1. Divide 146.88 by 4; by 40; by 36. 2. Divide 7.14 by 3; by .02; by .3. 3. Divide 714.06 by 18; by .18; by 1.8. 4. If in a fence 172.8 ft. long there are 18 panes, how long is each pane? 5. How many panes of fence 12.4 ft. long in a fence 124 ft. long? 6. If 14 bbl. of apples cost $4.50, what will 1 bbl. cost? What will 3.25 bbl. cost? 7. 2.5 lb. of butter cost 50. What is the price of 1 lb.? 14 lb. ? 8. 2 acres of land are sold for $160. What was paid for 25% acres at the same rate? 9. A man by working 8 hours a day can do a piece of work in 6 days. In how many days can he do it if he works 10 hours a day? 10. At $4.5 a barrel, how many barrels can be bought for $90 ? 11. At the rate of $.015 each, how many pencils can I get for $30? How many dozen? 12. In a town of 4200 inhabitants .9 are white, .07 are negroes, and the remainder are Chinese. How many of each? 13. How many sheep at $15 apiece will pay for 60 cows at $43.50 apiece? 14. How many eggs at $ a dozen will pay for 363 cords of wood at $6 a cord? (Answer in dozens.) 15. What will 24 bu. 1 pk. of corn cost at 87 a bushel? 16. A cargo of wheat weighing 19 T. 6 cwt. contains how many bushels, counting 60 lb. to a bushel? How many loads of 1800 lb. each in the cargo? If it cost $1.08 a cental (100 lb.) and was sold for 85 a bushel, what was the profit? 17. How many years, months, and days from January 1, 1890, to March 8, 1892? from September 16, 1891, to July 1, 1893 ? reams of paper cost at 8 a quire? 18. What will 46% 19. Bought a bale rate of a sheet. of paper at $2.25 a ream, and sold it at the What was the profit? 20. What is 8.2 T. of iron worth at 4 21. A barrel of flour weighs 196 lb. barrels weigh? a pound? How many tons do 87 SECTION II. FACTORS, MULTIPLES, AND FRACTIONS. Oral Exercises.. 1. Give five odd numbers. 2. Give all the odd numbers from 1 to 39. 3. Give all the even numbers from 2 to 40. 4. Give the factors of 6; 8; 12; 15; 20; 32; 48. 5. Name five other composite numbers. 6. Give a number that has no factors except itself or one. This is a prime number. Name all the prime numbers from 1 to 47. 7. Give five numbers divisible by 3. 8. What numbers are divisible by 3? Give examples. -9. Give some numbers divisible by 5. 10. What numbers are divisible by 5? -11. What numbers are divisible by 2? by 4? by 6? by 9? Give examples of each. 12. What are the factors of 30? 45? 60? 90? `13. What are the prime factors of 8? 12? 24? 30? 14. Name five numbers of which 2 is a factor. -15. Name five other multiples of 2. 16. Name five multiples of 3; of 4; of 6; of 8. 17. Name a common multiple of 2 and 4; of 4 and 6 ; 8; of 8 and 12; of 10 and 20. of 6 and 18. Name a common multiple of 8 and 12; of 6, 8, 12; of 2, 3, and 4; of 3, 4, and 6; of 9, 8, and 6; of 3, 5, and 10. 19. Name the least number which is a multiple of both 2 and 3; of 4 and 6; of 2 and 4; of 4 and 8; of 6 and 9; of 8 and 12. 20. What is the least common multiple of 6 and 12? of 6 and 10? of 6 and 15? of 10 and 15? of 20 and 30? of 8 and 12; of 9 and 12; of 12 and 20? E -4. Give the prime factors of all numbers in column A. Oral and Written Exercises. 1. Give the common factors of 8 and 12; 6 and 12; 8 and 18; 12 and 20; 15 and 18. 2. Give the common factors of 12 and 18; 15 and 24; 16 and 24; 24 and 30; 28 and 32. 3. What is the greatest common divisor of 10 and 20? 12 and 15? 15 and 25? 24 and 36? 36 and 48 ? 4. What is the greatest common divisor of 18 and 24? 15 and 45? 20 and 30? 32 and 48? 48 and 64 ? 5. Find the prime factors of 72; 84; 96; 108; 120; 144; 160; 180; 176; 196. 6. Find the prime factors of 240; 320; 480; 500; 560; 620; 720; 780; 840; 1000. 7. Find the common factors of 64 and 96; 108 and 184; 180 and 196; 320 and 480; 450 and 600. 8. Find the common factors of 84 and 100; 120 and 160; 136 and 125; 487 and 369; 876 and 390. What is the greatest common divisor of: 9. 24 and 48? 24 and 36? 24 and 32? 24 and 28? -10 36 and 84? 64 and 96? 120 and 330? 180 and 64? 11. 246 and 138? 228 and 162? 148 and 182 ? 232 and 160 ? 12. Find all the different factors of 8 and 12; 8 and 18; 12 and 18; 12 and 15; 15 and 20; 20 and 14; 24 and 30; 30 and 36; 36 and 40; 42 and 48; 48 and 60. 13. Find the least common multiple of 6 and 9; 12 and 15; 15 and 18; 18 and 24; 24 and 30. 14. Find the least common multiple of 40 and 80 ; 60 and 90 ; 120 and 180; 72 and 96; 81 and 108. 15. Find the least common multiple of 160 and 180; 90, 120, and 150; 80, 120, and 200; 360 and 487; 63 and 315. 16. Find the least common multiple of 8, 12, 24, and 36; 18, 20, 24, and 30; 42, 48, 60, and 90; 72, 84, 90, and 100. Find the least common multiple of the denominators of: and 11; 48 and; and • 17. 18 and 3; Forty-eighths Twenty-fourths Twelfths Sixths Thirds One Halves Fourths Eighths Sixteenths Thirty-second's Sixty-fourths 1. By laying a straight-edge on the above diagram, show how many of higher terms equals. Thus, 8, 1, etc. In the same way proceed with ; ; ; ; 12; ; ; ; ; ; etc. 2. From the above diagram change to lower terms;; }; Pa; 18; 18; 28; 12; 13; 28; 32; 13; 14; 84; 84; # 3. See if you can do the same thing with lines; thus: 8 16 4. When you reduce sixteenths to eighths, or eighths to fourths, have you larger or smaller fractional parts? Have you more or less parts? Show by lines. 5. In reducing thirds to sixths, have you larger or smaller fractional parts? Have you more or less parts? |