4. Divide $16,785 equally between 14 men. 5. Divide 1673,23 by 2,666. What is the quotient of 167,326 divided 6. by 13,27. REDUCTION OF DECIMALS. To reduce a Vulgar Fraction to a decimal. Rule. To the numerator annex a competent number of ciphers; then divide by the denomi nator, and the quotient will be the decimal required. *This character+signifies that the decimal is not complete; and that, by annexing ciphers to the remainder, it may be carried to a further degree of exactness. 5 ? 8. What decimal is equal to 128 9. What is the value of, expressed by decimals? 10. What of ? 11. What of ? 12. What of 16 ? To reduce the denominations of money, weights, and measures to decimals. Rule. Bring the given denominations first to a vulgar fraction, and reduce said vulgar fraction to a decimal. ,55 Ans. 2. Reduce 11 shillings to the decimal of a pound. 3. What decimal is equal to 8 shillings, the whole being 1 pound? Ans.,4. 4. Reduce 15 shillings to the decimal of a pound. 5. Reduce 8 pence to the decimal of a shilling. ,333x2=Ans. 6. Reduce 10 inches to the decimal of a mile. ,0001578+Ans. 7. Reduce 8 yards to the decimal of a mile. 8. What decimal of a pound is equal to 6 ounces, 14 pennyweights, 10 grains Troy? ,112÷2+ Ans. 9. What decimal of a pound is 17 shillings, 4 pence? Ans.,86875. 10. What decimal of one hundred weight, is equal to 3 quarters, 21 pounds? ,4685 x 2+5= Ans. 11. What decimal of a shilling and of a pound is 9 pence? Ans. ,8125s. and,0406257. To find the value of any decimal, whether of Coin, Rule. Multiply the given decimal by so many as it takes of the next lowest denomination to make one in that denomination of which the given decimal is a part, and point it off as usual; in like manner multiply the remaining decimals by the next lower denomination, rejecting the whole number cut off. Thus proceed through every descending denomination; the figures at the left hand of the several products determine the value of the decimal. EXAMPLES. 1. What is the value of ,8751.? I multiply the decimal, ,875 by 20, (the shillings in a pound,) and find the product 17,500, from which I point off the three lowest figures (being the number in the given decimal,) by the separatrix, and so it stands 17s. ,500, which ,500 is a new decimal part of a shilling, which I multiply by 12, (the pence in a shilling,) and find its value 6d.; and therefore the value of the given decimal is 17s. 6d. What is the value of ,751.? What is the value of ,66666s.? What is the value of ,0333337.? M Ans. 15s. Ans. 8d. Ans. 8d. 5. What is the value of ,875 of a yard? Ans. 3qrs. 2na. 6. What is the value of ,56006944 of a pound Troy? Ans. 6oz. 14pwt. 10gr. nearly. 7. What is the value of ,9375 of a cwt.? Ans. 3qrs. 21lb. Application and Use of Fractions. 1. Multiply 2 by 34 decimally.* 36÷4+,375.=Ans. 12+2+,491+=Ans. 2. From 91 take 2,99. NOTE. Answers carried to three places of decimals, will be deemed sufficiently accurate. 3. One man owed another 17 shillings, 64 pence, and paid him ,796 of a pound. How much remains due? £1-18s. 4d. 3qr. Ans. 4. A man sold at one time, 167 acres of land; at another, ,2,26; at another, 16311; and at another, 143. How much did he sell in all? 98×2+,895 Ans. of cloth measuring 16, How much remained un 3×2+,611=Ans. 5. From a piece was sold 91 yards. sold? *All answers in this rule are to be obtained be reduc ing fractions to decimals, and working accordingly. |