47. Fractions are said to have a common denominator when their denominators are alike. Any number that can be divided by each of the denominators of the given fractions may be taken for the common denominator. 1. Reduce and to fractions having a common denominator. ANALYSIS. 12 is exactly divisible by 4 and 3, and may therefore be taken for a common denominator. Since in 1 there are 1, in of 1 there must be of 13, or, and in of 1 there must be of 12, or. Therefore and are equal to and 2. Reduce and to fractions having a common denominator. 3. Reduce and to a common denominator. 4. Reduce and to a common denominator. 5. Reduce and 1⁄2 to a common denominator. 6. Reduce and to a common denominator. 7. Reduce and g to a common denominator. 8. Reduce,, and 9. Reduce,, and 10. Reduce, nator. to a common denominator. to a common denominator. and to a common denomi 11. Reduce, and to a common denominator. 1 12. Reduce,, § and and to a common denomi nator. 13. Reduce, nator. and to a common denomi 14. Reduce 11, 21 and to a common denomi nator. 4. If the denominator be divided by any number, the value of the fraction will be multiplied as many times as there are units in the divisor. 5. If both numerator and denominator be multiplied by the same number, the value of the fraction will not be changed. 6. If both numerator and denominator be divided by the same number te value of the fraction will not be changed. of a 48. 1. James has of a dollar, John dollar, and George of a dollar; how many fifths of a dollar have they all? how many dollars? ANALYSIS. They all have the sum of 3 + 3 + 4, equal to 10 dollars, equal to 2 dollars. Therefore, &c. her 2. Jane had of a dollar and her father gave of a dollar more; how much had she then? 3. Austin buys a pair of skates for of a dollar, a pair of mittens for g of a dollar, and a slate for of a dollar; what is the cost of all? 4. A grocer sold dozen eggs to one man, of a dozen to another, and of a dozen to another; how many dozen did he sell to all? NOTE. Fractions having different denominators must be reduced to a common denominator before adding or subtracting. 5. Mary paid of a dollar for some ribbon, of a dollar for a pair of gloves and of a dollar for a pair of hose; what was the cost of the whole ? 6. Sold of an acre of land to one man, to another and to another; how much was sold to all? 7. A laborer dug a rod of ditch the first hour, of a rod the second, the third and the fourth; how many rods did he dig in 4 hours? 8. A farmer sold of his grain to one man, to another, and to another; what part of his grain did he sell? 9. Henry paid of a dollar for a sled, a dollar for a kite and of a dollar for a string; what was the cost of the whole ? 10. Emma paid 21 dollars for a dress, 1 dollars for a pair of shoes and of a dollar for some ribbon; what was the cost of the whole? NOTE. Add the whole numbers and the fractions separately, and then unite their sums. 11. Milton saved of a dollar one week, of a dollar the next, 18 the next and 24 the next; how much did he save in 4 weeks? 12. Albert picked 2 bushels of apples from one tree, 32 from another and 3 from another; how many bushels did he pick from the 3 trees? 13. If it take 41 yards of cloth for a coat, 21 yards for a pair of pantaloons, and of a yard for a vest, how many yards of cloth will it take for the whole? 14. If a man walk 125 miles in the forenoon and 10 miles in the afternoon, how many miles does he walk during the day? 15. Harvey bought a sled for 62 cents and sold it for 12 cents more than he gave for it; how much did he receive for it? 15. Three men bought a horse. A paid 25 dollars, B paid 30 dollars and C paid 35 dollars; what was the cost of the horse? 17. If coal is worth 5 dollars a ton, and wood is worth 3 dollars a cord, what will be the cost of one ton of coal and two cords of wood? 12 31. What is the sum of 14, 105, and 51? 32. What is the sum of 7% +15% + 101? 33. What is the sum of 25+ 132 + 5? 34. What is the sum of 64 +74 + 43 ? 35. What is the sum of +11 +14 +101? 36. What is the sum of 3% + 5 + + 101? 37. What is the sum of 6+14+53 +18? 38. What is the sum of 20+ 7 + 111? 49. 1. Amos having of a dollar, gave of a dollar to a beggar; how much had he left? ANALYSIS. He had left the difference between and of a dollar; - of a dollar. Therefore, &c. 2. Norman had of a bushel of peaches; he soldg of a bushel; what part of a bushel had he left ? 3. Nancy paid of a dollar for a geography and of a dollar for a philosophy; for which did she pay the more, and how much? 4. Two men own a piece of property together; one owns of it; how much does the other own? 5. When rye is worth of a dollar per bushel and corn is worth of a dollar, what is the difference in the price? 6. A grocer sells full; what part of the 7. Henry can run that John can run 17; how much? of a box of tea from a box whole box is left? of a mile in the same time which runs the farther, and 8. Parley gave of a dollar for a vest and g of a dollar for a pair of shoes; what was the difference in the cost? 9. A gentleman, owning a boat, sold of it; how much of it did he still own? 10. If Robert earn 7 dollars a week and Herman earn 6 dollars a week, how much more than Herman does Robert earn? 11. Arthur gathered 107 quarts of chestnuts and sold 7 quarts; how many quarts had he left? 12. From a piece of cloth containing 12 yards, 5 yards were cut; how many yards remained? 13. If I put 15 dollars in the bank at one time, how much must I afterwards put in to make the sum 20 dollars? 14. From a hogshead of molasses, 9 gallons were drawn; how many gallons remained? 15. Edgar will be 14 years old 3 years hence; how old is he now? 16. From a jug of molasses containing 1 gallon, of a quart was used; how much was left? 17. If I buy a book for g of a dollar, how much change must be returned to me for a 3 dollar bill? 18. A lady, having 183 dollars, bought a bonnet for 5 dollars; how much money had she left and ? 19. What is the difference between and &? 23. What is the difference between 3 and ? and ? and 11? 24. What is the difference between 16ğ and 91? 25. What is the difference between 20 and 12? |