CANCELLATION 



1151 



CANCER 



Let us look at cancellation as used in a 

 concrete problem: 



"How many blocks of ice 36 inches by 24 

 inches can be packed in a layer in an ice house 

 60 feet wide and 90 feet long?" 



1 



10 JS 



Solution: Number of blocks = ***??, ??** 



oO X>4 



JG \ 

 1 



(a) Divide both terms by 24 

 (fc) Divide both terms by 6 

 (c) Divide both terms by 6 

 and the division appears 



10X90X1 

 1X1 



= 900 



Cancellation shortens the work in multipli- 

 cation and division of fractions; for example, 



12 34 

 17 A 35 



appear 



2X7X12X34 



381735 3X8X17X35' 



The numerator of the new fraction is the 

 product of 2, 7, 12, 34, while the new denomi- 

 nator is the product of 3, 8, 17, 35. We may 

 divide the numerator and denominator by 

 the same number without changing the value 

 of the fraction: 



(a) Divide both terms by 3 : (3 below and 12 

 above) ; 



(b) Divide both terms by 7: (35 below and 7 

 above) ; 



(c) Divide both terms by 2: (2 above and 8 

 below) ; 



(d) Divide both terms by 17 : (34 above and 17 

 below) ; 



(e) Divide both terms by 4 : (4 below and 4 

 above) ; and the product appears as below : 



1 



An illustration in mixed numbers follows : 



235 23 5 



(a) Divide both terms by 5 : (5 above and 5 

 below) ; 



(b) Divide both terms by 3: (36 above and 3 

 below) ; 



(c) Divide both terms by 2: (12 above and 2 

 below) ; and we have 



6 



25 ag" 25X6 



150 



1 1 1 



A problem in division of fractions becomes 

 a problem in multiplication of fractions, and 

 so cancellation is helpful in division of frac- 

 tions. For example: 



4 2 



13 26 



(2) 



7 1 



5 \jr( 



8 5* 7 8 J X 



3 2 



A.H. 



CANCER, kan'ser, the common name of a 

 dangerous malignant tumor that may grow in 

 the human body or in the bodies of other ver- 

 tebrate animals. The name comes from a 

 Greek word meaning crab, and was applied to 

 the tumor because the enlarged veins around 

 the swelling resemble the claws of a crab. 

 Though there are many different forms of 

 cancer, certain characteristics are common to 

 all of them. Cancerous growths are always 

 composed of a fibrous framework enclosing a 

 mass of cells and a milky- white cancer juice. 

 They have no definite limits, but involve sur- 

 rounding tissues, and, because of their ten- 

 dency to spread by means of the veins and 

 lymphatics, they often cause growths of sim- 

 ilar character in other parts of the body. 



Classification. A convenient mode of classi- 

 fication divides cancers into three groups 

 scirrhus, encephaloid and epithelial cancer. In 

 the first class are those which have a large 

 proportion of fibrous elements, which make 

 them very hard. They do not grow rapidly, 

 but are difficult to check because of their ten- 

 dency to spread and to ulcerate. Scirrhus 

 most commonly attacks the female breast, but 

 sometimes internal organs are affected. In 

 encephaloid the cell elements are found, in 

 greater proportion than the fibrous, making 

 this form of cancer very soft. Because of its 

 rapid growth it is sometimes known as acute 

 cancer. The internal organs or the limbs are 

 its most common seats. Epithelial cancer oc- 

 curs most frequently in the skin and mucous 

 membranes, or where these unite, as on the 

 lips. Though this form of cancer does not 

 spread so rapidly as the other forms nor cause 

 secondary growths to the same extent, it has 

 the same tendency to affect surrounding glands. 

 All forms tend to recur after removal. 



Causes. Cancer may be started by local 

 irritation, as by the stem of a pipe on the 

 lip, gallstones in the gall bladder and the rub- 

 bing of a corset steel on the breast. Contin- 

 ued irritation is the usual excitant of the 

 cancer, but a single accident may cause it. 

 Heredity seems to have some influence, 

 though this may be simply heredity of the 

 habits that tend to develop cancer, such as 

 smoking or always being well-fed. Careful 

 research and observation have established the 

 following facts: Nearly one-half of all can- 

 cers occur in the stomach and intestines; in 

 other words, in that part of the body in which 

 food is stored which has not always been dis- 

 infected by heat. Outside surfaces of the body 



