20. The population of England in 1851 was 16921888; of Scotland, 2888742; of Wales, 1005721; of Ireland, 6515794. What was the population of Great Britain and Ireland?

What is the

21. The area of Maine is 35000 square miles; N. H., 8030; Vt., 8000; Mass., 7250; R. I., 1200; Ct., 4750. area of New England?

22. The area of New England in 1853, was about 64230 square miles; of the Middle States, i. e. N. Y., N. J., Pa. and Del., 101971; of other states north of the Ohio and east of the Mississippi, 239349; south of the Ohio and east of the Mississippi, 442673; west of the Mississippi, 723997; of the Territories, 1734645. What was the area of our country? Ans. 3306865 sq. m.

23. William the Conqueror began to reign in England in the year 1066 and reigned 21 years; William II reigned 13 years; Henry I, 15 years; Stephen, 39 years; Henry II, 35 years; Richard I, 10 years; John, 17 years; Henry III, 56 years; Edward I, 35 years; Edward II, 20 years; Edward III, 50 years; Richard II, 22 years. In what year was Richard II

dethroned?

24. The distances of several places from Washington are as follows, viz. Augusta, Me., 595 miles; Concord, N. H., 481 miles; Montpelier, Vt., 516 miles; Boston, Mass., 440 miles; Providence, R. I., 400 miles; Hartford, Ct., 335 miles. What distance will that man travel who goes from Augusta to Washington, thence to Concord, thence back to Washington and so on until he has visited each place in succession and finally goes from Hartford to Augusta, a distance of 250 miles?

25. Suppose a member of Congress to be elected in each of the places named in Ex. 24, what will be their aggregate travel in going to Washington and returning to their homes once each?

26. A merchant bought 6 bales of cloth measuring 125, 99, 384, 762, 400 and 399 yards, respectively; how many yards did he buy?

27. A butcher bought eight oxen which weighed, after they were dressed, 517, 493, 862, 1127, 419, 768, 1243 and 987

pounds, respectively; how many pounds of beef did he purchase?

28. A, B, C and D, commencing trade together, furnished money as follows A, $3465; B, $2700; C, $5575; and D,

$6000. What was the total capital?

29. There are five numbers; the 1st is 476; the 3d is 9768; the 2d is the sum of the 1st and 3d; the 5th is the sum of the 1st, 2d and 3d; and the 4th is the sum of the 2d and 5th. What is the sum of the five numbers?

30. The difference of two numbers is 876954 and the smaller is 7869432. What is the larger? and what the sum of the two numbers?

31. The cost of the American army for five successive years, commencing in 1812, was $12187046, $19906362, $20608366, $15394700 and $16475412; what was the cost for five years?

32. 5487962 276

997867985

98746958 347 697842 999999947

369874 7689106 5879629

4 2 7 8 6 4 278 37 6 9 8 7 4 2 3 5721 5722

994120371 992310894 999 630126

5 3

6 5 2 3 0 2 158 901253042

2 1 3 2015 999999724 994512038

33.

478 6 9 3 2 5 2

989742624

396872748

769879 47 69 427 9 5 3 6 43 468 87 427 63 427410637

274812 37 4 4 4 4 693 5 4 6 8 7 39 40 9 5 3 201457 257 31271 994012377 99993529 521306748 10257376 60 3 1 27252 999230121 995230573 4 6 3 5 6 5 3 2

34.

2 4 6 987432 5 2 3 4 78761 5 3 2 487 649 77 2 4 9 6 7 7 8 624783624 728 637453 4 3 2 7 8 9 645 3 2 4 3 2 6728 67 4 2 3 5 978 47 2 6 4 1 324 2 6 4 7 3 1598 41 6247565 21 4 6 5 2911 5 6 4 5 6 2 161 4 5 6 099244 1 6 0 2 5 1436 264 05265 11 6 3 9 2 111 3 5 6 4 01240 3 6 5 4 10128 641901457

38. The cost of taking and printing the census of the United States in 1790, was $44377.28; in 1800, $66109.04; in 1810, $178444.67; in 1820, $208525.99; in 1830, $378545.13; in 1840, $832370.95; in 1850, $1318027.53. What has been the cost of these seven censuses? Ans. $3026400.59.

39. A farmer owns a farm worth $4775, a pair of oxen worth $115, a horse worth $100, six cows worth $30 each, and other property worth $1550; what is the value of his estate?

40. The area of North America in 1853, was about as follows, viz. - United States, 3,306,865 square miles; British America, 3,050,398; Mexico, 1,038,834; Central America, 203,551; Russian America, 394,000; Danish America, 380,000. What is the area of North America?

41. 66942 +48 +7432987 +463 + 87425 =

how many?

Ans. 7587865.

= =?

42. 874259876 + 427 + 895276528 +4307698742 43. 9227 +56 + 99 + 88+77 +66 +55 +44 + 22 +7 +33=?

44. $86.94 $17.06+ $45.64 $43.26 + $72.18 + $9.82 =?

45. $69432.87$469.84 $7694.1842693.14?

§ 4. SUBTRACTION.

35. SUBTRACTION* is taking a less number from a greater to find their difference.

The greater number is called the minuend; † the less, subtrahend;

the difference, remainder.

36. Subtraction is the reverse of addition.

RULE. 1. Write the less number under the greater,

under units, tens under tens, etc.

units

and draw a line beneath.

2. Beginning at the right hand, take each figure of the subtra

* Subtraction, from the Latin subtraho, to draw from under, to take away, to subtract.

† Minuend, from the Latin minuendus, to be diminished.

Subtrahend, from the Latin subtrahendus, to be subtracted from.

hend from the figure above it and set the remainder under the line.

3. If any figure in the subtrahend is greater than the figure above it, add TEN to the upper figure and take the lower figure from the SUM; set down the remainder and ADD ONE to the next figure in the subtrahend.

Ex. 1.

Minuend, 846
Subtrahend, 4 21

Remainder, 425

Ex. 2.

Minuend, 483
Subtrahend, 2 57
Remainder, 226

This example is solved by the first two sections of the rule and needs no explanation.

In this example we cannot take 7 units from 3 units, but if one of the 8 tens is put with the 3 units it will make 13 units, and 7 units taken from 13 units will leave 6 units. Now as one of the 8 tens has been put with the 3 units, there will remain but 7 tens and we may take the 5 tens from 7 tens; or, following the rule, we may add one ten to the 5 tens and take the sum (6 tens) from 8 tens, since the result will be 2 tens by either process.

Ex. 3.

(5) (9) (12) Minuend, 6 0 2 Subtrahend, 4 3 8 Remainder, 1 6 4

Here we cannot take 8 from 2, nor can we borrow from the tens' place, as that place is occupied by 0; but we can borrow one of the 6 hundreds and separate the one hundred into 9 tens and 10 units; then, putting the 9 tens in the place of tens and adding the 10 units to the 2 units, we can subtract 8 from 12, 3 from 9 and 4 from 5.

NOTE. — This process will probably be more readily understood by the young learner than that given in the rule, though the latter, being thought more convenient, is usually adopted.

37. PROOF. Add the subtrahend and remainder together and the sum should be the minuend.

NOTE. This proof rests upon the axiom that the whole of a thing is equal to the sum of all its parts; thus, the minuend is divided into the two parts · subtrahend and remainder; hence the sum of those parts must be the minuend.