49. of 84 are how many times 50. of 63 are how many times of 24? 2. REDUCTION OF FRACTIONS. 1. How many halves in an apple? How many thirds? How many fourths? How many fifths? 2. How many halves in 3 oranges? SOLUTION.-In 1 orange there are 2 halves, and in 3 oranges there 7. How many sixths in 4? 5? 8? 10? 4? 8. How many sevenths in 5? 3? 9? 7? 11? 9. How many eighths in 4? 10. How many ninths in 3? 11. How many tenths in 4? 12. How many thirds in 51? 6? 8? 10? 12? SOLUTION.-In 1 there are 3 thirds; in 5 there are 5 times 3 thirds, or 15 thirds; 15 thirds and 1 third are 16 thirds. Therefore in 5 there are 16 thirds. NOTE.-An improper fraction is one whose denominator is less than its numerator. SOLUTION.-In 1 there are 5 fifths; in 4 there are 4 times 5 fifths, or 20 fifths; 20 fifths plus 3 fifths are 23 fifths. 21. Reduce to improper fractions 21; 3; 4; 41. 22. Reduce to improper fractions 3; 5; 64; 81. 23. Reduce to improper fractions 4; 5; 65; 7%. 24. Reduce to improper fractions 3; 4; 6; 74. 25. Reduce to improper fractions 6; 7; 51; 87. 26. If 2 yards of cloth cost 14 dollars, how much will a yard cost? SOLUTION.—2 yards are equal to 3 yards. If yards cost 14 dollars, of a yard will cost of 14 dollars, or 2 dollars; and 3, or a yard, will cost 3 times 2 dollars, which are 6 dollars. 27. If 6 pounds of sugar cost 52 cents, how much does 1 pound cost? 28. How much will a bushel of beans cost if 24 bushels cost $8.10? 29. I paid 55 cents for 33 dozen of eggs; how much was that for 1 dozen? 30. If 5 tons of coal cost 33 dollars, how much will 1 ton cost? 31. I paid 34 cents for 23 yards of gingham; what was the price per yard? 32. A man can earn 40 cents in 23 hours; how much can he earn in 10 hours? 33. A train of cars runs 60 miles in 24 hours; how far does it go in 8 hours? 34. If I pay 44 cents for 2 pounds of meat, how much ought I to pay for 10 pounds? 35. George earns 100 dollars in 3 months; how much can he earn in 12 months? 36. There are 132 minutes in 2 hours; how many minutes in 6 hours? 37. In 31 days there are 78 hours; how many hours in 2 days? 38. If 2 pounds of cheese cost 38 cents, what are 5 pounds worth? 39. What is the cost of 3 pounds of butter if 21 pounds cost 63 cents? 40. A boy can walk 16 miles in 5 hours; how far can he walk in 12 hours? 1. How many ones in §? 3. SOLUTION. Since 1 equals, in there are as many ones as is In 20? In 30? In 18? 5. How many ones in 40? 6. Reduce 12 to a mixed number. NOTE. A mixed number consists of a whole number and a fraction. SOLUTION. Since 1 equals, in 12 there are as many ones as is contained times in 12, or 23. 7. 5 7. Reduce to mixed numbers 15; 1; 12; 10. 3 9. Reduce to mixed numbers 15; 15; 10; 16. 16 10. Reduce to mixed numbers 40; 17; 25; 25. 11. Reduce to mixed numbers 14; 21; 25; 30. 12. Reduce to mixed numbers 20; 30; 40; 45. 13. How much will 5 pairs of shoes cost at 33 dollars a pair? SOLUTION.-If 1 pair of shoes cost 3 dollars, pairs will cost 5 times 34 dollars. 5 times 3 dollars are 15 dollars; 5 times of a dollar are 1 dollars, or 3 doliars; 15 dollars plus 3 dollars are 18 dollars. Therefore 5 pairs of shoes at 3 dollars a pair will cost 18 dollars. 14. How much will 9 barrels of apples cost at 24 dollars a barrel? 15. What is the cost of 6 pairs of shoes at 31 dollars a pair? 16. If 4 dozen eggs cost 50 cents, how much does 1 dozen cost? 17. If a boy can walk 163 miles in 5 hours, how far can he walk in 1 hour? 18. What is the cost of 6 tons of coal at 5 dollars a ton? 19. I paid 1 dollars for 5 pounds of butter; how much is that a pound? 20. If 3 hats cost 6 dollars, how much will 5 hats cost? 21. How much can a man earn in 6 days at the rate of 21 dollars a day? 22. How much will 16 bushels of potatoes cost at the rate of of a dollar a bushel? 23. If 4 pairs of shoes cost 16 dollars, how much is that a pair? 24. If a boy can earn 64 dollars in 5 days, how much can he earn in 3 days? 25. How far can a man walk in 10 hours, if he can walk 5 miles in 2 hours? 26. At the rate of 5 dollars a ton, how much will 6 tons of coal cost? 27. How much will 6 pounds of butter cost at 123 cents a pound? 28. What is the cost of 8 pounds of rice at 6 cents a pound? 4. FRACTIONS TO HIGHER TERMS. 1. How many sixths in ? SOLUTION. In 1 there are ; hence in there are } of %, or . 2. How many fourths in ? 6. How many twelfths in ? ? ? ?? ? ? ? ? ? ? ?? ? ? ? 183 8. How many sixteenths in ? 14 9. How many eighteenths in ? 10. How many twentieths in &? ?? 11. How many twenty-fourths in ? ? 12. Reduce to twelfths. ANALYSIS.-equals; hence equals 3 times 12, or 12. 13. Reduce,, to twelfths. 14. Reduce,, to fifteenths. 15. Reduce,, to sixteenths. to twentieths. 17. Reduce,, to thirtieths. 18. Reduce,, to twenty-fourths. 19. Reduce to fifteenths. Since, by what number do we multiply both numerator and denominator of to obtain? NOTE.—To reduce a fraction to higher terms, multiply both numerator and denominator of the fraction by that number which will produce the required denominator. 20. By what must both numerator and denominator of? be multiplied to reduce it to 6ths? To 12ths? To 15ths? 21. By what must both numerator and denominator of be multiplied to reduce it to 8ths? To 12ths? To 20ths? |