FRACTIONS Review 238. 1. Write a fraction with figures. Define a fraction; the terms of a fraction. What does the denominator show? the numerator? 2. Write seventeen eighteenths; twenty-five fortieths; sixty-five seventy-fifths; eleven one-hundred-twentieths. 3. Reduce to its lowest terms; to twenty-fourths. When is a fraction expressed in its lowest terms? How may a fraction be reduced to higher terms? 4. Reduce 4 to eighths; 7 to fourths. What is an integer? a mixed number? How may integers and mixed numbers be reduced to fractions? 5. Reduce 2 to an integer; 16 to a mixed number. What is an improper fraction? a proper fraction? How may an improper fraction be reduced to an integer or a mixed number? What is the value of a fraction? 6. Add and . Subtract from §. & Z. What are similar fractions? What must be done to fractions that are not similar before they can be added or subtracted? 7. Define reduction. 8. Multiply by 4; 8 by 4. How do you multiply a fraction by an integer? 9. Divide by 2; 2 by 2. Tell how to divide a fraction by an integer. 10. Multiply 6 by 3. Divide 6 by 3. How do you multiply an integer by a fraction? Tell how to divide an integer by a fraction. reciprocal of a fraction? What is the EXERCISES 8 239. 1. Reduce to lowest terms: §; 12; 10; 12; 14; 12; 2. Reduce to an improper fraction: 41; 63; 91; 75; 81. 3. Reduce to an integer or a mixed number: 10; 12; 14; 16; 15; 18; 22; 28. 4. Reduce to fractions having the least common denominator: and; and ; and §; 1 and . Give answers promptly: 5. 2 + 3/ 13. ÷ 4 ÷2 28. 11÷3 36. 42-31 11. 12. 1 ÷8 37. There are 30 days in April and we received the daily paper on of them. How many papers did we receive? 38. If a newsboy made $6 profit by selling some papers for $3, how much did he pay for them? 39. Jane has gone to school as many years as Roy. She has attended for 4 years. How long has Roy attended? 40. When you study 43 hours a day in school and 23 hours at home, how long do you study each day? 41. How wide must I cut a strip of silk to make a ruffle 51 in. wide with a hem of 13 in. on one side and & in. on the other? 42. How many yards of silk, 21 in. wide, will be needed to make this ruffle 54 yards long, allowing yd. for the seams? 43. When a steamship had slowed down to speed, it was going at the rate of 5 miles an hour. What was its rate at full speed? 44. When my pencil was new, it was 71⁄2 inches long. After I had used it a week, it was only 5 inches long. How much of it did I use in a week? 45. A certain locality had 4 inches of rainfall in one month and 2 inches the next. How much was the rainfall for both months? 46. A door is 8 feet high and its height is 23 times its width. How wide is it? 47. What is the area of the top of a table that is 10 feet long and 3 feet wide? 48. If a town has 9 miles of asphalt pavement and 5 miles of macadam, how much more asphalt than macadam has it? 11. Reduce to an improper fraction: 75; 8; 14; 193; 27; 32; 40; 513. 12 12. Reduce to a whole or a mixed number: 76; 64; 25; 138; 156; 26; 345; 464; 760 6 12 Do as the signs indicate: 24 Find the cost of: 44. 25 plows at $63 each. 45. 18 horse rakes at $14,8% each. 46. 52 wagons at $4618 each. 47. 16 tons of hay at $13 per ton. 48. 612 bushels of corn at $ per bushel. 49. 1276 barrels of potatoes at $17 per barrel. 50. Find the annual cost of fuel to a manufacturer who uses 1800 tons of coal per year at $23 per ton. 51. A farmer put 1225 bushels of apples into barrels holding 21 bushels each. How many barrels were there? 52. If a Hudson River steamboat goes 144 miles in 9g hours, what is its average rate per hour? 53. A farmer in the state of New York one year raised 948 bushels of grain on 162 acres of ground. What was the average yield per acre? 54. An automobile went 128 miles one day, and 14 times as far the third day as the second. it run in the three days? as far the next, How far did Multiplication of Fractions 241. Multiplication of fractions by fractions. 1. What part of a circle is of of it? 2. What part of a circle is of of it? him? 3. What part of a rectangle is of of it? of of it?of of it? of of it? 4. What part of a rectangle is of of it? of of it? of of of it? of it? of 3. of; of; of; of; of; of 2; 1 2 3 242. Finding a fractional part of a fraction is called multi plying a fraction by a fraction. The word "of" between two fractions signifies multiplication, and when the sign x is used between two fractions, it may be read "of.” Such expressions are sometimes called compound fractions. 243. To multiply a fraction by a fraction, multiply the numerators together for the numerator of the product and the denominators for the denominator of the product. |