Among 400. (2501) Among 550. (1819) A. $16,271+ 15 Among 17. (58858) Among 19. (52663) Among 89. (11242) Among 98. (1021) Among 199. (5028) A. 138 dollars, Í mill-+

To multiply by, 1, §, 51, &c.

¶ XXVII. 1. How much is of 10? of 18? of 16? of 20?

RULE.

I. To multiply 4 by 2, we take 4, 2 times; to multiply by 1, we take 4, 1 time; and to multiply 4 by 4, we take 4, a time, that is, the half of 4, and to get this, it is plain that we must divide 4 by 2. From these remarks what appears to be the rule. for multiplying by 1, 1, 1, &c.? A. Divide the multiplicand by the figure below the line.

2. How much is of 20 of 20? of 12? of 12? of 12?

II. In these examples we divide by 5 to get of 20: then it is plain, that is 2 times as much as, that is, we multiply of 20, which is 4, by 2, making 8: but we might multiply 20 by the 2 first, and divide by the 5 afterwards; thus, 2×20=40÷5, 8 times, the same result as before: how, then, does it appear that we can proceed to multiply by &, I, , &c.? A. Divide the multiplicand by the figure below the line, and multiply this quotient by the figure above the line; or multiply first, and then divide.

Exercises for the Slate.

1. What will 2 yards of cloth cost at 28 cents a yard?

How do you multiply by the 2, in 24?

How do you proceed next? A. I get

then multiply the 4 by 5, making 20.

A. As usual?

of 28, making 4

What do you do with the 20? A. I add it to 56, making 76.

More Exercises for the Slate.

2. At 30 cents a bushel, what will 19 bushels of oats cost?

A. $5,72.

3. Tell me how by 5. A. 275.

4. What will 22

(245) What will 22

15

many yards 50 rods are, or multiply 50

yards of cloth come to, at $11 a yard?

(246) What will 23? (260) 31?

(42) 31††? (351) 99T? (1095) A. 2239. 5. What will 22 yards come to at $12 a yard? (33) What will 5? (66) 63 ? (80) 812 (105) 10? (122) 15%? (186) 25 ?

4. $898.

(306)

years

6. If a man's salary be $1200 a year, what will 2 come to? (2420) What will 3? (3630) 5%? (6040) 8888? (10710) 12838? (15598) A. $38398.

When the price is an ALIQUOT part of a dollar, or, PRACTICE.

of

How

↑ XXVIII. 1. At 50 cents a bushel, what will 2 bushel of apples cost? What will 4 bushels? How much is of 4. How much is of 8? What will 8 bushels cost, then? much is 12? How much will 12 bushels cost, then? How much is of 40? What will 40 bushels cost, then ' How much is of 100? What will 100 bushels cost, then? 2. At 25 cents a peck, what will 2 pecks of salt cost? 4 pecks cost? Will 8 pecks cost? How much is of 8? How much is of 16? Will 16 pecks cost, then? How much is of 20? Will 20 pecks cost, then? How much is of 400 ? Will 400 pecks cost, then?

Will

3. What will 2 oranges cost, at 12 cents apiece? Will 4 oranges? Will 8 oranges? Will 16 oranges? How much is of 16? How much is of 24? What will 24 oranges cost, then? How much is of 80? Will 80 oranges cost, then?

What

4. At 6 cents a pint, what will 2 pints of ale cost? will 4 pints cost? 8 pints? 16 pints? How much is 16 of 16? How much is 6 of 32? Will 32 pints cost, then?

Q. What part of a dollar is 50 cents? A. Because 2 times 50 are 100 c. = $1.

Q. What part of a dollar is 25 cents? Because 4 times 25 c. are 100 c. ==

$1.

Q. What are these even parts called?

Why? A.

A. 1. Why? A

A. Aliquot Parts.

Q. When, then, one number is contained in another exactly 2, 3, 4, &c. times, what is it called? A. An Aliquot Part. Q. What is the method of finding the cost of articles, by aking aliquot parts, usually called? A Practice.

Repeat the Table of the aliquot parts of a aoilar.

Cts.

50

334

25 =

20

16

12

10

6

5

Cts. Cts.

of a dollar, because 2×50 100=i. of a dollar, because 3X33-100=1. of a dollar, because 4X25 =100=1. of a dollar, because 5×20=100=1. of a dollar, because 6×16=100=1. of a dollar, because 8X12=100=1. of a dollar, because 10×10 =100=1. of a dollar, because 16× 61=100=1. of a dollar, because 20× 5=100=1.

RULE.

I. From the illustrations now given, what appears to be a concise rule for calculating the cost of articles, when the price is an aliquot part of a dollar? A. Divide the number of gallons, yards, &c. by the number of aliquot parts which it takes of the price to make a dollar.

II. What will the quotient be? A. The answer, in dollars Q. For example, what would you divide by when the price is 50 cents? 331 cents? 25 cents? 20 cents? 163 cents ? 12 cents? 10 cents? 64 cents? 5 cents?

Exercises for the Slate.

1. What will 360010 yards of cloth cost, at 12 cents a yard?

OPERATION.

8) 360010,00

$45001,25, Ans.

How do you get the divisor, 8? A. 12 cents= of a dollar.

How do you obtain the 25 cents in the answer? A. I annex 2 ciphers for cents, and continue dividing.

2. What cost 2640 bushels of rye, at 50 cents a bushel? A. $1320.

3. At 25 cents a bushel, what will 4680 bushels of potatoes Cost? (1170) Will 3600 bushels cost? (900) Will 4200 bushels Cost? (1050) A. $3120.

4. At 6 cents, or of a dollar, what will 6400 yards of

tape cost? (400) Will 32000 yards? (2000) Will 128000 yards. (8000). A. $10400.

5. What will 2700 yards of ribbon cost at 12 cents a yard (33750) Will 5400 yards? (675) Will 1080 yards? (135) A. $1147,50.

6. What will 42124 oranges cost at 5 cents, or of a dol lar apiece? A. $2106,20.

7. What will be the cost of 1200 yards of cloth, at 50 cents a yard (600) At 33 cents a yard? (400) At 25 cents a yard? (300) At 20 cents a yard? (240) At 12 cents a yard? (150) At 64 cents a yard? (75) A. $1765.

8. At 163 cents a pint, what will 2700 pints of brandy cost? (450) At 10 cents a pint, what will 5400 pints cost? (540) A. $990.

9. What will 36002 bushels of salt cost, at $1,12), or $1} of a dollar, a bushel? At $2,25 a bushel ?

10. What will 3700 acres of land cost, at $12,25 ($124) an acre? (45325) What will 3700 acres, at $15,50 ($15) an acre? (57350) A. $1026,75.

11. What will 27000 yards of broadcloth cost, at $3,50 ($3) a yard? (94500) At $2,33} ($24) a yard? (63000)" At $1,12} ($11) a yard? (30375) At $4,064 ($46) a yard? (10968750) At $1,05 ($12) a yard? (28350) A. $325912,50+.

Questions, involving the Principles of the foregoing Rules.

1 A man bought a farm for thirty-six hundred dollars, and stock for the same to the amount of seven hundred and twenty dollars; what did both cost? and how much did one cost more than the other? A. Both, $1320; the farm, $2880 the most. 2. What is the amount of the following numbers, viz., ten, thirty, one million, twenty-six thousand, one hundred and one? A. 1026141.

3. If the minuend be 26002, and the subtrahend 101, what is the remainder? (25901) If the subtrahend be 601, and the remainder 5025, what is the minuend (5626) A. 31527

4. If the multiplicand be 4200, and the multiplier 48, what is the product? (201600) If the product be 201600, and the multiplicand 4200, what is the multiplier? (48) A. 201648.

5. If the divisor be 25, and the dividend 5025, what is the quotient? (201) If the quotient be 201, and the divisor 25, what is the dividend? (5025) If the quotient be 201, and the dividend 5025, what is the divisor? (25) A. 5251.

6. If the sum of two numbers be 1800, and the greater 1000, what is the less? (800) If the less be 120, and the sum 1320, what is the greater? (1200) A. 2000.

7.

2700342+72+3+1=Ans. 2700418.

8. 367895437 72591=Ans. 367822846.

9. 25432 X 67345 Ans. 1712718040. 10. 360042÷8542=Ans. 4217§.

11. 27000000111 Ans. 9000000

30000

=

12. Bought 18 barrels of potatoes, each containing 3 bushels, at 25 cents a bushel; what did the whole cost? Ans. $13,50.

13. A farmer sold 30 bushels of rye, at 87 cents a bushel; 30 bushels of corn, at 53 cents a bushel; 8 bushels of white beans, at $1,25 a bushel; two yoke of oxen at $62 a yoke; 10 calves, at $4 apiece; and 15 barrels of cider, at $2,37) a barre ; what was the amount of the whole? A. $251,025.

14. A merchant, failing in trade, has on hand goods to the amount of $4800, and his borrowed money is $2400: the remainder, after paying his borrowed money, is to be equally divided among 121 creditors: how much will each receive? A. $19181.

15. A grocer bought 4 loads of wood, at $2,25 a load (9)· 8 bushels of rye, at $,50 a bushel (4); 30 pounds of butter, at 12 cents a pound (375); 340 pounds of cheese, at 6 cents a pound (2125); for which he paid 5 barrels of flour, at $6,25 a barrel (3125); 35 pounds of sugar, at 84 cents a pound (2975); 3 gallons of molasses, at 25 cents a gallon (75); 15 bushels of salt, at $1,12 a bushel (16875); what is the balance between tho articles bought and sold? A. $13,85.

16. What will be the price of 4 bales of goods, each bale containing 60 pieces, and each piece 49 yards, at 37 cents a yard' A. $4410.

17. How many oranges, at 2 cents apiece, can be bought for 4 cents? For $2, or 200 cents? A. 102. For $8600? For $10000? A. 930000.

18. How many yards of cloth, at $2 a yard, may be bought for 4 barrels of cider, at $3 a barrel? For 8 barrels? A. 15 For 28 barrels: For 50 barrels? A. 117.

19. How many gallons of molasses, at 23 cents a gallon, may be had for 60 bushels of oats, at 46 cents a bushel? At 60 cents a bushel? A. 300 gallons.