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is less than a cent. A cipher is set before the 9 cents to show that the 9 cents are hundredths. By annexing a cipher to 9, the dividend becomes 90 mills, and the first figure obtained in the quotient, is mills; the second tenths of a mill, found by annexing a cipher to the remaining 6 mills.

13. What is the quotient of 6 divided by 1252

- Ans. ,048. 14. What is the quotient of 26, divided by 2,62

2, 6 ) 2 6, 0 ( 1 0 Explanation.—20 con2 6 tains 2 ten times, and 6 -- contains 6 tenths, ten 0 - times, but dividing in the common way, we get only the figure 1 in the quotient, which is in reality 10. A cipher is written in the first decimal place, which being brought down, places a cipher in the quotient, and the 1 is thus removed into tens place. We may consider the divisor 26 tenths; then annexing a cipher to the dividend, that may be called 260 tenths, and the question would be, how many times can 26 tenths be subtracted from 260 tenths. When the decimal places in the dividend are not equal to those in the divisor, they must be made equal by annexing ciphers, otherwise the quotient figures will not express their true value.

15. If a person spend $100 in one year, what is that per day ? Ans. $0,273+. 16. The President of the United States receives a salary of $25000 a year; how much is that per day ? - - Ans. $68,493--. 17. A general wishes to distribute $12000 among his army, consisting of 3250 men; giving an equal share to each; what will each man receive 2 Ans. $3,693+. 18. At a dollar and seventy five cents a barrel for cider, how much is that per gallon Ans. 5 cents and 5-H mills.

19. Divide 1,656 by 1656.

1 6 5 6 ) 1, 6 5 6. ( 1

1 6 5 6 Explanation.—The 1 in the dividend is the , 1 thousandth part of the 1 in the divisor, and the 656 thousandths are the l thousandth part of the 656, and only a 1 thousandth part of the divisor can be taken from the dividend. The figure 1 in the quotient is the I thousandth part of an unit, and to make it express that we must prefix two ciphers. Ans. ,001.

JNote.—From the last example it appears that when the number of places in the quotient are not so many as what the number of decimal places in the dividend are more than those in the divisor, they must be made equal by prefixing ciphers. 20. If 112 lb. of iron cost $7,25 what is the cost of one pound 7 Ans. $,064-H. 21. If I pay $134 for my stage fare 220 miles, what do I give per mile ! Ans. 6 cents and 1 + mills. . 22. Divide 1 hundredth by 10. Quot. ,001. 23. Divide 2 millionths by 1 million. w - Quot. ,000000000002.

Promiscuous questions in Vulgar and Decimal
Fractions.

1. What is the sum of , , ,65 and ,078? Ans. 1,839–1–. 2. What is the difference between #4 and ,01792 Ans. ,7154+ 3. What is the product of 4 of a shilling into 2 of a pound 7 Ans. ,002.É. 4. What is the quotient of , 11 divided by 2 Ans. ,83+. 5. A gentleman gave a lot of land containing 126 acres to two sons,—giving one 9 acres more than the other ; how many acres did each son receive 2

Erplanation.—There are several methods by which this question may be performed. If we sub.

tract 9 from the whole number of acres, and divide the remainder by 2, the quotient would be his share, who has the least number of acres, and the 9 added to the quotient would give the other's share. Or, if the whole number of acres be divided by 2, and half of 9 be substracted from the quotient, the remainder would be the less number, and half of 9 added to half the given number of acres would be the greater number. Ans. One 67,5 and the other 58,5.

6. Divide 100 into two such parts, that one shall be 124 greater than the other. Ans. 56,25 and 43,75.

7. If water run into a cistern at the rate of 15 gallons an hour, and run out at the rate of 74 gallons in the same time, how much time will be required to fill the cistern, if it contain 500 gallous 2

- Ans. 64.51 hours.

8. For a certain pile of wood a gentleman agreed to give $34,67. After measuring it, he found that it contained 5 C. 96 ft. ; what did the wood cost him a cord 2 Ans. $6,029-H. * 9. At 34 cents a foot, what will 12 plank come to which measure 56 ft. 9 in. each 2 Ans. $23,835.

10. A merchant bought a hogshead of molasses for $23, and sold it for $6 more than he gave ; at what did he sell it for per gallon 2 Ans. $0.46–H.

11. A man buys a chest of tea weighing 40 lb. for $35; at what must he sell it for perpound to gain 10

dollars on the whole? Ans. $1,12#.

12. If two men start at the same time from different places, and travel towards each other-one at the rate of 4 miles an hour, and the other # of a mile less; in how many hours, and at what distance from each place, will they meet, if the distance between the two places be 66 miles?

Ans. They will meet in 9 hours—36 miles from one place and 30 from the other.

18

SECTION VIII.
PER CENT."

JDEFINITIONS.

1. Per Cent. implies that calculations are made by the hundred. 2. Rate Per Cent. specifies the particular number of units calculated on 100. 3. Interest is a sum of money given by a debtor to a creditor as a reward for the use of money. 4. Principal is the money on which interest is calculated. 5. Amount is the sum of the principal and interest. a 6. Commission is money paid to an agent for transacting business for another. 7. Discount is so much per cent. to be deducted from any given sum of money. 8. Insurance is a contract by which one person agrees to pay another the value of property when lost at sea, destroyed by fire, or in any other manner mentioned in the contract, for a certain per cent. paid the insurer by the insured.f 9. Premium is the sum of money paid the insurer by the insured. 10. Duties are certain sums of money paid to government by importers of goods, wares, merchandize, &c. * 11. Paris a word denoting that money, or stock, is worth its nominal value. 12. Stock is a general term for the capitals of trading companies, or a fund established by law.

6 per cent. is 6 cents calculated for 100 cents, 6 dollars for 100 dollars, 6 shillings for 100 shillings, * Per signifies by. Cent, is from the Latin word centum menu-6 pounds for 100 pounds, &c. 5 per cent. is 5 cents calculated for 100 cents, 5 dollars for 100 dollars, 5 pence for 100 pence, &c.

ing 1 hundred. * Insurance is generally made by corporate companies.

Interest, discount, commission, premiums, and generally, duties, are calculated by the hundred.

To find the commission and premium on any sum of money;—also to find the interest on any sum for 1 year.

RULE, Multiply the given sum by the rate per cent. JNote 1.—When interest is mentioned at so much per cent. it is always understood for one year unless otherwise stated in the question.

1. What is the interest of $126, at 6 per cent.”

Operation.
1 2 6 Illustration.—At 6 per cent.
, 0 6 6 cents is the interest for 100
- cents, or 1 dollar, for one year,
$7,5 6 Ans. and multiplying the number of

dollars by 6 cents, the product contains 6 cents once for each dollar in the multiplicand, (See Proof and Illustration, page 43,) consequently, the product must be the interest of the number of dollars multiplied. In the operation of question 1st, we multiply by 6 hundredths of a dollar, the product must therefore be divided by the denominator 100, which is effected by pointing off the two right hand figures, (See Illustration, page 189,) 7 must therefore be dollars and 56, hundredths of a dollar, that is, cents. 756 cents contain 6 cents as many times as there are dollars in 126, and is the interest for 1 year.

2. What is the interest of $560, at 6 per cent. * Ans. $33,60. * The rate percent. by which interest may be taken is establish

ed by the State Legislatures, and in most of the States is 6 per cent. In New-York it is 7 per cent;

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