FRACTIONS 



Study Fig. 16. Note that each of the small 

 divisions is equal to the product of }4 by %. 



FIG. 16 



1 2 



=% X '%! = 



1 8 



2 2 



Cancel when possible, as above. 

 Then follows the multiplication of mixed 

 numbers. 



(1) A farmer sells milk at 8% cents a quart. 

 He sells 9 quarts one day. What are his re- 

 ceipts? 



He receives for his milk 9x8^or75<f. (9X8) 

 + (9 XW> =72 + 3 = 75. 



(2) What will 13 feet of hose cost at 

 per foot? 



Cost=il3 X 16%<!= 

 . 16% 

 13 

 48 



_ 

 2082%=216% 



(3) What is the area of a flower-bed 5 feet 

 long and 3% feet wide? (See Fig. 17.) 



5ft. 



FIG. 17 



Lengrth = 5ft. 



Width = 3% ft. 



Area in sq. f t. = 5 X 3% = 1 8% 



Construct other diagrams similar to the one 

 shown in Fig. 17, showing the methods of solu- 

 tion of the following problems: 



3 x 41/4 



7X6% 



FRACTIONS 



(4) How many square yards in a floor 6% 

 yards long and 5V& yards wide? (See Fig. 18.) 



&yd. 



FIG. 18 



Length = 6% yd. 



Width = 5% yd. 



Area in sq. yd.= (6 X 5) + (6X V6) + (5 X%) + 



Area in sq. yd. = 30 + 3 + 3% + W = 

 The full process is shown below : 



6% 

 5% 



30 

 3% 

 3 



36% 



8% 

 4VS 



32 

 1% 

 4% 



37% 



(1) 

 (2) 

 (3) 

 (4) 



4 X8 =32 

 4 X %= 1% 

 %X8 = 4 

 ViX %= % 



A mixed number is multiplied by a mixed 

 number in another way, namely, by reducing 

 both mixed numbers to fractions, and multiply- 



ing; for example, 



Division of a Fraction by a Whole Number. 

 (1) % of an acre of land is to be planted in 

 lettuce, onions and radishes, giving to the 

 vegetables equal spaces. What amount of land 

 is planted in each? 



% of % A. = % A., or % A. -5-3 = 1/4 A. 



(2) A man gives his wife % of his fortune, 

 and divides the rest equally between his two 

 sons. What part of the fortune does each son 

 receive? 



%of%=%, or%-5-4=% 



% of Vr = Vu I 



^ of % = 



