RATIO AND PROPORTION. 1. One sixth of 12 is . 12 is -J of 2. One fifth of 12 is . 12 is \ of 3. One fourth of 11 is . 11 is £ of (a) Find 1 third of 275. (b) 275 is 1 third of what? (c) Find 1 half of 377. (d) 377 is 1 half of what? 4. Two fifths of 30 are . 30 is f of . 5. Three fifths of 30 are . 30 is | of . (e) Find f of 90. (f) 90 is § of what number? (g) Find | of 90. (h) 90 is | of what number? 6. 14 is of 21. 21 is r of 14. 7. 21 is of 28. 28 is of 21. 8. 28 is of 35. 35 is of 28. 9. Two fifths of 30 are 1 half of ■ . 10. Three fifths of 30 are 2 thirds of . (i) Two fifths of 90 are 1 half of what number? 11. Twelve is of 8, or and . times 8. A man can earn and ■ ■ times as much in 12 days as he can earn in 8 days. If he can earn $20 in 8 days, in 12 days he can earn . (k) If a man can earn $73 in 8 months, how many dollars can he earn in 12 months? 12. If 8 lb. of sugar are worth 500, 12 lb. are worth cents. (1) If 8 tons of coal are worth $34.20, how much are 12 tons worth? (m) If 12 barrels of apples are worth $27.60, how much are 8 barrels worth? PERCENTAGE. 11| per cent = .11| —\. (1) (2) 1. 11-J- per cent of 27 = 27 is \\\°]o of . 2. 10 per cent of 20 = 20 is 10% of . 3. 11| per cent of 18 = 18 is 11£% of . 4. 10 per cent of 30 = 30 is 10% of . 5. 50 per cent of 3 = 3 is 50% of . 6. 25 per cent of 9= 9 is 25% of . 7. 33$ per cent of 7 = 7 is 33£% of . 8. 20 per cent of 11 = 11 is 20% of . 9. 16f per cent of 19 = 19 is 16|% of . 10. 14f per cent of 15 = 15 is 14f % of . (3) (3) 11. 6 is per cent of 24. 6 is % of 18. 12. 6 is per cent of 12. 6 is % of 30. 13. 3 is . per cent of 24. 3 is % of 21. 14. 3 is per cent of 18. 3 is % of 27. 15. Helen bought a piece of flannel that was 40 inches long; by washing it shrank 10% in length; after washing it was inches long. 16. Before washing, a piece of flannel was 40 inches in length; after washing it was 35 inches long; it shrank by washing ■ per cent* 17. A dealer had 25 bu. of apples; he lost 20% of them by decay; there remained ■ ■ bushels. (a) A dealer had 2375 bu. of apples; he lost 20% of them by decay. How many bushels remained? «It shrank what part of its original length? PERCENTAGE. 1. 1L|% of 36 = lLi% of 38 = 2. 10% of 50 = 10% of 51 = 10% of 52 = (c) Find 10% of 870; (d) of 874. (2) 3. 7 is 11|% of . 7£ is 11|% of . (e) 371 is ll-J.% of what? (f) 3711 js H|% 0f what? 4. 8 is 10% of . 8£ is 10% of . (g) 89 is 10% of what? (h) 89.2 is 10% of what? (3) 5. 12 is % of 24. 12£|- is % of 50. 6. 6 is % of 60. 6 is % of 54. 7. 3^ is % of 7. 3£ is % of 10. 8. 36 is % of 72. 72 is % of 144. {D 9. One per cent of $700 is . 2% of $700 = 10. One per cent of $730 is . 2% of $730 = 11. One per cent of $732 is . 2% of $732 = (i) Find 3% of $732. (j) Find 4% of $732 (k) Find 5% of $732. (1) Find 6% of $732. (m) Find 7% of $320. (n) Find 7% of $326. (2) 12. Two dollars are 1 hundredth of $200. 13. Two dollars are 1% of . $4 are 2% of . 14. Six dollars are 3% of . $8 are 4% of . 15. Five dollars are 1% of . $10 are 2% of . REVIEW. 1. All integral numbers are either prime or composite. 17 is . 31 is . 95 is . 242 is . 370 is . 2. Reduce each of the following improper fractions to a whole number or to a mixed number: if-, -375-, -3S7-, If-, \s, (a) 324. (b) ifi, (c) 2M-. (d) -S-fL. 3. Reduce each of the following to its lowest terms: 8 9 IS 15 11 18. 10 my ¥T Ti 3TT "ST "iS T0~0" (e)AV (OAV (g)m (h)iW 4. Reduce the following to equivalent fractions having a common denominator: 1,-1, f (Change to .) |= -J = $ = (ft 3 5 1 (ft 8 3 1 /Vl 3*1 5. If £ of a bushel of potatoes costs 200, 2£ bushels will cost . (1) If ^ of a ton of straw costs $2.25, how much will 3.2 tons cost? 6. Change the following to tons: 4200 lb. (in) 5750 lb. (n) 7320 lb. (o) 3150 lb. 7. Find the area and the perimeter of each of the following rectangular surfaces: 7 feet by 5 feet. (p) 27 feet by 12 feet. (q) 15 inches by 15 inches. 8. If 2 gallons of molasses are worth 60^, 3 gallons are worth ■ ■ cents. (r) If 2 loads of brick are worth $12.60, how much are 3 loads worth? MISCELLANEOUS PROBLEMS. 1. In a school there are 35 pupils; % of the pupils are boys; of the pupils are girls; there are boys and girls. (a) In a school there are 392 pupils; | of the pupils are boys. How many girls are in the school? 2. If 3 melons cost 36^, at the same rate 5 melons will cost cents. (b) If 3 acres of land cost $525, how much will 5 acres cost at the same rate? 3. Harry exchanged 5 lb. of butter at 200 a pound for coffee at 250 a pound; he should receive pounds of coffee. (c) Harry's father exchanged 6 cords of wood at $5.20 a cord for cedar posts at 200 each. How many posts should he receive? 4. 3 + 2 + 6 + 4 + 5 + 8 + 1 + 7 + 9 + 4 + 7 + 3 + 2 = (d) 275 + 361 + 554 + 732 + 598 + 236 + 347 + 256 = 5. If Mark saves $4 a month, in 1 year he will save dollars. (e) If Mark's father saves $21.50 a month, how much will he save in 1 year? 6. A common brick is 8 inches long, 4 in. wide, and 2 in. thick; it has two faces each of which is 4 in. by 8 in., two faces each of which is in. by in., and two faces each of which is in. by in. (f) Find the sum of the areas of all the faces of a common brick. (g) Change 674 inches to feet and inches. |