FRACTIONS 



22SG 



FRACTIONS 



To add mixed numbers, find the sum of the 

 whole numbers; find the sum of the fractions, and 

 combine the results. Answers in addition of frac- 

 tions and of mixed numbers should be reduced to 

 their simplest forms. 



Subtraction of Fractions. (1) Jane has % 

 of a yard of flowered ribbon. She cut off % 

 of a yard for her doll's skirt; % of a yard for 

 her jacket, and made a pretty hand-bag out 

 of what was left, 



(a) % yd. - % ^ 

 yd. = % yd. = V4 yd. 



(b) % yd. - % 

 yd.zz% yd.zz^4 yd. 

 (See Fig. 11.) 



(2) Subtract (a) K from %; (b) % from %; 

 (c) % from %; (d) % from %; (e) % from %. 



(a) %-V4=% 



(b) %-%=% 



(c) %-%=% 



(d) %-%=% 



(e) %-%=% 



(3) Mr. Stevens owned 3 %4 of a section of 

 land; he sold to Mr. Miles *%4 of a section. 



(a) What part of a section had he left? 



(b) How much more land had Mr. Miles, then, 

 than Mr. Stevens? 



(a) 87^4 section 19^4 sectionzzi% 4 section 



(b) !%4 section 1%4 section = %4 section. (See 

 Fig. 12.) 



1/64 



.=% 4 Ib. 



(See Fig. 13.) 



(6) %-%=n. 



%-%=%-%=% 



(7) %-%=n. 



1 9i6-% = iyi5-19iB 



(8) %-%=n. 



j V6=^4 %4 = 1 /$4- (See Fig. 14.) 



-9- 



3? 



FIG. 12 



(4) A train ran % of a mile the first minute, 

 % of a mile the second. What was the increase 

 of speed the second minute? 



(5) How much 

 heavier is % of a 

 rectangular cake 

 of candy than % 

 of it, the whole 

 weighing one 

 pound? 



.-%e lb.=iVio 



(10) % a -%=n 

 7Ae-%6= 



(ID %.-Mc=n 



^e-Vie 



(12) % 6 -U=n 



(1) When fractions have the same unit of 

 measure subtract the numerator of the subtra- 

 hend from that of the minuend, as in the first set 

 of problems given above. 



(2) When fractions have not the same unit of 

 measure express them in terms of the same unit 

 or in terms of their least common denominator 

 and subtract as in 1. 



Addition and Subtraction of Unit Fractions. 

 A fraction whose numerator is 1 is called a 

 unit fraction, as, }, %. 



- 



The sum of two unit fractions is the sum of the 

 denominators over the product of the denomi- 

 nators. 



FIG. 13 



I/a -1/6 = 



7X6~ 

 ba 



