16. A grocer bought two tubs of butter, weighing together 7011/12 lb. One tub when empty weighed 7 lb., and the other 8 lb. How much butter did he buy?

16. Find the sum and the difference of (35%) and (43+5%).

17. Find the sum and the difference of (5×3%) and (734×3%).

18. If it takes a workman 1% of a day to do 2, of a piece of work, how much of it can he do in 5% of a day? How much in 3 of a day?

5.

19. If 3⁄4 of an acre of land is sold for $453/20, what is the remainder worth at double the rate?

20. If 1/15 of a box of merchandise is worth $71, what is worth ?

21. A grocer mixes 571/2 lb. of tea, at $10 a lb., with 421⁄2 lb. of tea at $10 a lb. What is the value of a lb. of the mixture?

22. A farmer sold 5% of his wheat at $110 a bushel, and received $796% for it. How many bushels did he sell, and how many did he have at first ?

23. Mr. Hill, having $500 to pay expenses, made a journey that lasted 6 weeks. On reaching home he had $46% left.(1) How much did he spend? (2) What was the average expenditure per week?

24. I bought a house and paid down 1/3 of the price, and in one year thereafter I paid 2% of the price. The two payments amounted to $43,780. What was the price of the house?

25. A clerk has a monthly income of $75, and spends $54% per month. How much does he save a year ?

26. By how much would he have to diminish his expenses, per month, to save $20% per year more than he now does?

27. A laborer borrowed from his employer $663/20, agreeing to pay it by having $245/100 deducted from his wages every week. How many weeks at that rate did it take him to pay his debt?

28. If of 7 lb. of coffee costs $/, how many lb. can be bought for $123/25 ? $245 ? $5% ?

29. What is the sum of the area of 5 fields, containing severally 938, 24/7, 8611/56, 5617/28, and 89/14 acres?

30. What is the cost of 232 lb. flour at $1/20 ? 15 lb. oatmeal at $25? 32 lb. raisins at $25? 171/2 lb. nails at 4¢? 1 doz. fire-shovels at 1214 apiece?

31. What number multiplied by 3% will give 2; what number divided by it will give 2/3 ?

32. What number multiplied by 2% of 113⁄4 will produce 1. 33. In a school of 100 pupils, of whom are boys, 7 boys and 4 girls are absent. What part of the boys are present? What part of the girls?

34. One third of the eighth part of what number is equal to 912?

35. How many cubic feet in a box 4 ft. long, 3 ft. wide, 71 ft. deep.? (See problems, page 103.)

36. If one faucet empties a cistern in 6 hours, and another in 9 h., in what time will both together empty it? What part of the contents will the two faucets discharge in 1 hour?

37. In what time will both empty it if the first begins to run after the second has run for 2 hours?

38. A can set the type for a certain book in 6 days, B in 8, C in 9, and D in 12 days. In what time can they do it working together? (What part will they all do in a day?)

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39. How long must a room 4 yards wide be to contain as many square yards in the ceiling as a room 7 yards long and 52 yards wide?

40. I can walk 20 miles in 5 hours, and my friend can do it in 6 hours. Starting at the same time from points 20 miles apart and walking toward each other, how far are we apart in 1 hour, and in what time from starting would we meet ?

164. The last chapter presented a mode of writing fractions in which the number of parts are indicated by one number and their names by another. This chapter shows how both the number and name of certain fractional parts may be represented by the decimal system.

Note.-Exercises on the following diagram are designed to familiarize the pupil with the relations of such parts. Bundles of jackstraws will also serve for illus

tration.

Illustration. If a square sheet of paper were ruled into 10 long slips, and each of these were subdivided into 10 small squares, and the small squares into 10 short slips, and each short slip into 10 tiny squares, as shown in the two slips below:

1. How many long slips would there be? How many small squares? How many small slips? How many tiny squares?

2. What part of the whole diagram is a long slip? A small square? A small slip? A tiny square?

3. What part of a long slip is a small square? A short slip? A tiny square? What part of a small square is a tiny square? etc., etc.

Note. The questions given above are only suggestive of exercises designed to make the pupil familiar with decimal parts and their relations.

165. The division of anything into ten equal parts, and the subdivision of these into ten smaller equal parts, and so on, are Decimal Divisions, and the parts are Decimal Parts.

Note. The dime is a decimal part of a dollar, the cent a decimal part of a dime, the mill a decimal part of a cent.

166. A Decimal Fraction is one or more of the decimal parts of a unit.

Decimals expressed in Figures.

167. The first illustration (page 173) represents 421 sheets of paper, and 2 tenths, 3 hundredths, 4 thousandths, 5 ten thousandths of a sheet; and as each figure of 421 indicates by its place whether it represents units, tens, or hundreds, so the figures 2, 3, 4, and 5 may be made to indicate by their places whether they represent tenths, hundredths, thousandths, or ten-thousandths. But to show that they represent parts and not wholes, that they are decimals not integers, a point, called the decimal point (.), is placed before them, and the number is written thus: 421.2345.

168. The cipher is used in decimals, as in integers, to mark vacant places. Thus, if the two long slips were omitted in the illustration, the number represented would be expressed by 421.0345. If there were no long slips nor small squares it would be written 421.0045, etc., etc.

EXERCISES ON DIAGRAM.

1. How many sheets and how many and what parts of a sheet are represented by 4.2? 2.05? 3.82 ? .35 ? .23? 1.01? 2.71 ? .182? .19? 41.41 ? 3.00? .4321? 10.1? 7.15? 6.01 ? .101? 17.208? 15.001? 21.0021? .0053 ?

Give first the descriptive names of the parts, as long slips, small squares, etc., then use the proper arithmetical terms, tenths, hundredths, etc, thus: 4 sheets and 2 long slips, or, 4 sheets and 2 tenths of a sheet.

2. Illustrate by diagram, on slate or blackboard, what is meant by .01, by .25, by .35, by 3.7, by 1.3, by 2.004, etc.

3. Is there any difference in value between 6.7 and 6.70? Between 3.7 and 3.07? Between 5.16 and 50.16? Between .81 and .8100? (In stating the differences, tell what parts of the diagram are represented in each case.)

4. Tell how many long slips, small squares, etc., must be cut from a sheet of paper to have .357 of a sheet? To have .5642 ? To have .045 ? etc.