SUBTRACTION 



(b) 27 ._ 10 + 17 



5608 



SUBWAY 



Another method: 



(c) 



10+ 8 = 18 

 2210 + 12 



_ 

 14 = 10+ 4 



14 



+ 8 

 "T2 



11 



22 



48 53_40 + 13 



5 = ~5~ - 5 



13 48 = 40+ 8 



40 



53 



In the above addition we understand how 12 

 is made by 4 and 8, and how 13 is made by 

 5 and 8, and see that when we come to subtract 

 we must think of 22 as 10+12, and 53 as 40+13 

 (see ADDITION). 



65 = 50 + 15 



49 = 40+ 9 

 16 = 10+ 6 

 91 = 80 + 11 



48 = 40+ 8 

 43 = 40+ 3 



Explanation: The subtraction is done begin- 

 ning at the right : 9 from 15, 6 ; 40 from 50, 10. 

 Then the sum of 10 and 6 is written to the left. 



(d) 193 = 100 + 80 + 13 



147 = 100 + 40+ 7 



46= 40+ 6 

 243 = 200 + 30 + 13 = 100 + 130 + 13 



198 = 100 + 90+ 8 = 100+ 90+ 8 



45= 40+ 5 



(e) In time the writing out in full may be 

 dropped and the separation done mentally, as 

 follows : 



243 



-198 



45 



Explanation: Take 10 from 40 or 1 ten from 

 4 tens and add it to 3, which gives 13. 8 from 

 13 leaves 5. Take 100 from 200 and add it to 

 30, making 130, or take 100, which is 10 tens, 

 and add it to 3 tens, making 13 tens. 9 tens 

 from 13 tens leaves 4 tens or 40. The result 

 is 45. This can be seen very clearly with dol- 

 lars, dimes and pennies. 



Other Methods. There are other methods of 

 subtraction in common use, but the above is 

 explained most easily to the young mind. The 

 Austrian Method sees subtraction as addition: 



657 



398 



259 



Explanation: 8 and 9, 17; 10 and 5, 15; 

 4 and 2, 6. The minuend is held in mind as 

 the sum of two numbers and the subtrahend as 

 one of these numbers. As the other number 

 is found in each column, it is placed in the 

 answer. 



657 



-398 



259 



Explanation: 8 from 17, 9; 10 from 15, 5; 

 4 from 6, 2. 10 is added to the minuend to 

 make 7, 17. To equalize matters 1 ten is added 

 to 9 tens in the subtrahend. 10 tens is added 

 to 5 tens in the minuend, and again to equalize 

 matters, 100 (which is equal to 10 tons) is added 

 to the subtrahend. It is seen clearly in the fol- 

 lowing form: 



657 = 600 + 50 + 7 

 -398 = 300 + 90 + 8 



It becomes for easy subtraction: 



600 + 150 + 17 

 400 + 100+ 8 

 200+ 50+ 9 = 259 



110 has been added to both minuend and sub- 

 trahend. This method is in common use 

 among adult people, and is less strain upon the 

 mind than the first method presented. But it 

 should not take the place of that method with 

 young children because of the difficulty to the 

 child mind of understanding it. It is easily 

 adopted later. 



Place Value. Read in connection with sub- 

 traction the articles ADDITION and NOTATION, 

 where place value is discussed. A.H. 



SUBWAY, or UNDERGROUND RAILWAY, 

 a tunnel or system of tunnels for the purpose 

 of placing a railroad beneath the level of the 

 street. Such systems are coming more and 

 more into use, and in some cities, especially 

 New York and London, they form a vast net- 

 work of underground railways. London was 

 the first city to adopt subways, and now has 

 five systems affording quick and economic 

 transportation to all parts of the city and sub- 

 urbs. A subway destined to grow to large 

 proportions was opened in Buenos Aires in 

 1913. 



In the United States subways have been con- 

 structed only in New York, Boston, Philadel- 

 phia and Chicago, but have for some time been 

 under consideration for other cities. The New 

 York subways form the largest underground 

 railway system in the world. Chicago's sub- 

 ways as yet are for freight only, and are nearly 

 seventy miles long, under the central business 

 district. The city still relies on its street rail- 

 ways and elevated railways to provide passen- 

 ger service, but passenger subways on a large 

 scale are planned. 



The first subway built in London was oper- 

 ated by steam locomotives. All subsequent 

 subways have been operated by electricity. 



