The pupil should be required in all rules to prove his results It is of practical importance; besides, it occasions less trouble to the teacher in detecting mistakes.

18. From 99 take 22; take 55.
19. From 176 take 58; take 42.
20. From 176 take 90; take 100.
21. From 1000 take 700; take 550.
22. From 1000 take 600; take 400.
23. From 1500 take 1000; take 1200.
24. From 1500 take 900; take 350.
25. From 2538 take 1624; take 299.
26. From 2538 take 999; take 2000.
27. From 7836542 take 7000; take 70.
28. From 80000 take 79999; take 78888.
29. From 80000 take 5000; take 12345.
30. From 900000 take 1; take 10.
31. From 900000 take 100; take 1000.
32. From 900000 take 10000; take 100.
33. From 1000000 take 1; take 10.
34. From nine millions take 3.
35. From nineteen millions take nineteen.
36. From forty millions take one million.

A. 121.

A. 252.

A. 162.

A. 750.
A. 1000.
A. 800.
A. 1750.

A. 3153.
A. 2077.
A. 15666014.
A. 1113.
A. 142655.
A. 1799989.
A. 1798900.

A. 1789900.
A. 1999989.

A. 8999997.
A. 18999981.
A. 39000000.

SIMPLE MULTIPLICATION.

IX. 1. What will 3 books come to, at 20 cents apiece? Why? A. Because 20 and 20 are 40, and 20 are 69, 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 ure 90, that is, 3 times 30 ure 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?

1

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 multiplicand 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.

When the Multiplier is 12, or less.

Operation by Slate illustrated.

X. 1. How much will 4 barrels of pork come to at 17 dollars a barrel?

OPERATION.

Multiplicand, 17 dollars.
Multiplier,

4 barrels.

:

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. 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.

Product,

68 dollars.

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).

From these remarks and illustrations we derive the

following

RULE.

I. How are the terms to be placed? A. The less under the greater, with units under units, tens under tens, &c.

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

III. How are the figures of the multiplicand to be multiplied by the multiplier? A. Separately.

IV. 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 cents?

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. 1175778.
A. 1851840.
A. 987648.
A. 3801732.
A. 6566628.

A. 86415047523.
A. 135795074679.
A. 1180600065.

¶ XI. When the Multiplier is more than 12.

1. There are 365 days in one year; how many are there in 36 years?

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 multiplicand 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.

When the Multiplier is 12, or less.

Operation by Slate illustrated.

IX. 1. How much will 4 barrels of pork come to at 17 dollars a barrel ?

OPERATION.

Multiplicand, 17 dollars.
Multiplier, 4 barrels.

:

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. 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.

Product,

68 dollars.

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).

From these remarks and illustrations we derive the

following

RULE.

I. How are the terms to be placed? A. The less under the greater, with units under units, tens under tens, &c.

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

III. How are the figures of the multiplicand to be multiplied by the multiplier? A. Separately.

IV. 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 6 cents?

lemons come to, at 8 cents apiece? At

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. 1175778.
A. 1851840.
A. 987648.
A. 3801732.
A. 6566628.
A. 86415047523.
A. 135795074679.
A. 1180600065.

↑ XI. When the Multiplier is more than 12.

1. There are 365 days in one year; how many are there in 36 years?