal parts, 

 and each part is $%. 



(2) Divide 5 yards of ribbon among 8 girls 

 equally. This division is indicated by % yard. 

 In % yard we see also what each girl receives ; 

 namely, % yard. 



So a fraction is an (a) indicated division, 

 and (b) the answer to such division. 



1 



13 



5 



200 



-8=% 

 7 = % 



4 = 20% 



The expression of division by the division 

 sign (-=-) should give way generally to the frac- 

 tion form because (a) of its more concise 

 form; and because (b) the quotient becomes 

 evident as the problem is set down; for ex- 

 ample, 2--i-9, %. 



Part Given to Find the Whole. Note in Fig. 

 28 that we have indicated the five equal parts 

 of a whole. 



1/2 Of 3/5 



FIG. 28 



% of a bolt of linen is worth $19. What is 

 it all worth? 



From the above drawing we see that a whole 

 bolt would be 2^ times as large as % of the 

 bolt. 



Solution : 



Cost of % of bolt =$19 

 Cost of bolt 



Make a drawing, and show how many times 

 one acre is as large as %e of an acre. It is 

 5% times as large. 



