FRACTIONS 



2291 



FRACTIONS 



(5) Matting % yard wide is used to cover 

 the floor of a hall 18 yards wide. How many 

 strips are required? 



(6) A rectangle has an area of %o square 

 inch; it is % inch wide. How long is it? 



(7) How many jugs each holding 1% gallons 

 can be filled from a barrel (31^ gallons)? 



Complex Fractions. Nellie has 3 pieces of 

 ribbon each % yard long. She gives Sarah 

 one-half of the ribbon by giving her one piece 

 and half of another piece. Sarah now has 



- of a yard, and Nellie has left -^f- of a 

 2i & 



yard (see Fig. 25). 



!/2 yd. 



/2yd 



FIG. 25 



A cake is cut by the baker into 8 equal parts. 

 % is sold. Mrs. Hughes, going to the shop, 

 buys % of what 

 is left. What 

 part of the cake 

 does she get? 

 She gets % of % 

 2% 



or 



8 



What 



part of the cake 



is left? ^. (See Fig. 26.) 



FIG. 26 



%0f 2% 3 - 



4% 

 23 



Study Fig. 27, below. 



Cost of cap = - of his money 



1 - 



Cost of gloves -|^ " " " 

 Cost of shoes = ^=- " " " 



Cost of ties =T7r " " " 



u 



Cost of candy r^- " " " 



o 



Cost of turkey =: " 

 Cost of all = " " 



1 is what part of 7 ? Answer, 



2 is what part of 7? Answer, 



21A 



2% is what part of 7? Answer, =^. 



3^ is what part of 7? Answer, -~. 



2% months is what part of a year? Answer, 



12' 



6 mo. 10 da. is what part of a year? Answer, 



12' 



1 ft. 3 in. is what part of a yd.? Answer, 



2 pk. 3 qt. is what part of a bu.? 

 2% 

 4 ' 



Answer, 



Such fractions as those given above grew 

 out of the conditions presented. 



A fraction which has a fraction or a mixed 

 number in either or both oj its terms is called 

 a complex fraction, 



The complex fraction, despite its name, is a 

 very simple and necessary tool in mathematics. 

 It serves (1) to express concisely and readily 

 what part one number is of another. For 

 example, 1 ft. 9 in. is what part of 1 yd.? 



9 in .=% ft. 1% ft.=^ yd. 



o 



8 mo. 24 da. is what part of 1 jr.? Answer, 

 8% 

 12* 



9/10 



FIG. 27 



Michael had $12 at Christmas. He spent $1 

 for a cap; $1% for gloves for his mother; $3^ 

 for shoes; Jl^i for neckties; $1% for candy, $3 

 for a turkey. What part of his money did he 

 spend for each purchase? 



The complex fraction serves (2) to express 

 division. Divide 4% yards of ribbon among 8 

 children. What part of a yard does each re- 



4% 

 ceive? Answer, . 



o 



A machine travels 2 1: J42 miles in 2^> min- 

 utes. What is the rate per minute? Answer, 

 2% 

 2% ' 



Reduction of Complex Fractions. The fol- 

 lowing problems illustrate the reduction of 

 complex fractions: 



