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Examples for Practice.
Pup. I now see the reason of this, and why dividing by 9 gives an answer in yards ; it is because 9 square feet make a square yard.
What is compound multiplication ?
When the given multiplier cannot be resolved into exact factors, what do you do?
When the multiplier exceeds 144, how do you proceed?
When the lower denomination can be resolved into even parts of the highest denomination, how do you obtain the price?
What is compound division ?
When the divisor is so large as to make it inconvenient dividing by it, how do you proceed?
When the divisor cannot be resolved into factors, what is to be done?
When the price of several hundred weight is giren, how do you find the price of one hundred weight? Of
1. In 36 hhds. of sugar, each weighing 12 cwt. 2 qr. 1 lb. how many hundreds, quarters, pounds, &c. ?
Ans. 452 cwt. 2 qr. 8 lb. 2. A man has 46 silver cups, each weighing 6 oz.. 10 pwt. 9 gr. what is the weight of the whole ?
Ans. 24 Ib. 11 oz. 17 pwt. 6 gr. 3. If a man travel 40 miles, 6 furlongs, and 36 rods in one day, how far will he travel in 26 days ?
Abs. 1062 mls. 3 fur. 16 rods. 4. 28 men bought 2 58 cwt. coffee, which was shared equally among them; what was each man's share ?
Ans. 92 cwt. or 9.cwt. 3 qr. 12 lb. 5. There are 248 cwt. 3 qr. of sugar to be divided among 29 men ; what is each man's share ?
Ans. 8 cwt. 2 qr. 8 lb. 1125 oz. or 82, cwt. 6. If a man travel 648 mls. 4 fur. in 26 days, how far would he travel per day?
Ans. 24 mls. 7 fur. 212. pls. or 240 mls. 7. In the Lunar circle of 19 yrs. of 365d. 5h. 48', 48". how many days, &c. ? Aps. 6939 d. 14h. 27' 12".
8. How many square feet in a board 17 ft. 7' long, and 1 ft. 5' wide ?
Ans. 24 ft. 10' 11". 9. What are the contents of a floor, 48 ft. 6' long, and 24 ft. 3 broad ?
Ans. 1176 ft. 1'6". 10. What are the contents of a ceiling, 43 ft. 3' long, and 25 ft. 6' broad ?
Ans 1102 ft, 10'6". 11. The length of a room is 20 ft its breadth 14 ft. 6', and its height 10 ft
. 4'; how many yards of painting are in it, deducting a fire place of 4 ft. by 4 ft. 4', and two windows, each 6 ft. by 3 ft. 2 ?
Ans. 737 yds. 12. There is a house which has 12 windows 4 ft. G' long, and 2 ft. 10' wide ; 8 windows 3 ft. 9 long, and : 2 ft. 6' wide ; 16 windows 4 ft. 2' long, and 3 ft. 1' wide ; how many square feet do all the windows contain ?
Ans. 433 ft. 6' 8".
one quarter? Of one pound, &c. ?
When the quantity given consists of several denomina-
What are duodecimals ?
How are the several denominations distinguished from
What is the product of feet by inches ? Inches by
What is the ordinary method of performing this rule !
How do painters and joiners find the contents of their work?
13. How many cubic feet* of wood in a load, 6 st. 7 long, 3 ft. 5' high, and 3 ft. 8' wide ?
Ans. 82 ft. 5' 8" 4'". 14. There is a stock of 14 boards; each board is 14 ft. 6' long, and i ft 10' wide ; how many feet are there in the whole stock?
Ans. 372 ft. 2'. 1.5. The sun passes through 15 degrees in an hour; two places differ in longitude 31° 37' 3"; what is the difference, in time, of the sun's coming to the meridian of those places ?
Ans. 2h. 6' 3". 16. How many square yards are there in the wainscotting of a room 18 ft. long, 16 ft. 6' wide, and 9.ft. 10' high?
Ans. 2920 ft. 6'. 17. Required the solid contents of a wall 53 ft. 6' long, 1.2 ft. 3' high, and 2 ft. thick.
Aps. 1310 ft. 9'.
SIMPLE AND COMPOUND INTEREST.
Tut. What is interest ?
Pup. Interest is what one man pays to another for the use of money.
Tut. Very well. Interest is an allowance made by the borrower to the lender. If A. should borrow money of B., be might traffic with that money, obtain gain, and thus be benefited by the use of it. But B. would be de. prived of the use of the money, and sustain a loss by baving lent it to A.
Hence the reason of the borrower's giving interest to the lender for the use of the money borrowed.
The money lent is called the Principal.
The principal and interest added together are called the Amount.
* A cubic foot is that which is a foot long, a foot wide, and a foot thick.
Interest is of two kinds, Simple and Compound. Sim. ple interest is that which is allowed for the principal only, or money lent.
Interest is considered as payable at the close of every year, from the date of the note or bond. When the borrower does not pay the ipterest, but keeps it in his own hands, it is considered as added to the principal, or money lent, and interest is allowed for it the same as for the
This is called Compound Interest. The rate per cent of interest is different in different places.
The medium rate is 6 per cent, or $6 a year for every $100 lent. The following is the
General Rule. If the interest is for only one year, multiply the principal by the rate, and from the product cut off two more places for deci. mals, than there are decimals in the multiplicand. The figures, at the left of the point will be dollars, and those at the right, cents and mills.
For more than one year, multiply the interest for one year, by the number of years.
For months, take proportional parts of the interest for one year, viz. for 6 months, į ; for 5 months, j and ; for 4 months, }, &c.
For days, take proportional parts of the interest for one month, calling 30 days a month.
What is the interest of $18,24 for two years and six months, at 6 per cent ?
$ 2,7360 interest for 2 years and 6 months. The reason of multiplying by the rate will appear plain, when you consider that 6, or any other figure expressing the rate, is 0,06 &c. of a dollar; or the rate is so many cents on the dollar for one year Hence the reason of pointing the product as we do. В it as 6 per cent is the more general rate, allowed by law, there is
not, perhaps, a better method of casting interest, than by the following Rule.
Write the given sum for a multiplicand, and half the even number of months for a multiplier ; if there be an odd month, call it 30 days, which add to the given days, if any, and seek how often 6 are contained in their sum, and place the figure for a decimal at the right of half the even number of months. Multiply the principal by these figures, and from the product point off two more fig. ures for decimals than there are decimal figures in both the factors. The figures to the left of the point will be dollars, and those to the right, cents and mills, and parts of a mill, which is the interest required.
When there is a remainder in taking one sixth of the days, reduce it to a vulgar fraction, for which take proportional parts of the multiplicand. "If the remainder be 1 = } divide the multiplicand by 6. If If =
by 2. If 4=
by 3 twice. If 5= 1 and
by 2 and 3." These quotients must be added to the product of the given sum by half the even number of months, and the sum will be the interest required.
When the days do not amount to 6, place a cipher at the right of half the even number of months, th
pro .ceed in all respects as before.
What is the interest of $ 18,48 for 2 years, 7 months and 4 days ?*
15,5 9240 9240 1848
*When the rate per cent is not mentioned in the obligation, it is always considered the interest established by law, which is called qwful interest.
In this example I first seek how many months there are, and find they are 31. I take half the even number months for the following reasons.
One dollar at 6 per cent interest, draws 6 cents in one year; and as there are 12 months in a year, the interest is half a cent per month on the dollar, consequently if we multiply dollars by half the number of months, we get the interest in cen When there are not 2 months, so that the half cannot be expressed by 1, it is evident that it must be done by a decimal expressing į, which is 0,5, and 5 times 6 are 30. When there are odd days, less than 6, it is evident that their value can be obtained by taking proportional parts of the multiplicand. When the days are less than 6, a cipher is annexed, that the quotient arising from the division of the multiplicand by a fractional part of 6, may stand in its proper place, otherwise it would be increased ten times.
What is the interest of $ 124,18 for 2 years and 3 months ?
Ans. $19,868. What is the interest of $ 240,16 for 3 years, 5 months and 1 day?
Ans. 49,672. What is the interest of $958,54 for 5 days ?
When the rate is any other than 6 per cent, first find the interest at 6 per cent, then divide the interest so found by such parts as the interest, at the rate required, exceeds or falls short of the interest at 6 per cent, and the quotient added to or subtracted from the interest at 6 per cent, as the case may be, will give the interest at the rate required.
What is the interest of $ 246,25 for 2 years and 6 months, at 5 per cent ?
Ans. $ 30,7813