REVIEW. 1. The prime factors of 45 are and " (a) What are the prime factors of 100? (b) of 125? 2. Two, 3, and 5 are the prime factors of (c) Of what number are 3, 3, 2, and 7 the prime factors? 3. Reduce to its lowest terms. (d) Reduce 125 and 48 to their lowest terms. 240 144 4. Reduce 8 to an improper fraction. 8 = 6. Reduce and common denominator. (g) Reduce and common denominator. 38 7. Multiply 60 by .7. This means, find 7 tenths of 60. One tenth of 60 = ; 7 tenths of 60 = (h) Multiply $537 by .07. This means, find 7 hundredths of $537. (See page 43.) 8. At $1 per ton, 4240 lb. of coal cost (i) Find the cost of 4240 lb. of coal at $7 per ton. 9. The volume of a rectangular solid 5 inches by 4 inches by 2 inches is cubic inches. (j) Find the volume of a rectangular solid 9 inches by 7 inches by 7 inches. 10. If 9 lb. of tea are worth $6, 12 lb. are worth (k) If 9 acres of land are worth $346.50, how much are 12 acres worth at the same rate? (12 is 13 times 9.) MISCELLANEOUS PROBLEMS. 1. From June, 1881, to June, 1899, it is years. (a) How many years from Aug., 1492, to Aug., 1897? 2. A man sold a horse for one hundred twenty dollars; this was seventeen dollars and twenty cents more than the horse cost him; the horse cost him (b) A man sold a farm for fourteen thousand seven hundred fifty dollars; this was eight hundred seventy-five dollars more than he paid for the farm. How much did the farm cost him? 3. From 5460 lb. of coal there were sold 2 tons. pounds remained. (c) From 18940 lb. of coal there were sold 83 tons. How many pounds were left? 4. From Mendota to Galesburg it is 80 miles; a train going 30 miles an hour, that leaves Mendota at 8:30, should arrive at Galesburg at (d) From Chicago to Denver it is about 1000 miles. If a train leaves Chicago for Denver at 9 o'clock Monday morning and goes at the rate of 30 miles an hour, when will it arrive at Denver? 5. If butter is 25¢ a pound and coffee is 30¢ a pound 3 lb. butter will pay for lb. coffee.. (e) Fifteen and one half pounds of butter at 244 a pound, will pay for how many pounds of coffee at 32¢ a pound? 6. If of a yard of lace is worth 154, 21 yards are worth cents. (f) If 3 of a yard of cloth costs $1.05, how much will 27 yards cost? SIMPLE NUMBERS.* 1. Four, 6, 8, 10, 12, etc., are multiples of 2. 2. Six, 9, 12, 15, 18, etc., are multiples of 3. 3. Twelve is a multiple of 2. 12 is also a multiple of 3, and of 4, and of 6. 4. Twelve is a common multiple of 2, 3, 5. Fifteen is a common multiple of and and 6. Common multiples of 4 and 6 are, 12, 24, The least common multiple of 4 and 6 is 12. 7. Common multiples of 6 and 8 are, 24, 48, The least common multiple of 6 and 8 is 8. Common multiples of 8 and 12 are, The least common multiple of 8 and 12 is 9. Common multiples of 6 and 9 are, The least common multiple of 6 and 9 is 10. The prime factors of 18 are and * Do much oral work in preparation for this page. By using these terms, make the pupil as familiar with multiple, common multiple, and least common multiple, as he is with house, schoolhouse, and stone schoolhouse. †Tell the meaning. Tell a number story. COMMON FRACTIONS. L. c. m. is the abbreviation for least common multiple. (s) 61 dollars)375 dollars. This means, find how many times $61 are contained in $375. (Change 61 and 375 to fourths.) Story. (t) 6)756 dollars. This means, find 1 sixth of $756. Story. (a) Multiply $432 by .25. This means, find 2 tenths of $432, plus 5 hundredths of $432. If 1 acre of land is worth $432, 1 hundredth of an acre is worth 5 hundredths of an acre are worth 2 tenths of an acre are worth (b) Multiply $325 by .23. (c) $482 x .32. (i) $426 x .45. *The pupil should understand that he multiplies $4.32 (not $432) by 5, and should be taught to write the decimal point in the partial product immediately after writing the tenths' figure, 6, of the partial product. †The pupil should understand that he multiplies $43.2 (not $432) by 2, and should be taught to write the decimal point in the partial product immediately after writing the tenths' figure, 4, of the partial product. |