10. How many times is a contained in § ? 11. If beef is of a dollar a pound, how much can be bought for of a dollar? 12. If a yard of muslin cost of a dollar, how much can be bought for of a dollar? In case the divisor and dividend have whole numbers with the fractions, the whole numbers must be reduced also, with the fractions, to a common denominator. Thus if we wish to find how many there are in 4 and , we must change the 4 and to twelfths, and the to twelfths also, and then divide as before. Thus; 4 and & is 11, and is 12• În 57 twelfths, there are 7 times 8 twelfths, and one twelfth left over. This one twelfth, is one eighth of the divisor. The answer then is 7 and . That is, 4 contains 3, just 7 times and of another time. Again; how often is 23 contained in 53? First, reduce the divisor and dividend to fractions of a common denominator. 2 is 2, and 5 is f. Divide 69 twelfths by 32 twelfths, and the answer is 2 and 5 twelfths left over. This 5 twelfths is 5 thirty secondths of the divisor. For five twelfths is of 32 twelfths. 1. How many times is 1 contained in 84 ? 2. How many times is 24 contained in 54 ? 3. How many times is 93 contained in 164 ? 4. lf you distribute 134 lbs. of flour among a certain number of persons, and give 25 lbs. to each, to how persons do you give? many 5. If 4 bushels of wheat last a family one week, how long will 124 bushels last them? 6. If 5 tons of hay will keep a horse 6 months, how many horses will 12g tons keep during the same time? 7. If a cistern is filled in 33 of an hour, how many times will the cistern be filled in 12g nours? and 8. If you distribute 18 dollars among the poor, give 24 dollars to each person, to how many do you give? 9. At 33 dollars a lb. how many pounds of gum can be bought for 244 dollars? 10. How many times is contained in 24 ? 11. How many times is 53 contained in 84? 12. How many times is 23 contained in 14g? 13. How many times is 34 contained in 73 ? 14. How many times is 54 contained in 12% ? REDUCTION. 1. In 29 gallons how many quarts? 2. In 65 pints how many gallons? (See page 162.) 3. In 2£. 14s. 9d. 3 qrs, how many farthings? 4. In 923469 farthings, how many pounds, shillings, and pence? 5. Reduce to a decimal. (See page 167.) 6. Reduce 2 to a decimal. 7. Reduce 123 to a decimal. 24 8. Reduce and to a common denominator. (See page 172.) 9. Reduce 10. Reduce 3 3428 to a common denominator. to a common denominator. 11. Reduce 128 to its lowest terms. (See page 175.) 12. Reduce 2496 to its lowest terms. 4832 13. Reduce 48 to its lowest terms. 14. Reduce of a guinea to the fraction of a pound. (See page 176.) 15. Reduce 46 to the fraction of a foot? 16. Reduce of 1⁄2 of 2 of a pound to the fraction of a shilling. 17. Reduce of of 3 shillings to the fraction of a pound. 18. What is the value of of a ton in lbs. ? (See page 177.) 19. How many ounces in of a lb. Apothecary's weight?1 20. How many pints in of a bushel? 21. Reduce 8 oz. 6 pwts. to the fraction of a lb. Troy. (See page 178.) 22. Reduce 4 days 16 hours to the fraction of a year. 23. Reduce 36 gals. 4 qts. to the decimal of a hogshead. (See page 180.) 24. Reduce 11d. 3 qrs. to the decimal of a shilling. What is the value of,169432 of a ton? (See page 181.) 25. What is the value of ,24694 of a £? What is the value of ,396 of an hour? 26. Reduce 7s. 8d. of each of the different currencies to the same value in Federal money. (See page 185.) 27. Reduce $6, 29 to the same value in each of the different currencies. (See page 186.) INTEREST. In conducting business, men often find it necessary to borrow money of each other, and it is customary to pay those who lend, for the use of their money until it is returned. The sum of money lent, is called the principal. The sum paid for the use of money, is called interest. It is customary to pay a certain sum for every hundred dollars, pounds, &c. Thus in New England six dollars a year is paid for the use of every hundred, and in New York seven dollars for every hundred that is borrowed. The expressions six per cent, seven per cent, &c. signify that six or seven dollars are paid for every hundred borrowed. Per signifies for, and cent. is the abbreviation of centum, the Latin word for hundred. Rate per cent., then, signifies rate by the hundred. When a man borrows a sum of money, he gives to the one of whom he borrows a writing in this form : $500,00. Hartford, April 1, 1832. On demand I promise to pay D. F. Robinson or order, five hundred dollars with interest, value received. Samuel Jones. This is called a note and is said to be on interest. In the rule called interest, what is meant by principal? interest? amount? per annum? per cent? pay six dollars a year for each hundred dollars, till the $500 are returned. In Connecticut the law does not permit men to receive any more than 6 per cent. interest; in New York it allows 7 per cent., and the rate by law varies in the different states. When the rate per cent. is not mentioned, it is always to be understood that the interest is what is allowed by the laws of the state where the note is given. Usury is taking more interest than the law allows. In all notes on interest, if no particular rate per cent. is mentioned, it is always understood to be legal interest that is promised. In this work 6 per cent. will be understood when no rate per cent. is mentioned. Sometimes it occurs that when a man has borrowed a sum of money, after a time he wishes to pay a part of the debt. In this case, when the payment is made, the note which was given to the lender is taken, and an endorsement is written on it, stating that such a part of the note was paid at a particular time. After this the borrower only pays interest for that part of the debt which remains unpaid. Notes are given either with or without interest. If the words "with interest" are not written, a note is understood to be without interest. If a note is given without in. terest, promising to pay at a certain time, after that time has expired, the note draws interest from that time. Notes are given sometimes, promising to pay the interest annually, but oftener the interest is not to be paid until the note is paid. When interest is paid only upon the sum lent, it is call. ed simple interest. But when the yearly interest is added each year to the principal, and then interest is taken upon both principal and interest, it is called compound interest. The laws of the several states forbid taking compound interest; but a man who has lent money, can collect the interest every year, and put it out at interest, and thus gain compound interest. Legal interest? usury? endorsements? What is meant by simple interest? compound? But when a man borrows, if the creditor does not collect the interest every year, he cannot be compelled to pay interest on the interest. In calculating interest, the rate per cent. is a certain number of hundredths of the sum lent. Thus if 1 per cent. is paid for $100, it is part of the sum lent. If 6 per cent. is paid, it is the part of the sum lent. 1 For this reason all calculations in interest are sums in decimal multiplication. We divide by the denominator to find one hundredth, by means of the separatrix, and multiply by the numerator to find the required number of hundredths. For example, if we wish to find the interest of $263 for one year, at 6 per cent. we must obtain the part of the $263. This is done by dividing by the denomi nator 100, by means of a separatrix, and multiplying by the numerator 6. In this case the multiplication is done first. $263 $15, 78 The rate per cent. therefore, may always be written as a decimal fraction of the order of hundredths. Write 24 per cent. as a decimal fraction. cent. 2 per cent. is ,02, and Write 4 per cent. as a 42 per cent. per cent. is, 005. Ans. ,025. 41 per 5 per cent. 74 per cent. 8 per cent. 82 per cent. -- 9 per cent. 91 per cent. is; decimally,,10.) cent. 121 per cent. 10 per cent. (10 1. If the interest on $1, for 1 year, be 6 cents, what will be the interest on $17 for the same time.? 101 per cent. per cent. 11 per 15 per cent. |