Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση
[blocks in formation]

-. XVII. We will now give a process, adapted to all cases in Multiplication.

1. A carpenter received 1,565 dollars for building a house. How much ought he to receive for building 17 houses at that rate?

Here 17 is the multiplier. First find how much he ought to receive for 7 houses; thus,

1565

Then find how much for 10 houses, by
annexing a cypher to 1,565; thus,

10955

15650

Ans. 26605

2. In a garrison, if the allowance of one man is 23 ounces of provision a day, how many ounces a day ought 634 men to have?

Here 23 is the multiplier.

First, find what it would amount to at 3 ounces per day; thus,

634

[blocks in formation]

In these examples we found the answer from multiplying by the units in the multiplier, (according to x1,) then, by the tens, (according to § xvi,) and, finally, adding the two products together.

We may do the same thing a little more concisely, thus:

3. How many yards in 29 pieces of cloth, each piece containing 132 yards.

[blocks in formation]

3828 Ans.

Then, add the two products, thus,

It will be seen that the cypher need not be placed at the right of the tens' product, if the first figure of that product be written under the order of tens. For it counts nothing in the addition. We may proceed in the same manner, if the multiplier consists of more figures. For example:

4. What are 953 sheep worth, at $1.75 apiece ? Operation. 953

175

Here, we multiplied first by the 5 units, then, by the 7 tens, and then by the 1 hundred. We 4765 likewise placed the right hand figures of the last 6671 two products, under their respective orders, omitting to annex the cyphers, required by the rule in Sect. XVI, because, in this case, unnecessary.

953

$1667.75 Thus we have a product corresponding to each order of the multiplier. These products are sometimes called PARTIAL PRODUCTS; their amount when added, the TOTAL PRODUCT.

If any order in the multiplier is filled by a cypher, there will be, of course, no partial product, corresponding to that order. Thus, 5. A man gave 185 dollars a pipe, for 107 pipes of wine. What cost the whole ?

Operation. 185

107

Here, the tens' order is filled by a cypher. It 1295 has, consequently, no partial product, 185

$19795 Ans.

Hence, the general rule for Multiplication.

I. PLACE THE MULTIPLIER UNDER THE MULTIPLICAND SO THAT THE SAME ORDERS MAY STAND UNDER EACH OTHER.

II. MULTIPLY THE MULTIPLICAND BY EACH SIGNIFICANT FIGURE IN THE MULTIPLIER, PLACING THE FIRST FIGURE OF EACH PARTIAL PRODUCT UNDER THE ORDER OF ITS MULTIPLIER.

III. ADD THE SEVERAL PRODUCTS AS THEY Stand. THE AMOUNT WILL BE THE PRODUCT REQUIRED.

NOTE. You will be sure to arrange your partial products correctly, if you place the right hand figure of each, exactly under the figure by which you are multiplying.

EXAMPLES FOR PRACTICE.

6. What will 15 tons of hay come to, at $20.78 pr. ton?

Ans. $311.70

7. What will 857 barrels of pork come to, at $18.93 pr. barrel?

Ans. $16,223.01

8. What cost 144 bushels of wheat, at $3.51 pr. bushel?

Ans. $505.44. What did they all Ans. $1,924.00. 10. At 15 cents pr. pound, what cost 600 pounds of sugar?

9. A man bought 52 oxen, at $37.00 a head. come to ?

Ans. $90.00.

11. What cost 33 bushels of rye, at 94 cts. pr. bushel ?

Ans. $31.02.

12. If a gallon of rum cost 58 cts., what cost 203 gallons?

Ans. $117.74.

13. If 1 pound of snuff cost 47 cts., what cost 314?

Ans. $147.58.

14. If a bushel of rye cost 75 cts., how much will 829 bushels cost?

Ans. $621.75.

15. If an acre of land cost 37 dollars, what will 949 acres cost?

16. 34,293 74 Ans. 2,537,682 | 18. 37,864×209

17. 47,042 91

Ans. $35,113. 7,913,576

4,280,822 19. 25,203×4,025 101,442,075

20. 269,181X4,629

21. 40,634×42,068

22. 134,092 87,362

23. 918,273,645×1,003,245

1,246,038,849

1,709,391,112

11,714,545,304

921,253,442,978,025

In § XI. it is shown that the product is the same, whichever of the factors is made the multiplier. Hence, in order to prove multiplication,

I. INVERT THE ARRANGEMENT OF THE FACTORS, AND MULTI-4

PLY AGAIN.

But this is sometimes inconvenient; therefore, in such cases,

II. IF THE FIRST PRODUCT WAS OBTAINED BY THE RULE IN § XI, XV, XVI OR XVII, OBTÁIN ANOTHER, BY THE RULE IN § XII, XIII OR XIV; AND IF THE FIRST WAS OBTAINED BY ONE OF THE LATTER RULES, OBTAIN ANOTHER, BY ONE OF THE FORMER. It is hardly necessary to illustrate these modes of proof. We will, however, give one example of each.

I. At $1.25 a pound, what cost 173 pounds of tea?

FIRST OPERATION.

173
125

865

346

173

216.25 Ans.

PROOF.

125

173

375

875

125

216.25 Ans. as before.

II. At 56 dollars a barrel, what cost 129,874 barrels of brandy?

Operation by § XII.

129874

8

Proof by § XVII.
129874

56 is a com

posite number,

whose factors 1038992

are 8 and 7.

Ans. 7,272,944

56

779244

649370

7,272,944 Ans. as before."

EXAMPLES FOR PRACTICE.

1. At 27 dollars a piece, what cost 234 pieces of broadcloth? 2. At 52 dollars a barrel, what cost 72 barrels of brandy?

3. What will 763 hundred weight of sugar cost, at 15 dollars a hundred weight?

4. At 35 dollars a ton, what cost 749 tons of iron ?

5. At 33 cts. pr. yard, what cost 16 pieces of cloth, each containing 29 yards?

6. A ship sailed 26 days at the rate of 125 miles a day, and afterwards, 43 days at the rate of 98 miles a day. How far did she sail in all ?

7. 72,600X31,000. 8. 49,000X52,000. 9. 607,080X539,063 10. 41,725X687,900

11. 38,603X950,950

12. 712,314×23,000,333

13. 37,969,868×98,647,564 14. 363,464,565×271,892,955 15. 437,920,213234,678,956 16. 234,567,890,123×345,678,900,124

§ XVIII. We have seen in a preceding section, that money is reckoned in the United States in Dollars, dimes, cents, &c. These are the denominations of Federal Money. In other countries, it is reckoned differently. It is important that we should understand the English mode of reckoning money, because there are various currencies of money, as they are called, in this country, whose denominations are the same, though different in value. The following are the denominations of ENGLISH,

or,

STERLING MONEY.

4 farthings (marked qr.) make 1 penny, (marked) d.

12 pence

20 shillings

21 shillings

66

[blocks in formation]
[ocr errors]

1 pound

[blocks in formation]
[ocr errors][merged small]

NOTE. £ is the mark for pounds. When it is placed before the pounds, the marks for the lower denominations are omitted, but when after, they must be employed. Thus, £3; 7; 9; 2 is written, instead of 3£. 7s. 9d. 2qrs. 1 farthing is sometimes written d.; 2 farthings, id.; and 3 farthings id.

EXAMPLES FOR PRACTICE.

1. How many farthings in 6 shillings? In 5 shillings? In 7? 2. How many shillings in 2 pounds? In 3 pounds? In 4 pounds? 3. How many pence in 2 shillings? In 3 shillings? In 4? In 5? 4. How many farthings in 1 shilling? In 2 shillings?

5. How many pence in 1 pound? In 2 pounds? Ans. 240. 480. 6. At 2 pence apiece, how many pence will 17 oranges cost? 7. How many pence in a guinea? In 2 guineas? Ans. 252. 504. 8. How many farthings in a pound? A. 960. In 1 guinea? A. 1,008. 9. How many shillings in 275 pounds? Ans. 5,500.

10. How many farthings in 341 guineas? Ans. 343,728. 11. How many pence in 3 pounds, 5 shillings, and 6 pence? NOTE. First find the pence in 3 pounds, then in 5 shillings, then add these to 6 pence. Ans. 786.

12. How many shillings in 27 guineas, and 18 shillings?

13. How many farthings in 4 pounds, 9 shillings, and 5 pence 14. How many farthings in 8. 11s. 10d. 2qrs.? Ans. 8,250.

15. How many qrs. in 2,853£. 19s. 9d. 3 qrs. ? Ans. 2,739,831. 16. How many qrs. in 78,364£. 15s. 7d. 1qr.?

We will now give some tables of Weights and Measures. The following are the denominations of

AVOIRDUPOIS WEIGHT.

16 drams (dr.) make 1 ounce, marked oz.

66

1 pound

66 lb.

66 sto.

16 ounces

14 pounds

66

4 qrs. or 112 lbs.

28 pounds

20 hundred weight

1 stone

[blocks in formation]

NOTE. By this weight are weighed all coarse and drossy articles, which are liable to waste, as groceries, flour, hay, tallow, &c.; and likewise all metals, except those usually called the precious metals; viz. gold and silver. It will be observed that 112 lbs. make 1 cwt. But merchants in our large towns, particularly in seaports, allow only 100 lbs. to the cwt.

Merchants are accustomed to make allowances upon goods, bought and sold by Avoirdupois Weight, for the weight of the box, cask, or bag, which contains them; and also for waste, dust, &c. The weight, before these allowances are deducted, is called gross weight; after they are deducted, it is called net weight. In some Arithmetics, rules are given for deducting these allowances, under the head of TARE AND TRETT, which are the names, given to certain deductions. These rules, however, are superfluous, for the student, familiar with principles, will easily make them for himself."

17. How many qrs. in 5 cwt.? How many in 8? In 6? In 12? 18. How many oz. in 2 lb.? In 3? In 4? In 5?

19. How many lbs. in 5 cwt.?

Ans. 560.

« ΠροηγούμενηΣυνέχεια »