15. 12 is 2 thirds of what number? 30. 26 is 13 ninths of what number? 31. 2 thirds of 12 is 2 fifths of what number? 32. 3 fourths of 12 is 3 eighths of what number? 33. 3 fourths of 8 is 2 sevenths of what number? 34. 3 fifths of 25 is 5 fourths of what number? 35. 2 sevenths of 14 is 4 ninths of what number? 36. 4 sevenths of 21 is 3 tenths of what number? 37. 2 thirds of 15 is 5 fourths of what number? 38. 7.eighths of 48 is 3 halves of what number? 39. 8 ninths of 36 is 4 fifths of what number? 40. 7 thirds of 18 is 3 fifths of what number? 41. A watch cost $16, and 3 halves of the cost of the watch is 8 thirds of the cost of the chain. What was the cost of the chain? 42. A horse was sold for $96, which was 8 sevenths of what it cost; what was the cost of the horse? 43. In a certain school there are 36 ladies, and 5 fourths of the number of ladies equals 3 fifths of the number of gentlemen. How many gentlemen were there in the school? 44. Mary is 14 years old, and 4 sevenths of her age is 2 thirds of Hezekiah's age; what is his age ? 45. A piece of cloth containing 12 yards was sold for $60, which was 5 fourths of what it cost; how much did it cost, and what was the gain on each yard? 46. A has 48 geese, and 3 fourths of his number is equal to 9 sevenths of B's number; how many geese has B? 47. The head of a fish is 12 inches long, and 3 fourths of the length of the head is 3 fifteenths of the length of the body. Required the length of the fish. 48. A farm was sold for $1200, which was only 6 sevenths of what it was worth. How much was lost by the bargain? 49. $48 is 3 fifths of the cost of 12 yards of cloth; for what must it be sold a yard to gain $16 on the whole? 50. A man gave 60 dollars for a suit of clothes, which was 1 fifth of his yearly income; 1 sixth of the remainder he spent for a watch, and what then remained was 4 fifths of his brother's yearly income. What was the yearly income of each? REMARK.-The above expressions are called fractions. The figure above the short horizontal line is called the numerator, and the figure below the line is called the denominator. For example, in the fraction, the 3 is the numerator, and the 4 is the denominator. The denominator of a fraction shows into how many equal parts the thing is divided; and the numerator shows how many of these parts are taken. 1. If you cut an orange into 3 equal parts, what is 1 of these parts called? 2. If a lemon be cut into 4 equal pieces, what will 1 of these pieces be called? 2? 3? 4? 3. If a bushel of apples be divided into 6 equal parts, what will 1 of these parts be called? 3? 4? 6 ? 4. If a basket of peaches be divided in 8 equal parts, what will 3 of these parts be called? 5 6 7 ? 5. How can you find 2 thirds of an apple? 6. How can you find 3 fourths of an orange? 7. In how many times 1? SOLUTION.-In 1 there are 2 halves, therefore 1 half the number of halves equals the number of ones. 1 half of 4 is 2; therefore, equals 2. 8. In 10. In 11. In 12 12. In 14 13. In 14. In 12 15. In 16. In 17. 18 In 18. In 8 19. 22. how many times 1? how many times 1? how many times 1? how many times 1? how many times 1? how many times 1? how many times 1? how many times 1? how many times 1? how many times 1? how many times 1? In 21 how many times 1? 20. In how many times 1? 21. In 12 how many times 1? In 16 how many times 1? 23. In 20 how many times 1? 34. In 18 how many times In 36 how many 8 times 1? In 4 how many times 1? In 50 how many times 1? 36. In 45 how many 35. 10 times 1? 37. In 1 how many times 1? 38. 1? how many times 1? 41. What kind of a fraction is it called, when the numerator is less than the denominator ? 42. What kind of a fraction is it called, when the denominator is greater than the numerator? 43. When is the value of a fraction greater than a unit? 44. When the denominator is less than the numerator, what kind of a fraction is it called? 45. What kind of a fraction is it called, when the numerator is larger than the denominator? REMARK.-This is called reducing fractions to whole or mixed numbers. A mixed number is a whole number with a fraction added to it. Thus 3 is a mixed number. Whenever the numerator is less than the denominator, the value is less than a unit, and the expression is called a proper fraction; -but when the numerator is equal to or greater than the denominator the value is equal to or greater than a unit, and the expression is called an improper fraction. of an apple, and John gave him { 1. James had more; how many had he then ? 2. Mary had of an orange, and her father gave her of an orange more; how many had she then? 3. Robert had of a melon, and bought of another; how many had he then ? 4. Susan had of a pint of walnuts, and gave of a pint to her sister; how much had she left?. 5. James bought 19 of a pound of candies, and on his way home ate of a pound; how much had he left? of 6. John gave of a pound of raisins to James, a pound to Mary, and kept of a pound himself; how many had he at first! 7. Mortimer gave of a dollar for a hat, $13 for a vest, and had $33 remaining; how much had he at first? 8. Jane had 5 pounds of cinnamon, and Harriet had 23 pounds; how many more had Jane than Harriet? |