CANCELLATION 



1150 



CANCELLATION 



meaning dog, for at that time a large, fierce 

 breed of dogs, now extinct, lived there. The 

 islands are thirteen in number, the most im- 

 portant of which are Teneriffe, Grand Canary, 

 Palma, Hierro, Gomera, Lanzarote and Fuer- 

 teventura. The remaining six are uninhabited. 

 All are rugged, volcanic and mountainous, fre- 

 quently presenting precipitous cliffs to the sea. 

 The most notable peak is that of Teneriffe, 

 which rises to a height of 12,182 feet. The 

 Canaries are not reached directly from America, 

 but by way of European ports. They belong 

 to Spain, and are governed as a province. 



The climate is mild and healthful and the 

 soil is so fertile that the islands in ancient 

 times earned the name of Fortunate Islands. 

 There are no rivers of note, but there are 

 numerous streams. These contain no fish ex- 

 cept eels; in the surrounding seas, also, fish 

 are scarce. All kinds of domestic animals have 

 been introduced and thrive well. Agriculture 

 is primitive, but the fertile soil produces large 

 quantities of grain, fruit, vegetables and flow- 

 ers. 



Little is known of the Guanches, the tribe 

 who originally inhabited these islands. They 

 were for the most part exterminated by their 

 conquerors, the remnant being absorbed by 

 intermarriage. The present inhabitants are 

 darker than the northern Spaniards, and are 

 well formed and hardy. Population, estimated, 

 1910, 475,000. 



CANCELLATION, kan sella' shun, is a "short 

 cut" in mathematics. Its purpose is to avoid 

 long and difficult multiplications and divisions, 

 both in whole numbers and in fractions. It is 

 based upon these principles: 



(1) Both dividend and divisor may be divided 

 by the same nurrfber, and the quotient is un- 

 changed ; or, a common factor may be dropped 

 from dividend and divisor and the quotient re- 

 mains unchanged. 



(2) The numerator and denominator may be 

 divided by the same number and the value of 

 the fraction remains unchanged ; or, a common 

 factor may be dropped from numerator and 

 denominator and the value of the fraction re- 

 mains unchanged. 



In division, the most common use of can- 

 cellation is the division of both terms by 10, 

 100, and so forth. For illustration: 



(1) 6500 -f- 1300. Divide each number by 100 

 by striking off two zeros in each ; then the prob- 

 lem becomes 65 -^ 13 = 5. 



(2) 75000-^250. Upon dividing both terms by 

 10 the problem becomes 7500 -=-25 = 300. 



But it is also used in the division of both 

 terms by other factors than 10, 100, etc.; for 

 example : 



2200-=-55=quotient 



Divide dividend and divisor by 11, and the 

 problem becomes 



See what common factor is taken out in the 

 following : 



(3) 650-^-39 = 9 



50 -=-3 =16%. (Factor taken out is 13.) 



(4) 960-7-36 = 9 



80-7-3 =26%. (Factor taken out is 12.) 



(5) 225000-7-450 



22500-7-45 



1500^-3 = 500. (Factors taken out are 

 10 and 15.) 



(6) 108000-7-7200 



1080-7-72 



30-7-2 = 15. (Factors taken out are 

 100 and 36.) 



(7) 99180-f-360 



9918-7-36 



1102-7-4 = 275%. (Factors taken out are 

 10 and 9.) 



Taking out of factors other than 10, 100, 

 etc., is not so general as it should be. Chil- 

 dren's attention should be drawn to it (see 

 FACTORING). Here is an illustration to show 



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the common factor and why it can be dropped : 



96-=-36=quotient. 



This reads, "How many 36's in 96?" 96 is 

 made up of eight 12's; 36 is made up of three 

 12's, as shown in the diagram; then the prob- 

 lem is seen to become, "How many 3 rows in 

 8 rows?" and then, "How many 3's in 8?" 

 This put into arithmetical form appears: 

 i 



(8X12), (3X12) or 



Cancellation is used very much more freely 

 when division is written in fraction form than 

 when it appears with the division sign (-=-); 



150 

 for example, 13500H-270 =^^=i|2 = 5 o. 



(a) Divide both terms by 10 



(b) Divide both terms by 9 



(c) Divide both terms by 3 



