REVIEW. 1. The sum of three numbers is 27; two of the numbers are 8 and 10; the other number is (a) The sum of three numbers is 2756; two of the numbers are 784 and 975. What is the other number? 2. Arthur rode on his bicycle three consecutive hours; the first hour he rode 12 miles; the second hour, 10 miles, and the third hour 8 miles; his average speed per hour miles. was (b) The attendance at a certain school for one week was as follows: Monday, 35; Tuesday, 38; Wednesday, 37; Thursday, 36; Friday, 34. What was the average daily attendance ? * 3. At $7 per ton, 21 tons of coal cost (c) At $3481⁄2 an acre, how much will 5 acres cost? (d) At $348.50 an acre, how much will 6.5 acres cost? (e) Compare the answers to (c) and (d). How much is their difference? 4. The first day of January, 1897, was Friday. Tell the day of the week of the first day of January of each of the following years: 1898, ; 1902, ; 1899, ; 1900, ; 1901;† ; 1905. ; 1906, ; 1910, ; 1907,; 1908,; 1909, (f) Upon what day of the week will the first day of Janu ary, 1925, occur? 5. A plot of a certain garden is drawn on a scale of 20 feet to an inch. A line 33 inches long represents feet. (g) A certain map is drawn on a scale of 25 mi. to an inch. A line 15 in. long represents how many miles? * 2 times 7 and 1 half of 71⁄2. † Remember that the year 1900 is not a leap year. MISCELLANEOUS PROBLEMS. 1. In a pane of glass 9 in. by 12 in. there are inches. sq. (a) How many square inches in 36 panes of glass each 9 in. by 12 in.? (b) How many square feet? 2. Mr. Black received $30 per month as rent for a house. In one year he received dollars. (c) At $35 per month, how much is the rent of a house for 2 years and 6 months? 3. I paid $2.00 for coffee at 25¢ a pound; I purchased pounds. (d) Paid $34.75 for coffee at 25¢ a pound. How many pounds were purchased? 4. In a floor 12 ft. by 12 ft. there are square feet; (e) In a lot 24 feet by 96 feet, there are how many square feet? (f) How many square yards? 5. If a train moves at the rate of 20 miles an hour, to move 110 miles will require hours. (g) If a train moves at the rate of 35 miles an hour, how long will it take to go 1000 miles? 6. A boy bought 10 chickens for 25¢ each, and 10 for 35¢ each; the average price paid was cents. (h) A man bought 10 horses at $135 each and 10 at $124.50 each. What was the average price? 7. A man sold a horse at of what it cost him, thereby losing $10; the horse cost him dollars; he sold it for dollars. (i) A man sold a farm for of what it cost him, thereby losing $1275. How much did the farm cost him? (j) For how much did he sell it? SIMPLE NUMBERS. Review page 11. 1. Name five odd numbers; five even numbers. 3. Name five integral numbers; five fractional numbers; five mixed numbers. 4. 13 and .7 are numbers. 4 and 7.2 are Review page 31. 5. Name five prime numbers; five composite numbers. 6. Which of the following are prime and which are com posite? 2, 22, 5, 37, 45, 49, 53, 72, 87. Review page 41. 7. What are the prime factors of 36? Of 33 ? Of 35? Of 34 ? 8. Of what number are 2, 2, 3, and 5 the prime factors Review page 51. 9. Name three common multiples of 4 and 6. 10. What is the least common multiple of 4 and 6? (i) A farmer bought 30 sheep; for 5 of them he paid $6 per head; for 10 he paid $5 per head; for the remainder he paid $70. How much did the 30 sheep cost him? (j) What was the average price per head? COMMON FRACTIONS. Review page 12. 1. Name three fractions that have a common denominator; three that do not have a common denominator. 2. Change the following to equivalent fractions having a common denominator: and . Review page 32. 3. Tell the terms of each of the following: 4. Reduce each of the following to its lowest terms: 5. Reduce each of the following to a whole or mixed number: 10, 25, 24, 18, 13. (c) 385. (d) 476. 3 32 97 Review page 42. 6. Reduce each of the following to an improper fraction: 9, 7, 113, 53. (e) 285. (f) 47%. (g) 943. (h) 86152. (u) Find the product of 794 multiplied by 63.* .(v) Find the quotient of 8351⁄2 bu. divided by 24 bu.* (w) Find the quotient of 654 bu. divided by 9.* *Solve, and tell a suggested number story. '6.40 3.7 4.480 19.20 23.680 73.42 3.56 4.4052 36.710 220.26 261.3752 .005)38.455** 7691. .05)38.47'5+ 769.5 .5)38.4 75‡ 76.95 5)38. 4758 7.695 .5)78.0 || DECIMAL FRACTIONS. Review pages 13, 23, 33, 43, 53, 63, 73, and 133. Observe again the fact that when a problem in multiplication of decimals has been solved accurately, the number of decimal places in the product is equal to the number of decimal places in the multiplicand and multiplier counted together. This fact should be used as a test of the accuracy of the work rather than as a rule for "pointing off." Observe that when the decimal point in the first partial product has been located, the remainder of the "pointing off" may be done mechanically by placing the point in each of the other partial products and in the complete product, directly under the one in the first partial product. Review pages 83, 93, and 103. All abstract work in division of decimals may be regarded as belonging to Case I.; that is, the pupil may consider that he is to find how many times the divisor is contained in the dividend. Before beginning to divide, place a separatrix (V) in the dividend immediately after that figure in the dividend that is of the same denomination as the right hand figure of the divisor. When in the process of division this separatrix is reached, the decimal point must be written in the quotient. * Find how many times 5 thousandths are contained in 38455 thousandths. Find how many times 5 hundredths are contained in .05)78.00 3847 hundredths. 1560. Find how many times 5 tenths are contained in 384 tenths. ? Find how many times 5 units are contained in 38 units. Find how many times 5 tenths are contained in 780 tenths. ¶ Find how many times 5 hundredths are contained in 7800 hundredths. |