4. A farmer set out 40 trees in an orchard, and his neighbor 70; which set out the most, the farmer or his neighbor? How many the most?

5. What is the difference between 30 and 60? 20 and 50? 60 and 80? 30 and 45? 40 and 78 ? 50 and 120; that is, between 5 tens and 12 tens? 70 and 150 ?

6. A grocer who had 20 cheeses sold 15; how many had he left? Explanation. 5 from 20 leaves how many? 10 from 15 leaves how many ?

7. If you have 40 cents, and pay away 25 of them for a book, how many will you have left?

8. A man who lives 16 miles from Boston, travelled 12 miles towards that city; how far was he from it then?

9. If you take 19 eggs from a basket that contains 32, how many will you leave?

10. If you take 13 chestnuts from 18, how many will you leave? How many will you leave if you take 21 from 37 ? 32 from 40? 26 from 35? 57 from 72? 62 from 70? 200 from 300? 150 from 230 ?

LESSON 23.

For the Slate.

1. A young man having 665 dollars, paid 464 dollars for a piece of woodland; how much money had he left ?

OPERATION.

665

46 4

201 dollars. Ans.

Explanation. We first write 464, the smaller number, under 665 the larger, with units under units, tens under tens, &c., and draw a line beneath. We now say 4 from 5 leaves 1, we place this 1 under the units, and so proceed to take 6 tens from 6 tens, and 4 hundreds from 6 hundreds; thus, 6 from 6 leaves 0, 4 from 6 leaves 2.

The smaller number, which we subtract, is called the subtrahend, the larger number the minuend, and the number obtained, the difference or remainder; thus, in the preceding example, 464 is the subtrahend, 665 the minuend, and 201 the difference or remainder.

How do we proceed in example 1, lesson 23, to subtract 464 from 665? What is called the subtrahend? Minuend? Difference or remainder? In example 1, lesson 23, what is the subtrahend? Minuend? Difference or remainder?

2. A planter, who had 96 bales of cotton, sent 45 of them to Charleston; how many were left ?

Ans. 51.

3. If you have 688 mill-logs, and get 133 of them sawed, what number will remain ?

Ans. 555.

4. A man who had 45,647 feet of boards, sent away 21,546 feet; what quantity did he keep? Ans. 24,101 feet. 5. A merchant, worth 8,946 dollars, lost 805 dollars in a speculation; how much was he then worth?

Ans. 8,141 dollars. 6. A farmer in Michigan raised 1,507 bushels of wheat, and sold 1,103 bushels; what quantity did he retain ? Ans. 404 bushels.

LESSON 24.

1. A man who had 43 acres of land, sold 26 acres ; how many acres did he keep?

OPERATION.

43 26

17 acres. Ans.

Explanation. Being unable to take 6 units from 3, we borrow 1 of the 4 tens, add it to 3, and take 6 from 13; having now only 3 tens left in the upper number, we take 2 tens from 3 tens.

Another better way. Being unable to take 6 units from 3, we add 10 to 3, and take 6 from 13; as we have added 1 ten to the upper number, to balance it, we now add 1 ten to the lower number, and take 3 tens from 4 tens. We proceed in subtracting thus; 6 from 13 leaves 7, 1 carried to 2 makes 3, 3 from 4 leaves 1.

2. A farmer raised 636 bushels of potatoes, and after saving 457 bushels for himself, sold the remainder; how many bushels did he sell? Ans. 179. Explanation. Add 1 hundred, or 10 tens, to 3 tens, in order to subtract, and then carry 1 hundred to the 4 hundred.

3. A ship had 35 persons on board, including the passengers and crew; how many passengers were there if the crew consisted of 9 men? Ans. 26.

4. If you have 8,005 dollars, and buy a farm for 5,126 dollars, how much money will you have left?

Ans. 2,879 dollars.

Explain how we subtract 26 from 43, in example 1, lesson 24. How

do we proceed in subtracting 26 from 43?

5. A company of merchants commenced trade with one hundred and twelve thousand three hundred and five dollars; at the end of a year they had eighty-one thousand three hundred and seven dollars remaining; how much had they lost? Ans. 30,998 dollars.

LESSON 25.

From what precedes we get the following

RULE FOR SUBTRACTION.

Write the smaller number under the larger, with units under units, tens under tens, &c., and draw a line beneath. Subtract the units in the lower number from the figure above, and put the remainder directly below; proceed in the same way with the tens, hundreds, &c. If a figure in the lower number be larger than the figure above, add 10 to the one above, subtract, and then carry 1 to the next figure or place below. If you take 3 walnuts from a heap that contains 8, there will be 5 left. If you now add the 3 walnuts to the remainder 5, there will be 8 in the heap again.

Therefore, as we sometimes make a mistake in subtracting, we can prove the work,

By adding the smaller number to the remainder; if the sum be equal to the larger number, the work will generally be right.

1. Subtract 673 from 1,782.

OPERATION.

1782

673

PROOF.

To 1 1 0 9 remainder,

Add 673 smaller number,

1,1 0 9 remainder. 1,7 8 2 same as the greater number. Note. Each example should now be proved.

(2.) From 6 0025

take

(3.)

4 6

From 32 457 3 8 1 9746 take 1472 33518869

How do you write the numbers in Subtraction? What do you subtract first? Where do you put the remainder? How then do you proceed? What if a figure in the lower number be larger than the figure above?

If you take 3 walnuts from a heap that contains 8, how many will be left? If you now add the 3 walnuts to the remainder 5, how many will there be in the heap again?

How, then, can we prove the work in Subtraction?

1. From 64,321,535,488,327 take 10,035,780,321,199. 2. From 9,000,052 take 1,643,215.

3. From 750,081 take 3,011.

4. 81 men were engaged in quarrying stone; after a number were discharged, there were 33 left; how many were discharged?

Ans. 48. 5. George Washington died in the year 1799, aged 67 years; in what year was he born?

Ans. in 1732. 6. A man who had 11,375 dollars in his possession, paid all his debts, amounting to 3,287 dollars; how much money had he left ?

Ans. 8,088 dollars.

7. By how much do 48,323 dollars exceed 19,295 dollars ? Ans. 29,028 dollars. 8. A brickmaker had a kiln containing 43,000 bricks ; after he had sold 25,376, how many remained? Ans. 17,624.

9. If you buy 275 bushels of wheat for 400 dollars, and sell 125 bushels for 198 dollars, how many bushels have you left, and what have they cost you?

Ans., you have 150 bushels left, and they have cost you 202 dollars.

10. If you have 23 apples, and a boy gives you 16 more, how many will you have after giving your sister 15, and your brother 8 ?

LESSON 27.

Ans. 16.

1. A merchant who had 5,635 pounds of coffee, sold 1,210 pounds to one man, and 3,145 to another; how much had he then left? Ans. 1,280 pounds. 2. A tree seventy-five feet high, was broken off by the wind, and the part that fell was thirty-nine feet long; how high was the stump left standing? Ans. 36 feet.

3. A grocer sold a quantity of butter for 103 dollars, and made 27 dollars on it; how much did it cost him? Ans. 76 dollars. 4. How many years is it since the Pilgrims landed at Plymouth, in the year 1620 ?

5. If a clerk collects 2,750 dollars from one person, and 1,385 from another, and pays out of it 275 dollars to one man, and 323 to another, how much will be left?

Ans. 3,537 dollars.

6. In 1830 France contained 32,052,465 inhabitants, and the British Empire 22,297,621; how many more people had France than the British Empire ? Ans. 9,754,844.

7. If I travel 2,332 miles from home, and then return 1,421 miles, how far am I from home then? Ans. 911 miles. 8. A man gave 15,235 dollars for a ship, and sold her for 12,250 dollars, how much did he lose?

Ans. 2,985 dollars. 9. If you buy a horse and chaise for 235 dollars, and sell the chaise for 147 dollars, what will be the cost of the horse to you? Ans. 88 dollars. 10. There is a bin that holds 2,000 bushels; if there are 9 bushels of corn in it, how many more will it hold ? Ans. 1,991 bushels.

MULTIPLICATION.

LESSON 28.

To be performed in the mind.

1. If one orange costs 3 cents, what will 2 oranges cost? 2 times 3 are how many then? 3 times 2 are how many? 2. Mary recites 3 lessons a day; how many will she recite in 5 days?

3. A merchant bought 4 barrels of flour at 6 dollars a barrel; what sum must he pay for the whole? What number then are 4 times 6? 6 times 4?

4. What shall I pay for 6 yards of cloth, at 2 dollars a

yard?

5. What sum must you pay for 7 weeks' board, at 3 dollars a week ?

6. A man walked 4 miles an hour for 8 hours; how far did he go in that time? 8 times 4 are how many then ? 4 times 8 ?

7. George bought 5 camels' hair pencils at 5 cents apiece; what did he pay for them?

8. A gardener gave 9 children 2 apples apiece; what number did they all receive?

9. How many days are there in 10 weeks, there being 7 days in a week?

10. What sum must I give for 6 pounds of sugar at 8 cents a pound? How many are 6 times 8 then? 8 times 6?