15 in 31 units 2 units times; we write the 2 units in the quotient. 15 × 2 units = 30 units, which, subtracted from 31 units, leaves 1 unit as a remainder. Indicating the division of the 1 unit, we annex the fractional expression, 1/15 unit, to the integral part of the quotient. Therefore, 34531 divided by 15 is equal to 2302-1/15. [B. Greenleaf, _Practical Arithmetic_, '73, p. 49.] LONG DIVISION: INDUCTIVE EXPLANATION Dividing by Large Numbers 1. Just before Christmas Frank's father sent 360 oranges to be divided among the children in Frank's class. There are 29 children. How many oranges should each child receive? How many oranges will be left over? _Here is the best way to find out:_ 12 and 12 _Think how many 29s there are in 36. 1 is right._ ______ remainder _Write 1 over the 6 of 36. Multiply 29 by 1._ 29 )360 _Write the 29 under the 36. Subtract 29 from 36._ 29 _Write the 0 of 360 after the 7._ --- _Think how many 29s there are in 70. 2 is right._ 70 _Write 2 over the 0 of 360. Multiply 29 by 2._ 58 _Write the 58 under 70. Subtract 58 from 70._ -- _There is 12 remainder._ 12 _Each child gets 12 oranges, and there are 12 left over. This is right, for 12 multiplied by 29 = 348, and 348 + 12 = 360._ * * * * * 8. _In No. 8, keep on dividing by 31 until you have ________ used the 5, the 8, and the 7, and have four 31)99,587 figures in the quotient._ 9. 10. 11. 12. 13. _____ _____ _____ ____ _______ 22)253 22)2895 21)8891 22)290 32)16,368 Check your results for 9, 10, 11, 12, and 13. 1. The boys and girls of the Welfare Club plan to earn money to buy a victrola. There are 23 boys and girls. They can get a good second-hand victrola for $5.75. How much must each earn if they divide the cost equally? _Here is the best way to find out_: $.25 _Think how many 23s there are in 57. 2 is right._ ----- _Write 2 over the 7 of 57. Multiply 23 by 2._ 23|$5.75 _Write 46 under 57 and subtract. Write the 5 of 575 46 after the 11._ ---- _Think how many 23s there are in 115. 5 is right._ 115 _Write 5 over the 5 of 575. Multiply 23 by 5._ 115 _Write the 115 under the 115 that is there and subtract._ ---- _There is no remainder._ _Put $ and the decimal point where they belong._ _Each child must earn 25 cents. This is right, for $.25 multiplied by 23 = $5.75._ 2. Divide $71.76 equally among 23 persons. How much is each person's share? 3. Check your result for No. 2 by multiplying the quotient by the divisor.