DIVISION 



1818 



DIVISION 



ing the eggs in 6's, how many breakfasts 2 

 dozen will provide. 24-+6=4. 



(c) A peck of potatoes may be measured 

 off in 6's or 4's or 8's or whatever mother says 

 is the daily average used. The problem may 

 be 50^-4, 6 or 8; the dividend is the number of 

 potatoes in the peck, the divisor the number 

 used per day, and the quotient the number of 

 days a peck will last. 



(d) The same may be done with apples. 



(e) Child's allowance for a week may be 

 divided into groups of pennies for daily spend- 

 ing. 



(f) Divide large groups of pennies into 

 groups of 5, or 6, or 8, etc. 



Short Division. We shall see how short 

 division is derived from multiplication: 



221 884-^4 = n 



4_ 



800 4|884 



80 200 



4_ 20 



884 1 



221 



How many 4's in 800? Look at the problem 

 in multiplication and see that we put 200 4's 

 in 800. How many 4's in 80? Look at the 

 multiplication and see that we put 20 4's in 80. 

 How many 4's in 4? One. 



So we have in the quotient 221. The teacher 

 here emphasizes that this means there are 

 221 4's in 884. Another illustration: 

 963-=-3=n 



321 



3 



900 

 60 



3 



963 



3|963 



300 



20 



1 



321 



Another : 



(1) (2) 



4|848 4|848 



200 212 



10 



2 



212 



Read the answer here 200, 10 and 2 to see its 

 agreements with the answer to the left. 



As the child writes the answer, he should 

 read it in full ; for example in 2|846, the answer 



423 



is read 4 hundred, as the 4 is written, twenty 

 as the 2 is written, and 3. Then follow easily 

 such problems as these: 



3[1200 6[180() 8|2400 



400 300 300 



41804 3|1209 7|707 



200 .- 400 100 

 1 3 1 



201 403 101 



Have the pupils speak and write in full the 

 answers to each division above; as, "How many 

 3's in 1200?" Answer "400." "How many 8's 

 in 2400?" Answer "300." "How many 4's in 

 800?" Answer "200." "In 4?" Answer "1." 

 The difficulty which such problems usually pre- 

 sent to children is thus cleared away. It helps 

 them to avoid such common expressions as 

 "4's in zero," "3's in zero," etc., which are 

 meaningless to the child. 



7|2814 

 400 



2 



402 



9|3627 

 400 



403 



907 



The above three are typical of another diffi- 

 culty which is here avoided by this same writ- 

 ing and reading of answers in full. In the 

 first problem the child thinks, "How many 7's 

 in 2800?" He says "400," and seeing 14, says 

 "402." In the second he thinks, "How many 

 9's in 3600?" and says "400," and seeing the 27,. 

 realizes there are 3 more, and says "403." 



Division with Reduction. Such division 

 comes from multiplication where there is "car- 

 rying" or reduction (see MULTIPLICATION). We 

 shall look at such multiplication and division 

 side by side: 



2152 = 40 + 12 



20+ 6 = 26 



723-f-3 = n 



31723 = 600 + 120 + 3 



200+ 40 + 1 = 241 



_ 



12 

 j40 

 52 



241 

 3 



COO 



120 

 3 



723 



Many simple cases of this kind should be 

 worked out in multiplication and in division, 

 that the child may see that in division he is 

 taking apart a number along the lines upon 

 which it was built up, or along its constructive 

 lines. Several illustrations follow: 



16lx6 = 



6 



600 

 360 



6 



966 

 93x8=n 



966-=-6 = n 



6|966 = 600 + 360 + 6 



100 + 60 + 1 = 161 



744-=-8 = 



8|744 = 720 + 24 

 90+ 3 



720 



24 



744 



1732-=-4 = n 

 411732 = 1600 + 120 + 12 



400+ 30+ 3 = 433 



