FRACTIONS 



2283 



FRACTIONS 



Dime/ \Dime \Dime \Dime 



Dime/ \Dime/ vDime 



FIG. $ 



Two boys use two-fifths ; three boys use 

 three-fifths; four boys use four-fifths of the 

 piece. All the boys use five-fifths of the piece, 

 or all of it. If only three boys take their parts 

 there will be left two-fifths of the piece. If 

 four boys take their parts only one-fifth of 

 the piece is left. 



John and Eric have a dollar which they are 

 to divide equally between them. They may 

 use as their measure one dime, one quarter, 

 one penny or one-half dollar. 



(1) If they change the dollar for dimes, they 

 have 10 dimes, and each one takes 5 dimes, 

 or five-tenths of the dollar (see Fig. 3). 



(2) If they change the dollar for quarters, 

 each one takes two quarters and has two- 

 fourths of the dollar (see Fig. 4). 





FIG. 4 



(3) If they change their dollar for pennies, 

 each one takes 50 pennies, and has fifty-hun- 

 dredths of the dollar. But in each case, each 

 boy has one-half of the dollar because there 

 are two boys who receive equal parts of the 

 dollar. 



So we see here that five-tenths, two-fourths, 

 fifty-hundredths and one-half of a dollar are 

 all of the same value. 



The fractions named above are written thus: 

 %o, %, 5 %oo, %. We see that t% =$%; that 

 $%=$^; that $5%oo=$&; that $5%oo=l%> . 

 that $ 5 94oo=$74. 



Common fractions are written as above; 

 the number below the line tells the number of 

 parts into which the whole is divided, and the 

 number above the line tells how many of these 

 parts we are considering, or are working with. 

 The number below, which is called the de- 

 nominator, shows the unit of measure, while 

 the number above the line, called the numer- 

 ator, shows how many such units of measure 

 we are considering. For example, % foot means 

 that V4 foot is used as a unit of measure, and 

 the whole length measured contains three of 

 the measuring units. Fig. 5 shows the measur- 



ing unit, the whole length undivided, and the 

 whole length measured. 



J4ft 



FIG. 5 



The denominator and numerator together are 

 called the terms of a fraction. 



Reduction of Fractions to Higher and Lower 

 Terms. The process of reducing fractions to 

 higher or lower terms, without changing the 

 value, enters into numerous practical problems. 



(1) From Fig. 

 6 (upper dia- 

 gram) we see that 



%=%; %=%; 

 %=%. 



(2) From Fig. 

 6 (middle dia- 

 gram) we see that 



FIG. 6 



%5&< *7Q " *"V>.1 

 I /^-x /O > /* 



(4) In general, 

 we see that two 

 fractions of dif- 

 ferent form may 

 have the same value. 



(a) Divide a yard into three equal parts; 

 one part is % of a yard, or 12 inches. 



(b) Divide a yard into six equal parts; one 

 part is % of a yard. 



YQ yard is only } as long as the % yard ob- 

 tained (a) by dividing the yard into three 

 equal parts; to obtain a part 12 inches in 

 length, we must use as a measure two % yard, 

 or % yard. It follows then that % yard equals 

 } yard. 



As the denominator grows larger, the unit 



