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4. 67 years.

1492; how many years had elapsed at the time when hostilities commenced, in the revolutionary war, 1775 ? A. 283 years.

11. Gen. Washington was born in 1732, and died in 1999; how old was he?

12. William has 15 cents; he owes Rufus 6 cents, and James 4; now how many will he have left, after paying Rufus and James ?

13. A merchant owes to the Exchange Bank 2365 dollars, to the Bank of North America 15000 dollars, and his whole stock is worth no more than 42000 dollars; how much will he have left, after paying both banks ? A. 24635.

14. If you buy 20 apples for 40 cents, and sell 15 for 35 cents, how many apples will you have left, and how much will they cost you ?

15. A grocer buys 560 bushels of rye for 530 dollars, and sells 200 bushels for 400 dollars ; how many bushels will he have left, and what will they cost him? A. 360 bushels, and they cost him 130 dollars.

16. A wine merchant bought 3600 gallons of wine ; and sold at one time 2400 gallons, at another 1000 gallons ; how many gallons has he on hand ? 'A. 200.

17. From 200 take 150; take 190.

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* To prevont the learner from copying his answer from the book, the following examples have answers formed by adding together two separate results. Each of these results is, in all such cases, however simple the process, given in the Key, which goes along with the work. 18. From 99 take 22; take 55.

6. 121. 19. From 176 take 58; take 42.

.4. 252. 20. From 176 take 90; take 100.

A. 162. 21. From 1000 take 700; take 550.

A. 750. 22. From 1000 taķe 600; take 400.

A. 1000. 23. From 1500 take 1000; take 1200.

A. 800. 24. From 1500 take 900; take 350.

A. 1750 25. From 2538 take 1624; take 299.

A, 3153. 26. From 2538 take 999; take 2000.

A. 2077.
27. From 7836542 take 7000; take 70. 1. 15666014.
28. From 80000 take 79999; take 78888. A. 1113
29. From 80000 take 5000; take 12345. A. 142655.
30. From 900000 take 1; take 10.

A. 1799989.
31. From 900000 take 100; take 1000. A. 1798900.
32. From 900000 take 10000; take 100. A. 1789900.

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33. From 1000000 take 1; take 10.
34. From nine million take 3.
35. From nineteen million take nineteen.
36. From forty million take one million.

A. 1999989.
A. 8999997.
A. 18999981,
A. 39000000.

SIMPLE MULTIPLICATION. TIX. 1. What will 3 books come to, at 20 cents apiece? Why? A. Because 20 and 20 are 40, and 20 are 60; that is, 3 times 20 are 60.

2. What will 3 bushels of apples come to, at 30 cents a bushel? Why? A. Because 30 and 30 are 60, and 30 more are 90 ; that is, 3 times 30 are 90.

3. What will 2 cows come to, at 10 dollars a head? At 12 dollars ? At 14 dollars ? At 18 dollars ? At 20 dollars? At 25 dollars ? How many are 2 times 10, then? 2 times 12? 2 times 14? 2 times 18? 2 times 20? 2 times 25 ?

4. What will 30 yards of cloth come to, at 2 cents per yard? What will 14 yards ? 16 yards ? 12 yards ? 25 yards ? 30 yards ? 60 yards? 80 yards? How many are 2 times 30 ? 14? 16 ? 12? 25? 30 ? 60 ? 80 ?

5. What will 3 yards of cloth come to, at 10 cents per yard? What will 4 yards? 6 yards? 12 yards? 20 yards? 30 yards? 60 yards ? 80 yards ? How many are 10 times 3? 4? 6? 12? 20 ? 30 ? 60 ? 80 ?

6. What will 4 oranges cost, at 10 cents apiece? Why? A. Because 10 and 10 are 20, and 10 are 30, and 10 more are 40; that is, 4 times 10 are 40.

Q. What, then, is multiplication a quick way of performing ?
A. Many additions.

Q. What is the number called, which is to be added to itself, or re peated several times ?

A. The Multiplicand.

Q: What is the number, which shows how many times the multipli cand is to be repeated, called ?

A. The Multiplier.
Q. What are both inultiplier and multiplicand sometimes called 1
A. Factors, or Terms.
Q. What is the result, or number found by multiplying, called ?
A. The Product.

1 X. WHEN THE MULTIPLIER IS 12, OR LESS.

Operation by Slate illustrated. 1. How much will 4 barrels of pork come to, at 17 dollars a barrel ? OPERATION.

Q. Since 4 times 7 are the Multiplicand, 17 dollars.

same as 7 times 4, we see that

it makes no difference which Multiplier, 4 barrels.

number is considered the mul

tiplier : why is the 4, then, Product, 68 dollars. made the multiplier in this ex

ample? A. For the sake of convenience, it being the smaller number. Q. How do you get the 8 units in the product? A. I say, 4 times 7 (units) are 28 (units), or 2 tens and 8 units, writing down the 8 units, and carrying the 2 (tens), as in Addition.

Q. How do you obtain the 6 (tens)?

A. I say, 4 times 1 (ten) are 4 (tens), and 2 (tens), to carry, make 6 (tens). PROOF.

PROOF. Q. As 3 times 17 17

and 1 time 17 evidently make 3 1 less than 4, the for

4 times 17, how can you prove mer multiplier.

the above operation ? 51

A. I can

2 multiply 17 by 3, one 17 the multiplicand.

less than 4, making 51; then

add 17 (the multiplicand) to 51, 68 like the result of the

making 68; which, being like

the result in the first operaother operation,

tion, proves the work to be therefore right.

right. From these remarks and illustrations we derive the following

RULE. Q. How are the terms to be placed ?

A. The less under the greater, with units under units, tens under tens, &c.

Q. At which hand do you begin to multiply ?
A. At the right hand.

Q. How are the figures of the multiplicand to be multiplied by the multiplier ?

A. Separately.
Q. How do you carry and write down?
4. As in Simple Addition.

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More Exercises for the Slate. 2. What will 125 pounds of cheese cost, at 6 cents a pound? A. 750 cents.

3. What will 420 pounds of pork come to, at 9 cents a pound? A. 3780 cents.

4. What will 167 barrels of flour come to, at 9 dollars a barrel ? A. 1503 dollars.

5. What will be the price of 8 hogsheads of wine, at 129 dollars per hogshead? A. 1032 dollars.

6. A merchant sold 895 oranges, at 11 cents apiece; what did they come to? A. 9845 cents.

7. What will 236 lemons come to, at 8 cents apiece? At 6 cents ? 236 236

1888 6

8

1416

1416
1888

3304 Ans. X For the answers to each individual process, the teacher can consult the Key. 8. Multiply 120 by 2; by 3.

A. 600. 9. Multiply 1211 by 5; by 6.

A. 13321. 10. Multiply 1211 by 7; by 8.

A. 18165. 11. Multiply 65321 by 9; by 6.

A. 979815. 12. Multiply 65321 by 8; by 10.

A. 1175778. 13. Multiply 123456 by 11; by 4.

A. 1851840. 14. Multiply 123456 by 3; by 5.

A. 987648. 15. Multiply 345612 by 3; by 8.

A. 3801732. 16. Multiply 345612 by 12; by 7.

A, 6566628. 17. Multiply 12345006789 by 3; by 4. A. 86415047523. 18. Multiply 12345006789 by 5; by 6. A. 135795074679. 19. Multiply 236120013 by 2; by 3. A. 1180600065.

1 XI. WHEN THE MULTIPLIER IS MORE THAN 12. 1. There are 365 days in one year; how many are there in 36 years?

Q. How do you get the 2190 ? OPERATION.

A. By multiplying 365 by 6, as 365 days.

in X.

Q. How do you obtain the 1095 ?

A. By multiplying 365 by 3, as

before. 2190

Q. Now, as you have seen that 1095

figures increase their value ten

times, by being removed one place 13140 days, Ans. farther towards the left, can you tell

me why 1095 is so removed, thereby making the 5 to fall under the multiplier 3?

36 years.

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A. Multiplying by the 3 tens, that is, 30 units, gives a product 10 times greater than if the 3 tens were 3 units; hence the 5 must be placed in the tens' place

To explain why you add the two products together.
Q. What does multiplying 365 by 6 give ?
A. The number of days in 6 years.
Q. What does multiplying 365 by 3 tens give ?
Ă. As the 3 (tens) are 30 units, multiplying by 30 will, of
course, give the number of days in 30 years.

Q. Why, then, do you add these two products together?

Ā. To get the whole number of days in 30 and 6 years, that
is, in 36 years.
From this example we derive the following

RULE.
Q. How do you write the numbers down, and multiply?
A. As in TX.
Q. Where do you write the first figure in each product ?
A. Directly under its multiplier.
Q. How do you proceed next?
A. Add all the products together as they stand.

More Exercises for the Slate.
2. What will 315 bushels of rye cost, at 42 cents a bushel ?
A. 13230 cts.

3. There are 63 gallons in a hogshead; how many gallons are there in 25 hogsheads ? A. 1575 gallons.

4. What will 426 gallons of molasses cost, at 46 cents a gallon? A. 19596 cts.

5. If 363 men can do a piece of work in 137 days, how long will it take one man to do the same ? A. 49731 days.

6. What will 234 barrels of beef come to, at 15 dollars 2 barrel ? At 13 dollars a barrel ? H. 6552 dollars.

7. If a man receive 256 cents for one day's work, how many cents will he receive, at that rate, for 17 days? For 29 days? A. 11776 cents. For 116 days? For 105 days? A.56376,

8. If the stage runs 9 miles an hour, how many miles will it run, at that rate, in 12 hours? In 19 hours ?

A. 279 miles. In 25 hours? In 36 hours ? A. 549 miles.

9. If a man save 161 dollars in a year, how much will it amount to in 19 years ? In 35 years ? A. 8694 dollars. 10. Multiply 62123 by 13.

A. 807599. 11. Multiply 35432 by 14; by 15.

A. 1027528. 72. Multiply 65217 by 16; by 17.

A. 2152161. 3. Multiply 207812 by 19; by 21.

A. 8312480. . Multiply 207812 by 25 ; by 35.

A. 12468720.

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