21. Five loads of wheat measured thus: 21 bu. 3pk. 2qt. 1pt.; 14bu. 5 qt.; 23 bu. 2 pk. 1pt.; 18 bu. 1pk. 1 pt.; 22 bu. 7 qt. 1 pt.: how much in all? Ans. 100 bu. 22. A farmer raised of oats 200 bu. 3 pk. 1 pt.; barley, 143 bu. 2qt. 1 pt.; corn, 400 bu. 3 pk.; wheat, 255 bu. 1 pk. 5 qt. how much in all? Ans. 1000 bu.

23. I bought a silver dish weighing 2lb. 10 oz. 15 pwt. 21 gr.; a bowl weighing 1 lb. 1 oz. 16 pwt. 14gr.; a tankard, 2lb. 8 oz. 5 pwt. 12gr.: what did all weigh?

Ans. 6lb. 8oz. 17 pwt. 23 gr.

24. A druggist mixed together four articles: the first weighed 33 43 19; the second, 43 33 29; the third, 43 18gr.; and the fourth, 63 53 20 18gr.: what was the weight of all? Ans. 1 lb 33 23 16gr.

25. A grocer sold 5hhd. of sugar: the first weighed 8cwt. 1qr. 11lb.; the 2d, 4 cwt. 2qr. 14 lb.; the 3d, 5 cwt. 191b.; the 4th, 7cwt. 3qr.; the 5th, 7cwt. 3 qr. 9lb.: what did all weigh? Ans. 33 cwt. 3qr. 3lb.

27. Two men depart from the same place: one travels 104 mi. 1 fur. 10 rd. due east; the other, 95 mi. 6 fur. 30 rd. due west: how far are they apart? Ans. 200 mi.

:

28. A man has 3 farms in the 1st are 186 A. 3R. 14 P.; in the 2d, 286 A. 17 P.; in the 3d, 113 A. 2R. 9 P.: how much in all? Ans. 586 A. 2R.

29. Add together, 17 sq.yd. 3sq. ft. sq. yd. 141 sq. in.; 23 sq. yd. 7 sq. ft.; 116 sq. in. Ans. 88 sq. yd.

29

119 sq. in.; 18 sq. yd. 5 sq. ft. 8sq. ft. 88 sq. in.

30. A has 4 piles of wood: in the first 7 C. 78 cu. ft.; the

2d, 16C. 24 cu.ft.; the 3d, 35 C. 10 cu. ft. how much in all?

127 cu. ft.; the 4th, 29 C.

Ans. 88 C. 111 cu.ft.

the first contained 17 yd.

31. Bought 5 pieces of cloth; 3qr. 2na.; the 2d, 13 yd. 2qr. 1 na.; the 3d, 23 yd. 2na.; the 4th, 27 yd. 1qr. 2na.; the 5th, 29 yd. 1qr. 2na.: find the amount. Ans. 111 yd. 1 qr. 1 na.

32. I sold to A, 73hhd. 43 gal. 3qt. 1 pt. of wine; to B, 27 hhd. 3 gal.; to C, 15 hhd. 3qt. 1pt.; to D, 162 hhd. 1qt.: how much in all? Ans. 277 hhd. 48 gal.

33. I sold beer as follows: 1bl. 28 gal.; 1 bl. 17 gal.; 5 bl. 2gal.; 1 gal. 2 qt. 1pt.; 7 gal. 2qt. 3qt.; and 33 gal.: what is the quantity?

1pt.; 18 gal. Ans. 10 bl. 34. What day of the year is the 1st of May in common years?

35. What the 4th of July in leap years?

Ans. 121st.

Ans. 186th. 36. Through how many degrees does a ship pass, in sailing from Cape Horn, latitude 55° 58′ 30′′ south, to New York, lat. 40° 42′ 40′′ north?

Ans. 96° 41' 10".

SUBTRACTION OF COMPOUND NUMBERS.

ART. 102. The process of finding the difference between two numbers of different denominations, is termed Subtraction of Compound Numbers.

1. I have 67 bu. 1pk. 3qt. of wheat: how much will remain after selling 34 bu. 2 pk. 1qt.?

SOLUTION. In writing the numbers, the less is placed under the greater, for convenience Place units of the same denomination under each other, because a number can be subtracted only from one of the same name.

OPERATION. bu. pk. qt. 67 1 3

34 2 1

32 3 2

Then subtract 1 (quart) from 3 (quarts), which leaves 2 (quarts) to be placed in the column of quarts. In the next column, 2 (pecks) can not be taken from 1 (peck), but we can take 1 bushel from 67 bushels, reduce it to pecks, and add them to the 1 peck; this gives 5 pecks, from which take 2 pecks, and 3 pecks are left, to be placed in the column of pecks.

Then take 34 bushels from 66 bushels, as in Simple Subtraction, and write the remainder, 32 bushels, in the column of bushels. Instead of diminishing the upper number (67 bu.) by 1, the result will be the same to increase the lower number (34 bu.) by 1. Art. 26.

REVIEW.-102. What is Subtraction of Compound Numbers ? writing the numbers, why place the less under the greater?

In

Rule for Subtraction.-1. Write the numbers, the less under the greater, placing units of the same denomination under each other.

2. Begin with the lowest order, and, if possible, take the lower number from the one above it, as in Simple Subtraction.

3. But, if the lower number of any order be greater than the upper, increase the upper number by as many units of that denomination as make one of the next higher; subtract as before, and carry one to the lower number of the next higher order. Proceed in the same manner with each denomination.

PROOF. As in Subtraction of Simple Numbers.

REM.-In Simple Subtraction, when any lower.figure is greater than the upper, we borrow ten, ten units of a lower order making a unit of the next higher. In Compound Numbers, when the lower number of any order is greater than that above it, borrow the number of units in that order which makes a unit of the next higher.

12. If 2bu. 1 pk. 1qt. be taken from a bag of 4bu., what quantity will remain?

Ans. 1 bu. 2 pk. 7 qt.

13. From 100 bushels, take 24 bu. 1 pt.

Ans. 75 bu. 3pk. 7qt. 1pt.

14. From 191b. 9oz. of silver, take 91b. 9oz. 10pwt. Ans. 91b. 11 oz. 9pwt. 14gr.

10 gr.

15. A silver bar of 81b. 2oz. 11 pwt., is divided into 2 parts; the less weighs 21b. 4 oz. 7 pwt. 16 gr. find the weight of the greater. Ans. 5lb. 10 oz. 3pwt. 8gr.

16. From 3b 33 13 19 12 gr., take 1b 73 29 Ans. 1lb 83 10 14gr.

18 gr. 17. I bought 46 lb. 9oz. of rice after selling 191b. 4dr., how much remained? Ans. 27 lb. 8 oz. 12 dr.

18. A wagon loaded with hay weighs 32cwt. 2qr. 161b.; the wagon alone weighs 8cwt. 2qr. 17 lb.: what is the weight of the hay? Ans. 23 cwt. 3qr. 24lb. 19. It is about 25000 miles round the earth after a 1 fur. 1 rd., what distance will Ans. 24899 mi. 6 fur. 39 rd.

man has traveled 100 mi. remain ?

20. I had 146 A. 2 R. of land. 2R. 14P.: how much was left?

I gave my son 86 A. Ans. 59 A. 3R. 26 P.

21. From 8C. 50 cu. ft. of wood, 75 cu.ft. how much is left?

22. From 25 E. Fl., take 14 E. Fl.

there is taken 3C. Ans. 4 C. 103 cu.ft.

1qr. 3 na.

Ans. 10 E. Fl. 1qr. 1na.

23. From 11 yards of cloth, there is cut 3yd. 2qr.

2na.

what remains?

Ans. 7 yd. 1qr. 2 na.

only 51 gal. 1 qt. 2gi. reAns. 11 gal. 2 qt. 1 pt. 2 gi.

25. From 5 da. 10 hr. 27 min. 15 sec., take 2da. 4hr. 13 min. 29 sec. Ans. 3 da. 6 hr. 13 min. 46 sec.

REVIEW.-102. Why place units of the same denomination under each other? At which column begin to subtract? Why? How is the subtraction performed? Repeat the Rule. What is the proof?

102. REM. In subtraction of Compound Numbers when the lower number of any order is greater than the upper, what is to be done

ART. 103. To find the Time between any Two Dates.

Subtract the first date from the last, numbering the months according to their order. See note 3, page 98.

NOTE. In finding the time between two dates, and also in Interest, consider 30 days 1 month, and 12 months 1 year.

26. A note, dated April 14th, 1835, was paid Feb ruary 12th, 1837: find the time between these dates.

OPERATION.
yr. mon. da.

2

1837
1835 4

SOLUTION.-In writing the dates, observe that February is the 2d month, and April, the 4th. In subtracting, 14 days can not be taken from 12; therefore add 30 to the 12 days, subtract, and carry 1 to the 4 months. As5 months can not be taken from 2 months, add 12 to the latter, subtract, and carry 1 to the years.

12

14

1 9 28

27. The Independence of the United States was declared July 4th, 1776 what length of time had elapsed on the 5th of March, 1857?

28. A certain man was born was his age Aug. 1st, 1848?

29. A man was born Nov. born June 28th, 1832: what ages?

Ans. 80 yr. 8mon. 1 da. June 24th, 1822: what Ans. 26 yr. 1mon. 7 da. 25th, 1807; his son was is the difference of their Ans. 24 yr. 7 mon. 3 da.

30. The latitude of the Cape of Good Hope is 33° 55′ 15" south; that of Cape Horn, 55° 58′ 30′′ south find the difference of latitude. Ans. 22° 3' 15".

31. The latitude of Gibraltar is 36° of North Cape, in Lapland, 71° 10′ difference of latitude?

6′ 30′′ north; that north: what their Ans. 35° 3' 30".

32. A ship departs from latitude 10° 25′ 48′′ north, and sails north to latitude 50°: through how many degrees of latitude has she sailed? Ans. 39° 34′ 12′′.

33. Take 5 quires 11 sheets from a ream of paper, and how much will remain? Ans. 14 quires 13 sheets.

34. A man started to market with 6 doz. doz. eggs: he broke half a doz. doz.: how many were left? Ans. 792.