FRACTIONS 



2287 



FRACTIONS 



The difference between two unit fractions is the 

 difference between the denominators over the 

 product of the denominators. 



Subtraction of Mixed Numbers. (1) From a 

 bucket of candy weighing IQ 1 ^ Ibs., a box 

 weighing 7%6 Ibs. was filled; how much candy 

 was left in the bucket? 



19i%- 6 lb.-7% 6 lb. = 12Hl 6 lb. 



(2) From 5% 6 subtract 3^6- 



5%6-3fi6 = 2% 6 



(3) From 12% subtract 9%. 



12|*-9%=3% 



(4) From 9% subtract 4%. 



9^-4^=5^ 



When the fraction in the subtrahend is larger 

 than that in the minuend, there is another step 

 in the process, as shown below. 



(1) 28%-12%=:n 



12 



12%=12%5 = 



We cannot take %s out of %s, so we take 1 out 

 of 28 and reduce it to i%s and combine this with 

 the %5 ; then we have 27^5. From this we sub- 

 tract 12% 5 . 



(2) From a fruit cake weighing 3% pounds, 

 a baker cut 1% pounds. How much had he 

 left? 



3%lb.-l%lb.:r:lH4 2 lb. 



There is another method which is of sufficient 

 interest to give it a place here, although it is 

 not used generally. For example: 

 3 % 



-i 



Take 1 out of 3, leaving 2. Subtract the whole 

 numbers and have 1 ; subtract % from the 1 we 

 took from 3 and have 1/4. We still have % in the 

 minuend, and the answer is 



Use this method with the following: 



6% 19% 



4% 15% 



Problems. 1. What is the distance around 

 a room 14% feet long and 12% feet wide? 

 How much longer is it than it is wide? 



2. The ice froze % inch one night, % inch the 

 next night, and % inch the next night. How 

 thick was the ice? 



3. A farmer sent to town 3 loads of hay. 

 One weighed 1% tons, another 1% tons and the 

 other 1% tons. How many tons did he send 

 in all? 



4. Which load was the heaviest, and how 

 much heavier than each of the others was it? 



5. A boy buys papers at 1%^ each, and sells 

 them at 2tf each. How much does he make on 

 25 papers? 



Multiplication of Fractions. The first process 

 is the multiplication of a fraction by a whole 

 number. 



( 1 ) A newsboy makes %<} on each paper he sells. 

 He sells 12 papers in % hour. He makes 12 x%^ or 

 2%tf. One evening he sold 60 papers. He made 

 60X%< or i2%tf or 24j. 



(2) A school-store dealer bought 1 dozen pen- 

 cils at %tf for each pencil. He spent 12 x% or 

 3 %* or 7%*. 



(3) 



(4) 



(5) 



(6) 



(7) 



xf 



1 



Cancel when possible to shorten the work. 

 Reduce answers to whole or mixed numbers. 



(8) %of 27 = 



(9) % of 40 = 



(10) 



Taking a fractional part of a number, as 

 % of. 27, is called multiplication oj a whole 

 number by a fraction.' But this is the same 

 as multiplication of a fraction by a whole 

 number, and the processes are the same as 

 shown above. 



The next step 



