the Cape of Good Hope? From Pittsburgh to the Cape of Good Hope? Ans. to last, 74° 23' 39".

27. Chicago is 10° 33′ 40.35′′ West longitude from Washington City; and New York is 3° 3' 59.2" East longitude from Washington. Through how many degrees of longitude must a person travel in going from Chicago to Washington? In going from Chicago to New York?

Ans. to last, 13° 37′ 39.55".

28. What is the sum of £.628125, £.284375, and .15s.?

Ans. 18s. 4d. 3.2 far.

29. Find the sum of .703125 mi., .965625 mi., and .025 fur.

Ans. 1 mi. 5 fur. 15 rd.

30. Find the sum of .282 T., .96 cwt., and .325 lb.

Ans. 6 cwt. 60 lb. 5.2 oz.

31. Find the sum of .815625 lb. Troy, .7 lb. Troy, .16 oz.

36. What is the sum of 43 cords and 64 cord feet?

37. To lb. Troy add & oz.

38. What is the sum of

Ans. 5 cd. 5 cd. ft. 12 cu. ft.

Ans. 9 oz. 9 pwt. 4 gr.

of a ton and § cwt.?

Ans. 13 cwt. 88 lb. 14 oz. 3§ dr.

39. What is the sum of § of a gallon and of a gallon?

Ans. 1 gal. 2 qt. 13 gi.

40. What is the sum of of a circumference, of a

degree, and of a minute?

Ans. 200° 38' 5".

of a furlong and

Ans. 5 fur. 9 rd. 3 yd. 2 ft. 11 in.

41. What is the sum of of a mile, of a rod?

SUBTRACTION

243.

Oral Exercises

EXAMPLE. What is the difference between 3 gal. 2 qt., and 1 gal. 2 qt. ?

SOLUTION.-2 qt. from 2 qt. leave nothing; 1 gal. from 3 gal. leaves 2 gal. Therefore, the difference between 3 gal. 2 qt., and 1 gal. 2 qt., is 2 gal.

PROBLEMS.

1. Find the difference between 10 bu. 3 pk., and 5 bu. 2 pk.; 6 bu. 1 pk. ; 7 bu. 3 pk. ; 8 bu. 2 pk. ; 9 bu. 3 pk. 2. What is left after taking from .5 bu. .35 bu.? .22 bu.? .16 bu. ? .125 bu.? .64 pk. ? .72 pk.? pk.?

3. Take from mi. mi.; fur.; fur.; fur.

4. How much is ch. less

rd.? less 25 1.? less 20 ft.?

less .4 ch.? less .25 ft. ? less 10.5 1.?

5. A merchant bought a hogshead of molasses containing 54 gallons, and sold from it 13 gallons and 2 quarts; how much remained?

6. A man owning 40 acres 2 roods and 20 perches of land, sold 94 acres and .5 of a rood; how much remained? 7.4 tons + 10.5 cwt. 1.25 tons = ?

Written Exercises

EXAMPLE 1.-From 19 cwt. 47 lb. 5 oz., take 12 cwt.

96 lb. 13 oz.

SOLUTION.

19

cwt. lb. OZ. 47 5

12

96

13

6

50

8

EXPLANATION. We first, as

a matter of convenience, write the numbers of the subtrahend under those of the minuend, so that the denominations of the same name stand in the same column, with units under units, tens under tens, &c. For convenience, we commence at the lowest denomination, and say mentally, 13 oz. from 5 oz., impossible; but adding 1 lb. = 16 oz. to 5 oz. of the minuend, we have 21 oz., from which subtracting 13 oz. there remain 8 oz.; and we write 8 under the oz. column.

Since 16 oz. (= 1 lb.) have been added to the minuend, we must add 1 lb. to the subtrahend (76).

97 lb. from 47 lb., impossible; to 47 lb. we add 100 lb. (= 1 cwt.) making 147 lb.; 97 lb. from 147 lb. leave 50 lb. and we write 50 under the lb. column.

We then add 1 cwt. (: from 19 cwt. leave 6 cwt.

100 lb.) to 12 cwt., making 13 cwt.; 13 cwt. Result, 6 cwt. 50 lb. 8 oz.

The preceding explanation may be illustrated as follows:

It will readily be observed that 100 lb. 16 oz. (= 101 lb.) have been added to the minuend; and 1 cwt. 1 lb. (= 101 lb.) have been added to the subtrahend. The difference, therefore, remains the same (76). The dark letters show the original example; the quantities in parentheses the addends.

EXAMPLE 2. From bu. take pk.

1ST SOLUTION.

bu.- pk. 4 pk.- pk.=341 pk.=3 pk. 2 qt. 1 pt.

2D SOLUTION.

bu.

pk. qt. pt.
3 4 0

pk. =

1 014 3 2 1

EXPLANATION.-We reduce the denominate fractions to the same denomination; then subtract, and reduce the remainder to a simple or compound denominate number. Or, we reduce the denominate fractions to simple or compound denominate numbers and then subtract as in the preceding example.

EXAMPLE 3.-From 129.716 cords take 15.048 cd. ft.

RULE I.-Write the parts of the subtrahend under those of the same denomination in the minuend.

Beginning at the right, subtract, if possible, each number in the subtrahend from that above it, and write the difference underneath.

When any number in the subtrahend is greater than that directly above it, add as many ones to the upper number as make 1 of the next higher denomination.

From this sum subtract the lower number, and add 1 to the next denomination to the left, before subtracting.

II.-Reduce common and decimal fractions to the same denomination; then subtract and reduce the remainder to a denominate number.

Or,

Reduce common and decimal fractions to denominate numbers, and then subtract according to Rule I.