RATIO AND PROPORTION. 1. One fourth of 20 is . 20 is | of — 2. One half of 11 is . . 11 is | of — 3. One third of 10 is —-. 10 is > of — 4. One fifth of 45 is . 45 is £ of — 5. Two thirds of 60 are . 60 is f of — 6. Two thirds of 36 are . 36 is f of — 7. Two thirds of 15 are . 15 is -| of — 8. Two thirds of 21 are . 21 is f of — 9. 10 is of 15. 15 is fof 10, or—times 10. 10. 15 is of 20. 20 is of 15, or — times 15. 11. 20 is of 25. 25 is of 20, or — times 20. 12. 25 is of 30. 30 is of 25, or — times 25. 13. Three fourths of 16 are 2 thirds of . 14. Two thirds of 15 are 1 half of . 15. Three fourths of 24 are 2 thirds of . 16. Two thirds of 12 are 1 third of . 17. Eight is of 12. A man can earn as much in 8 days as he can earn in 12 days. If he can earn $21 in 12 days, in 8 days he can earn dollars. 18. Fifteen is and times 6. A man can earn times as much in 15 days as he can earn in 6 days. If he can earn $10 in 6 days, in 15 days he can earn ■ dollars. (a) If a man can earn $104 in 6 weeks, how much can he earn in 15 weeks. *It may be well, after the pupil has solved "mentally " such problems as Nos. 6 and 6, to require him to solve them with a pencil—this, as a preparation for similar problems in which larger numbers are used. t Allow the pupil to say, " 15 is 3 halves of 10," but remind him that the expression "3 halves of 10," means, s times 1 half of 10. PERCENTAGE.* 50 per cent = .50 = £. GOt (5)f 1. 50 per cent of 10 = 10 is 50% of . 2. 25 per cent of 12 = 12 is 25% of . 3. 33$ per cent of 12 = 12 is 331% of . 4. 20 per cent of 10 = 10 is 20% of . 5. 50 per cent of 8 = 8 is 50% of . 6. 25 per cent of 8 = 8 is 25 % of . 7. 20 per cent of 15 = 15 is 20% of . 8. 33£ per cent of 15 = 15 is 33$% of . (3)t (3)f 9. 5 is per cent of 10. 5 is % of 20. 10. 5 is per cent of 15. 5 is % of 25. 11. 4 is per cent of 8." 4 is % of 12. 12. 4 is ■ per cent of 16. 4 is % of 20. 13. 3 is per cent of 6. 3 is % of 15. 14. Henry had 25 cents; he spent 20 per cent of his money; he spent cents. 15. Peter spent 10 cents; this was 25 per cent of all he earned; he earned cents. 16. Roscoe earned 60 cents and spent 30 cents; he spent per cent of what he earned. *To THE Teachek.—Frequently review this page, and give many similar oral problem» as a preparation for page 27. fThese figures designate the percentage cases to which the problems below them belong. PERCENTAGE. 1. 50% of 18 is ■ . 50% of 19 is (a) Find 50 per cent of 724; (b) of 725. 2. 25% of 16 is . 25% of 17 is (c) Find 25 per cent of 896; (d) of 897. 3. 33^% of 18 is . 33$% of 19 is (e) Find 33$ per cent of 726; (f) of 727. 4. 20% of 25 is . 20% of 26 is (g) Find 20 per cent of 875; (h) of 877. (*> 5. 7 is 50% of . 7£ is 50% of —. BEVIEW. 1. Tell which of the following are odd numbers and which are even numbers: 14, 17, 19, 20, 24, 27. 2. The fractions -fc, -fr, and \^ have a denominator. 3. Change -| and £ to equivalent fractions having a common denominator. I can change thirds and fifths to . 2 _ 4 _ ? — T 4. Add -f and £. I can change 7ths and 3ds to . I = Yt i = Tt-" twenty-firsts and twentyfirsts = twenty-firsts. 5. Divide | by fa. This means, find how many times fa is contained in f. I can change 5ths to . | = 7iy. One twentieth is contained in twentieths times. 6. Multiply 6.05 by 3. Three times . (a) Find the product of 34.02 multiplied by 4. 7. Divide $6.28 by 2. This means, ■ 10* . (b) Find the quotient of $475.65 divided by 5. 8. When hay is $12 a ton, 1500 lb. cost dollars. 9. When coal is $7 a ton, 3000 lb. cost dollars. 10. A 2-inch square is how many times as large as a 1-inch square? 11. A 2 inch cube is how many times as large as a 1-inch cube? (c) How many square inches in an oblong 9 inches by 23 inches? 12. Three fourths of 20 are 1 half of . (d) Three fourths of 84 are 1 half of what number? * See note 10, page 9. MISCELLANEOUS. 1. Mr. A owned 15L acres of land;.he sold 6^ acres; he then had acres. (a) Mr. B owned 546^ acres of land; he sold 228Lacres How many acres had he remaining? 2. A bushel of oats weighs 32 lb.; 2 bushels of oats weigh pounds; 3 bushels weigh pounds. (b) Sixty bushels of oats weigh how many pounds less than one ton? 3. Two pounds of coffee @ $.23 a pound cost . (c) Find the cost of 84 pounds of coffee @ $.23 a pound.* 4. From a piece of cloth containing 12 yards there were sold 54- yards and 2£ yards; there were left yards. (d) From a piece of cloth containing 55 yards, there were sold 24| yd. and 17f yd. How many yards were left? 5. A boarding-school uses one gallon of milk each day; at 50 a quart the milk for one week costs . (e) A boarding-school uses 4 gal. of milk each day; at 5^a quart how much will the milk for the month of October cost? 6. John bought 20 oranges at 30 each and sold them at 50 each; he gained cents. (f) John's father bought 25 bushels of potatoes at 320 a bushel and sold them at 450 a bushel. How much did he gain? * In multiplication of decimal fractions, require the pupil to locate the decimal point in the product immediately after he has written the figure to the right of the decimal point in any whole or partial product. Thu3, in the *•.& multiplication of $.23 by 84 he writes (and thus locates) the decimal point of the product immediately after writing the figure 9 in the first partial pro- •.j2 duct. This will be quite clear to the pupil if he understands that he first —— finds 4 times .23; then 80 times .23; then the sum of these two partial S!9-32 products. |