7. A piece of land 160 rods long and as wide as the schoolroom is about acres. (j) How many square rods in a rectangular piece of land 47 rods by 6 rods? Is this more or less than 1 acre? Is it more or less than 2 acres? 8. One cord is cubic feet. cord = (k) How many cubic feet of wood in a pile 7 feet by 5 feet by 6 feet? Is this more or less than 1 cord? Is it more or less than 2 cords? save MISCELLANEOUS PROBLEMS. 1. If a man can save $5 a month, in 3 years he can dollars. (a) If a man can save $27 in a month, how much can he save in 9 years? 2. Byron bought 2 doz. oranges for 404; he sold them at 34 each; he gained cents. (b) A merchant bought 35 barrels of apples for $85; he sold them at $2.75 a barrel. How much did he gain? 3. Henry had 25 chickens; a hawk caught 20% of them; he sold the remainder at 22¢ each; he received dollars and cents. (c) Henry's father had 75 bushels of apples; he lost 20% of them by decay; he sold the remainder at 85¢ a bushel. How much did he receive for them? 4. If coffee costs $ a pound, for 1 dollar I can buy pounds. 1}= (d) If tea costs $3 a pound, how many pounds can I buy for $57? (Change $57 to fifth-dollars.) 5. The sum of two numbers is 34; one of the numbers is 12; the other number is (e) The sum of two numbers is 346.2; one of the numbers is 75.36. What is the other number? 6. In a piece of slate 1 foot square and 1 inch thick there are cubic inches. (f) How many cubic inches in a piece of slate 2 feet square and 2 inches thick? (g) If g of a ton of coal is worth $4.20, how much is 1 ton worth? SIMPLE NUMBERS. 1. One tenth of 6 is 3. One tenth of 300 is. 1 tenth of 40 is 1 tenth of 25 is 1 tenth of 325 is number is one -th of the 4. One half of 1 tenth of a number. One third of 1 tenth of a number = th of 5. One third of 1 hundredth of a number is one the number. (f) Divide 972 by 300. (h) Divide 895 by 500. (g) Divide 972 by 400. (i) Divide 976 by 800. REVIEW. 6. Common multiples of 15 and 6 are The least common multiple of 15 and 6 is 7. The prime factors of 63 are 8. 3, 3, and 5 are the prime factors of is exactly divisible by 3; by 5; by (1) and etc. Forty-five ; by (m) (n) (0) 160 sq. rd.)2400 sq. rd. 15)2445 sq. rd. 128 cu. feet.)1536 cu. ft. COMMON FRACTIONS. 1. Add and . The 1. c. m. of 15 and 6 is = 3* = 30 13* (a) Find the sum of 4567, 341, 245%, and 564. 8. Divide 8 by 3. (4)* 8* 16* 22* multiplied by 24. Change 8 to -ths. divided by 3. Story. Change to ths. This means 15* divided by 8. Story. 346 (m) 37513 435 2465 *These figures refer to notes on pages 6 and 7. See also foot-notes, page 62. DECIMAL FRACTIONS. 1. One tenth of $6 is .1 of $6.25 is 2. One hundredth of $6 is .01 of $6.25 is $.0625. 3. Read each of the following in two ways: $.2436,* $.0532, $.6403, $.0042, $.0002, $.6042, $.8002. (a) Multiply $6.25 by 4.23. This means, find 4 times $6.252 tenths of $6.25 +3 hundredths of $6.25. (b) Multiply $7.35 by 3.46; (c) $4.45 by 5.24. * (1) 24¢, 3 m., and 6 tenths of a mill. (2) 2436 ten-thousandths of a dollar. TO THE TEACHER.-Read the foot-note on page 133; also, the first part of page 143. If the pupil finds difficulty in "pointing off," teach him to use a separatrix in the multiplicand as suggested on page 133. While multiplying 6.25 by 3 hundredths, it may appear V06.25 on the slate thus: 4.23 Do not at this stage of the work allow the pupil to "point off" by counting the decimal places in the multiplicand and multiplier. Rather, lead him to think the meaning of the problem. See foot-notes, page 53. |