3. One week to minutes. 4. 20,160 minutes to weeks. 5. 4 da. 6 h. 56 min. to min. 6. 5776 min. to days. 7. 32 hr. 32 min. 41 sec. to seconds. 8. 87,990 sec. to hours. PROBLEMS. 1. Express 49,796 sec. in higher denominations. 3. How many days from April 10th to September 12th? 5. Giving three months to each, which is the longer, summer or winter? 6. Which of these are leap years: 1600, 1660, 1666, 1700, 1776, 1790, 1794, 1800, 1898, 1900? 7. How many seconds are there in 7 hr. 38 min. 49 sec.? 8. How many days and hours in week? 9. Find the number of hours in a week. 10. What part of a week is 1 day 18 hours? 11. A man borrows some money July 17 and promises to repay it in 60 days. On what day is it due? 12. How many leap years in the nineteenth century? 13. How many hours in the month of August? 14. If you read French 30 min. each day for 5 yr., how much time do you thus spend? 15. On what day will of a common year end? of a leap year? CIRCULAR MEASURE. Circular Measure is used to measure angles. A Circle is a figure made by a bounding line which is everywhere equally distant from a centre-point. The Circumference of the circle is the bounding line. An Arc is any part of the circumference, as BD. A Quadrant is an arc equal to of the circumference, as BE. A Degree is 30 of the circumference of a circle. An angle whose sides meet at the centre is measured by the arc included between its sides. E B The angle BCD is measured by the arc BD. A right angle is measured by a quadrant, or 90°. 1. 56' 25" to seconds. 5. 35° 48' 59" to seconds. 2. 3830" to minutes. 6. 99,800" to degrees. 3. 23° 36' to minutes. 7. 4 S. 29° 26' 33" to seconds. 8. 490,833" to signs. 4. 856' to degrees. 2. How many minutes in 2 quadrants? 3. How many seconds in a right angle? 4. 21 quadrants are what part of a circumference? 5. In 811,480" how many signs? 6. In what time does a fixed point in the earth's surface pass through 15° 15′ 15′′? 7. Where is a degree of latitude equal to 60 geographical miles? 8. Sixty-nine and 16 hundredths statute miles equal one degree on what surface? 1. What would 9600 sheets of foolscap cost at $.25 per quire? 2. Find the cost of 4 dozen brushes @ $.55 each. 3. A dealer bought paper at $8 per ream and sold it at $.30 a quire. Did he gain or lose, and how much? 4. In an octavo book of 960 pages how many sheets? 6. How many sheets in 2 bundles 1 ream 15 quires 10 sheets? 7. How many units in 8 gross 9 dozen? 8. If 12 dozen of buttons are worth $1.08, what are 11 buttons worth? 9. The use of 48 screws per day implies the use of how many gross in 6 weeks? 10. 500,000 copies of a daily newspaper are sold on an average per diem. Reckoning 3 sheets for each copy, how many reams of paper are used in a month? REDUCTION OF DENOMINATE FRACTIONS. SPECIAL EXERCISES. Reduction Descending. 1. Reduce of a rod to units of lower denominations. 2. Reduce .795 lb. Troy to units of lower denominations. Process. .795 lb. 9.540 20 190.800 288 72 36 Explanation. Since 12 oz. = 1 lb., 12 times the number of pounds 9.540 oz. the number of ounces; 12 times .795 Since 20 pwt. 1 oz., 20 times the number of ounces = the number of pwt. .540 x 12 10.8 pwt. Hence .795 lb. = = 9 oz. 10.8 pwt. 3. Reduce gal. to gills. Process. × 4 × 2 × 4 = 5 gi. = EXERCISES. 289 1. Reduce: 1.2 of a bushel to the fraction of a pint. 3. rd. to yards, feet, and inches. 4. .065 of a gallon to integers of lower denominations. 5. of a ton to lower denominations. 6. of an acre to lower denominations. 7. .007 of a bushel as a decimal of a pint. 10. .436 of a ream to integers. 11. .875 of a leap year to integers. Reduction Ascending. 1. Reduce & gi. to the fraction of a gal. of qt.; hence gi. 4 36 1 gal., therefore 1 pt., therefore the number of gal.; |