EXERCISES 1. State the law governing the placing of the decimal point in division. How can this be simplified through the suggestion given in Art. 204 ? Carry out the following divisions and check: 14. Find the cost of 6450 lb. coal at $ 4.50 per ton. How much is this per 1000 lb. ? 15. Find the cost of 8560 lb. coal at $3.75 per ton. 16. A bushel of shelled corn weighs 56 lb. Find the cost of 840 lb. shelled corn at $ 1.17 per bushel. 17. A bushel of wheat weighs 60 lb. Find the value of 3820 lb. wheat at $1.98 per bushel. 18. If 833 bu. of wheat are harvested from 45 acres, what is the yield per acre? 19. A farmer picked 1540 bu. of corn from a field of 65 acres. What was the yield per acre? 20. What is the gain or loss in buying a house for $ 2850 and selling it for $2325? What part of the purchase price is gained or lost? 21. A train went 468.6 mi. in 16.25 hr. What was its hourly rate of speed? 22. At the rate of 28 mi. per hour, how far will a train go in 8.5 hr.? in 18 hr. ? 23. How long will it take a train going at the rate of 30 hour to go 450 mi.? 378.6 mi.? mi. per XIII SHORT CUTS IN COMPUTATIONS 206. Short Cuts.-The value of short cuts in simplifying computations and in saving time cannot be overestimated. At first short cuts will, of course, take longer time than the known processes, just as writing shorthand takes more time at first than the known longhand. Practice and continual watchfulness for short cuts will soon show their value.* 207. Short Cuts in Addition.-To add 8 increase ten's digit by 1 and decrease unit's digit by 2. Thus, 458 (40+ 10) + (52) = = 53. To add 9 increase ten's digit by 1 and decrease unit's by 1. Thus, 489 (40+ 10) + (8 = - 1) = = 57. This principle can also be applied to adding a one digit number to any number ending in 8 or 9, as 5+ 58, or 739. Formulate this short cut fully. To add two numbers of two digits each, first find the sum of the tens' digits, to this 1 must be added if the sum of the units' digits is 10 or more, to this annex the last digit of the sum of units' digits. Thus, in 52 + 24 we have 5 + 2 7 and 2 + 4 6, or 76; in 47 + 35 we have 4 + 3 + 1 = 8 and 7 + 5 = 12, or 82. Explain fully. = = *Note to Teacher.-The short cuts are placed together in one chapter for convenience of reference. In order, however, to show the students the value of short cuts they must be taken slowly and with the other work of the book at the rate of one or two articles per week. As soon as a short cut has been learned, require its application whenever occasion arises in the exercises of this book as well as in other computations. 5. Let the teacher give you other lists like this to 10. Let the teacher give you other lists like this for practise. 11. Give some illustrations in which it would be convenient to add 2 numbers of 2 digits each without the use of pencil and paper. Let the class carry out these additions. 208. Further Short Cuts in Addition.-Additions can of ten be simplified by adding and subtracting the same num One number may sometimes be broken up into the sum of two other numbers. Thus, Three or more numbers may often be rearranged advantageously. Thus, 4735+23 = 47+ 23 +35 70+ 35 = ? +23 = EXERCISES Carry out the following without using pencil and paper: 10. Let the teacher suggest other exercises for practice. 11. A grocery bill contained the following amounts: 37 ¢, 25 ¢, and 23 ¢. Give the total amount. 12. John's sales of magazines for 4 weeks were 17, 15, 13, and 12. How many magazines did he sell during the 4 weeks? 13. Henry earned 35¢ one day and 47 ¢ the next day. How much did he earn during the two days? 14. Mary put into her savings-bank 47 ¢, 25 ¢, and 33 ¢ for each of 3 weeks. How much did she put into her savings-bank during these 3 weeks? 15. During each of four weeks Harriet sold 7 doz., 12 doz., 13 doz., and 18 doz. of eggs. How many dozen of eggs did she sell the first three of these weeks? How many dozen did she sell during the four weeks? 1000 = 9910 209. Short Cuts in Subtraction. To subtract from a power of 10, as 100 or 1000, think of it as 90+10 or 990+ 10. Begin at the left and subtract each digit from 9, except unit's digit, which is subtracted from 10. In subtracting numbers of two digits, if 563 = 563 437 the unit's digit of the subtrahend is the larger, add enough to it to make zero and then add an equal amount to the minuend. Why will this give the correct difference? 43 - 27 = (43 + 3) — (27 + 3) EXERCISES Subtract the following rapidly: = 46 30: = ? 5. A lady paid 25 é a can for salmon that she bought two years ago for 18 é a can. for it this year? How much more did she pay 6. What change will be received from a $10 bill if the purchase was $4.35? $6.35? $7.85? 7. What change will be received from a $5 bill if the purchase was $2.65? $3.26? $2.97 ? |