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IX.

SIMPLE MULTIPLICATION.

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 inore 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 repeated several times?

A. The Multiplicand.

Q. What is the number, which shows how many times the multi sand is to be repeated, called?

A. The Multiplier.

Q. What are both multiplier and multiplicand sometimes called
A. Factors, or Terms.

Q. What is the result, or number found by multiplying, called?
A The Product.

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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.

Multiplicand, 17 dollars.
Multiplier,

Product,

4 barrels.

68 dollars.

Q. Since 4 times 7 are the same as 7 times 4, we see that it makes no difference which number is considered the multiplier : why is the 4, then, made the multiplier in this example?

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.

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).

17

PROOF.

31 less than 4, the former multiplier.

51

17 the multiplicand.

68 like the result of the other operation,— therefore right.

PROOF. Q. As 3 times 17 and 1 time 17 evidently make 4 times 17, how can you prove the above operation?

A. I can multiply 17 by 3, one less than 4, making 51; then add 17 (the multiplicand) to 51, making 68; which, being like the result in the first operation, proves the work to be 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?
A. As in Simple Addition

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?

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For the answers to each individual process, the teacher can consult the Key.

8. Multiply 120 by 2; by 3. 9. Multiply 1211 by 5; by 6. 10. Multiply 1211 by 7; by 8. 11. Multiply 65321 by 9; by 6. 12. Multiply 65321 by 8; by 10. 13. Multiply 123456 by 11; by 4. 14. Multiply 123456 by 3; by 5. 15. Multiply 345612 by 3; by 8. 16. Multiply 345612 by 12; by 7. 17. Multiply 12345006789 by 3; by 4. 18. Multiply 12345006789 by 5; by 6. 19. Multiply 236120013 by 2; by 3.

A. 600.

A. 13321.

A. 18165.

A. 979815.
A. 1175779.

A. 1851840.
A. 987648.
A. 3801732.
A. 6566628.
A. 86415047523.
A. 135795074679.
2. 1180600065.

¶ XI. WHEN THE MULTIPLIER IS MORE THAN 12.

1. There are 365 days in one year; how many are there in

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?

A. 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? A. 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 a barrel? At 13 dollars a barrel? A. 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? 1776 cents. For 116 days? For 105 days? A. 56576.

8 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 amount to in 19 years? In 35 years? A. 8694 dollars. 10. Multiply 62123 by 13.

11. Multiply 35432 by 14; by 15. 12. Multiply 65217 by 16; by 17. 13. Multiply 207812 by 19; by 21. 14. Multiply 207812 by 25; by 35.

A. 807599.

A. 1027528.

A. 2152161.

A. 8312480.
A. 12468720.

15. Multiply 32100421 by 65; by 85. 16. Multiply 32100421 by 27; by 33.

A. 4815063150.

A. 1926025260.

17. Write down one thousand, multiply it by 25, add five housand to the product, subtract twenty-nine thousand nine nundred and ninety-nine from the amount, and see if the re mainder be 1.

¶ XII. WHEN THE MULTIPLIER IS 10, 100, 1000, &c. Q. How many are 10 times 5? Now, if we annex a cipher to the 5, thus, 50, it will produce the same effect: why is this?

A. Because, by annexing a cipher to 5, the 5 is removed to the tens' place; hence the value is increased 10 times.

Q. What effect would two ciphers have, or three ciphers, &c.? A. Two ciphers would remove any figure two places towards the left, and of course increase it 100 times, and so on for 1000, &c.

RULE. Q. What, then, appears to be the rule?

A. Annex to the multiplicand all the ciphers in the multiplier.

Exercises for the Slate.

1. What will 36 bushels of rye cost, at 100 cents a bushel A. 3600 cents.

2. What will 100 bushels of salt cost, at 87 cents a bushel? What will 1000 bushels ? What will 10000 bushels? What will 10 bushels? A. 966570 cents.

3. Multiply 8978 by 10; by 100; by 1000; by 10000; by 100000; by 1000000. A. 9975545580.

T XIII.

WHEN THERE ARE CIPHERS AT THE RIGHT HAND OF EITHER OR BOTH THE FACTORS.

RULE. Q. From the illustrations given, ¶ XII., how does it appear that we can multiply?

A. Multiply without the ciphers first, and annex them to the product.

Exercises for the Slate.

(1.)

Multiplicand, 63500

50

Q. How do you get the 3 ciphers in the product?

A. There are 2 at the right of the multiplicand, and 1 at the 3175000 right of the multiplier making 3

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