86400 in a day, 604800 in a week, 2419200 in a month, and 31557600 in a year: how many seconds in the time named above?

7. Suppose a merchant to buy the following parcels of cloth: 3912 yards, 1856, 2011, 4540, 937, 6338, 3603, 1586, 2044, 2951, 4228, 1345, 1011, 6138, 960, 607, 5150, 13886, 617, 7513, 4079, 743, 612, 2519, 1238, and 2445 yards: how many yards in all?

8 What is the sum of two millions bushels of corn, five hundred and thirty-one thousand bushels, one hundred and twenty bushels, fourteen thousand bushels, thirty thousand and twenty four bushels, five hundred and sixty bushels, and seven hundred and two bushels?

9 The mail route from Albany to New York is 144 miles, from New York to Philadelphia 90 miles, from Philadelphia to Baltimore 98 miles, and from Baitimore to Washington City 38 miles: what is the distance from Albany to Washington?

10. A man dying leaves to his only daughter nine hundred and ninety-nine dollars, and to each of three sons two hundred dollars more than he left the daughter. What was each son's portion, and what the amount of the whole estate?

Ans.

Each son's part
Whole estate

dollars. dollars.

11. The number of acres of the public lands sold in 1834 was 4658218; in 1835, 12564478; in 1836, 25167833. The number sold in 1840 was 2236889; in 1841, 1164796; in 1842, 1129217. How many acres were sold in the first three,

and how many in the last three years?

Ans. {

1st 3 yrs.
last "

12 What was the population of the British provinces in North America in 1834, the population of Lower Canada being stated at 549005, of Upper Canada 336461, of New Brunswick 152156, of Nova Scotia and Cape Breton 142548, of Prince Edward's Island 32292, of Newfoundland 75000?

Ans.

13. By the census of 1850, the population of the ten largest cities was as follows: New York 515547; Philadelphia 340045; Baltimore 169054; Boston 136881; New Orleans 116375; Cincinnati 115436; Brooklyn 96838; St. Louis

77860; Albany 50763; Pittsburgh 46601: what was their entire population?

14. By the census of 1850, the number of deaf and dumb in the United States was 9803; of blind 9794; of insane 15610; of idiots 15787: what was the aggregate?.

Ans.

15. By the census of 1850, the population of the District of Columbia was 51687; of the Territory of Minnesota 6077; of New Mexico 61547; of Oregon 13294; of Utah 11380: what was the population of the Territories, including the District of Columbia?

16 By the census of 1850, the population of Maine was 583169; of New Hampshire 317976; of Vermont 314120; of Massachusetts 994514; of Rhode Island 147545; and of Connecticut 370792: what was the population of the six New England States?

17. By the census of 1850, the population of New York was 3097394; the population of New Jersey 489555; of Pennsylvania 2311786; and of Delaware 91532: what was the population of the four Middle States?

18. By the census of 1850, the population of Maryland was 583034; of Virginia 1421661; of North Carolina 869039; of South Carolina 668507; of Georgia 906185; of Florida 87445; of Alabama 771623; of Mississippi 606526; of Louisiana 517762; and of Texas 212592: what was the whole population of the ten Southern States?

Ans.

19. By the census of 1850, the population of Tennessee was 1002717; of Kentucky 982405; of Ohio 1980329, of Indiana 988416; of Illinois 851470; of Michigan 397654; of Wisconsin 305391; of Iowa 192214; of Missouri 682044; of Arkansas 209897; and of California 92597: what was the entire population of the eleven Western States?

Ans.

20. By the census of 1850, the population of the six New England States was 2728116; of the four Middle States 5990267; of the ten Southern States 6644374; of the eleven Western States 7685134; and of the five Territories 143985: what was the entire population?

21. Write the population of each State and Territory, in cluding the District of Columbia, and add the whole as a single example.

SUBTRACTION.

36. 1. John has 3 apples and Charles has 2: how many have both?

If John's apples be taken from the sum, 5 apples, how many apples will remain! 2 from 5 leaves how many ! 2. If James has 5 apples and gives 3 to Charles, how many will he have left! 3 from 5 leaves how many? Let the following table be carefully committed to memory: SUBTRACTION TABLE.

PRINCIPLES AND EXAMPLES.

37. John has 6 apples and gives 4 to Charles: how many has he left?

The 2 is called the difference between the numbers 6 and 4 and this difference added to the less number 4, will give the greater number 6: hence,

THE DIFFERENCE between two numbers, is such a number as added to the less will give the greater.

SUBTRACTION is the operation of finding the difference between two numbers.

When the two numbers are unequal, the larger is called the minuend, and the less is called the subtrahend. Their difference, whether they are equal or unequal, is called the remainder.

OF THE SIGNS.

38. The sign, is called minus, a term signifying less. When placed between two numbers it denotes that the one on the right is to be taken from the one on the left.

J

Thus, 6-4-2, denotes that 4 is to be taken from 6. Here, 6 is the minuend, 4 the subtrahend, and 2 the remainder.

1. James has 27 apples, and gives 14 to John: how many has he left?

37. What is the difference between two numbers? What is Subtraction? What is the larger number called? What is the smaller number called? What is the difference called? In the first example, which number was the minuend? Which the subtrahend? Which the remainder?

38. What is the sign of Subtraction? What is it called? What does the term signify? When placed between two numbers what does it denote ?

The 27 is made up of 7 units and 2 tens and the 14, of 4 units and 1 ten. Subtract units from 7. units, and 3 units will remain; subtract 1 ten from 2 tens and 1 ten will remain: hence, the remainder is 13.

27 Minuend.

14 Subtrahend.

13 Remainder.

2. What are the remainders in the following examples:

had

3. A farmer had 378 sheep, and sold 256: how many he left?

We first write the number 378, and then 256 under it, so that units of the same order shall fall in the same column. We then take 6 units from the 8 units, 5 tens from 7 tens, and 2 hundreds from 3 hundreds, leaving for the remainder 122.

378

256

122

4. A merchant had 578 dollars in cash, and paid 475 dol lars for goods: how much had he left?

5. What are the remainders in the following examples:

39. We see, from the above examples,

1st. That units of the same order are written in the same column; and

2d.

That units of any order are always subtracted from units of the same order.

40. To find the difference when any figure of the minuend is less than the one which stands under it.

1. What is the difference between 843 and 562 ?

39. What principles are shown by the examples?

40. Can you subtract a greater number from a less? When the upper figure is the least, how do you proceed? Does this change the difference between the numbers? What then may we always do?