T64. It will frequently be) It will frequently be required required to find the value of a to reduce integers to the fraction fraction, that is, to reduce a frac-of a greater denomination. tion to integers of less denomina tions. 13 s. 4 d. is 160 pence; there of a are 240 pence in a pound; theresome fore, 13 s. 4 d. is 160 2-pound. That is, of a Reduce the shilling may be obtained pence; of a shilling is 4 d. That is, Multiply the nu-given sum or quantity to the least merator by that number which denomination mentioned in it, for will reduce it to the next less deno- a numerator; then reduce an inmination, and divide the product teger of that greater denominaby the denominator; if there be a tion (to a fraction of which it is remainder, multiply and divide required to reduce the given sum as before, and so on; the several or quantity) to the same denomiquotients, placed one after ano-nation, for a denominator, and ther, in their order, will be the they will form the fraction re quired. answer. Note. Let the pupil be required to reverse and prove the following examples. 21. What is the value of of a guinea? 22. Reduce 3 roods 17 poles to the fraction of an acre. 23. A man bought 27 gal. 3 qts. 1 pt. of molasses; what part is that of a hogshead? 24. A man purchased of 7 cwt. of sugar; how much sugar did he purchase? 25. 13 h. 42 m. 513 s. is what part or fraction of a day? SUPPLEMENT TO FRACTIONS. QUESTIONS. 1. What are fractions? 2. Whence is it that the parts into which any thing or any number may be divided, take their name? 3. How are fractions represented by figures? 4. What is the number above the line called?-Why is it so called? 5. What is the number below the line called ?-Why is it so called?-What does it show? 6. What is it which determines the magnitude of the parts': -Why? 7. What is a simple or proper fraction? an improper fraction? —a mixed number? 8. How is an improper fraction reduced to a whole or mixed number? 9. How is a mixed number reduced to an improper fraction? - a whole number? 10. What is understood by the terms of the fraction? 11. How is a fraction reduced to its most simple or lowest terms? 12. What is understood by a common divisor? by the greatest common divisor? 13. How is it found? 14. How many ways are there to multiply a fraction by a whole number? 15. How does it appear, that dividing the denominator multiplies the fraction? 16. How is a mixed number multiplied? 17. What is implied in multiplying by a fraction? 18. Of how many operations does it consist? What are they? 19. When the multiplier is less than a unit, what is the product compared with the multiplicand? 20. How do you multiply a whole number by a fraction? 21. How do you multiply one fraction by another? 22. How do you multiply a mixed number by a mixed number? 23. How does it appear, that in multiplying both terms of the fraction by the same number the value of the fraction is not altered? 24. How many ways are there to divide a fraction by a whole number?-What are they? 25. How does it appear that a fraction is divided by multiplying its denomi nator? 26. How does dividing by a fraction differ from multiplying by a fraction? 27. When the divisor is less than a unit, what is the quotient compared with the dividend? 28. What is understood by a common denominator? the least common denominator? 29. How does it appear, that each given denominator must be a factor of the common denominator? 30. How is the common denominator to two or more fractions found? 31. What is understood by a multiple? by a common multiple? by the least common multiple ?-What is the process of finding it? 32. How are fractions added and subtracted? 33. How is a fraction of a greater denomination reduced to one of a less? of a less to a greater? 34. How are fractions of a greater denomination reduced to integers of a less? integers of a less denomination to the fraction of a greater? EXERCISES. 1. What is the amount of § and § ? of 12, 3 and 4? 2. To of a pound add of a shilling. of and ? Ans. to the last, 2011. Amount, 18 s. Note. First reduce both to the same denomination. 220 Rem. 54 d. Rem. 11 pwt. 3 grs. 6. From shilling take of a penny. 7. From g of an ounce take of a pwt. 8. From 4 days 7 hours take 1 d. 93 h. Rem. 2 d. 22 h. 20 m. 9. At $3 per yard, what costs of a yard of cloth? ¶ 65. The price of unity, or 1, being given, to find the cost of any quantity, either less or more than unity, multiply the price by the quantity. On the other hand, the cost of any quantity, either less or more than unity, being given, to find the price of unity, or 1, divide the cost by the quantity. Ans. $15. 1. If # lb. of sugar cost of a shilling, what will of a pound cost?* This example will require two operations: first, as above, to find the price of 1 lb. ; secondly, having found the price of 1 lb., to find • This and the following are examples usually referred to the rule Propor tion, or Rule of Three. See T 95, ex. 35 the cost of 22 of a pound. 7 s.÷ 15 (11 of 75 s. ¶ 57) = 91 s. the price of lb. Then, s. X 22 (23 of 14 5 ¶ 53)=2812 s. 4 d. 34871q., the Answer. 165 costs 7 s. 095 Or we may reason thus: first to find the price of 1 lb. : # lb. 15. If we knew what lb. would cost, we might repeat this 13 times, and the result would be the price of 1 lb. H is 11 parts. If lb. costs s., it is evidentlb. will cost + of 15-165 s., and 18 lb. will cost 13 times as much, that is, 91s. =the price of 1 lb. Then, of 9 s. = 4812 s., the cost of of a pound. 2312 s. = 4 d. 34871 q., as before. This process is called solving the question by analysis. After the same manner let the pupil solve the following questions: how much 2. If 7 lb. of sugar cost of a dollar, what is that a pound? of = how much? What is it for 4 lb.? of What for 12 pounds? 12 of how much? Ans. to the last, $14. 3. If 6 yds. of cloth cost $3, what cost 94 yards? 4. If 2 oz. of silver cost $2'24, what costs 4 oz.? 5. If oz. costs $1, what costs 1 oz.? Ans. $84. Ans. $1'283. 6. If lb. less by costs 131 d., what costs 14 lb. less by of 2 lb. ? 7. If Ans. 4 £. 9 s. 9. d. 25 Ans. $59'062 +. yd. cost $3, what will 40 yds. cost? 8. If of a ship costs $251, what is of her worth? 9. At 3 £. per cwt., what will 9 lb. cost? 10. A merchant, owning of a vessel, sold $957; what was the vessel worth? Ans. $53'785+. d. of his share for Ans. $1794'5375. of an ell Eng. cost? 12. A merchant bought a number of bales of velvet, each containing 12917 yards, at the rate of $7 for 5 yards, and sold them out at the rate of $11 for 7 yards, and gained $200 by the bargain; how many bales were there? He gave 7 and sold for 11 of a dollar a yard; hence find what he gained a yard, &c. 13. If a staff, 5 ft. in length, cast a shadow is that steeple whose shadow measures 153 feet Ans. 9 bales. 6 reet now nigh Ans. 144 feet. |