5. Reduce 759 pints to higher denominations. 6. Reduce 8573 pints to higher denominations. 7. What is the cost of 2bush. 3pk. of grass seed, at $2 a peck? TIME. 118. Time is used in measuring duration. The natural divisions of time are days, months, (moons), seasons, and years. The artificial divisions are seconds, minutes, hours, weeks, etc. 12 Calendar Months (=365 or 366 Days), 1 Civil Year, c. yr. 24= 1440= 86400 1. m. 1 = 7 168 10080 = 604800 J. yr. 1 = 4 = 28 672 = 40320 = 2419200 1=13525=3651-8766-525960=31557600 SCALE. Descending, 4, 7, 24, 60, 60; Ascending, 60, 60, 24, 7, 4. 118. For what is Time used? What are its natural divisions? Artificial divisions? Table? NOTE 1. The names of the seasons and of the calendar months and the number of days in the several months, are as follows: — NOTE 2. The number of days in each month may be easily remembered by committing the following lines : Thirty days hath September, Till leap year gives it one more. NOTE 3. A solar year, that is, a year by the sun, is very nearly 365 days, 5 hours, 48 minutes and 50 seconds. 1. How many seconds in 18h. 27m. 30sec. ? 5. Reduce 452897 seconds to higher denominations. CIRCULAR MEASURE. 119. CIRCULAR MEASURE is used in surveying, navigation, geography, astronomy, etc., for measuring angles, determining latitude, longitude, etc. 118. Scale? What are the names of the calendar months? How many days in each? In what season is each? The number of each from the beginning of the year? Length of a solar year? 1 = SCALE. 12 = 360 = 30, 12. Descending, 12, 30, 60, 60; Ascending, 60, 60, B D C NOTE. A curved line is a figure bounded by a curved line, all parts of the curve being equally distant from the center of the circle. The Circumference is the curve which bounds the circle. An Arc is any portion of the circumference, as A B or B D. An arc equal to a quarter of the circumference, or 90°, is called a quadrant. A Radius is a line drawn from the center to the circumference, as CA or C B. A Diameter is a line drawn through the center and limited by the curve, as AD. 119. For what is Circular Measure used? Table? Scale? What is a Circle? Circumference? Arc? Quadrant? Radius ? Diameter? MISCELLANEOUS EXAMPLES IN REDUCTION. 1. In 7£ 15s. 6d. 3qr. how many farthings? 2. Reduce 67219qr. to pounds sterling, etc. 4. 5. Change 27619gr. to pounds, etc. In 7oz. 5dr. 2sc. 12gr. of opium, how many grains? 6. Reduce 17 tons 16cwt. 3qr. to quarters. 7. Change 627243oz. to tons, etc. 8. In 7yd. 3qr. 2na. lin. how many inches? 10. Change 5fur. 13rd. 7ft. 10in. to inches. 12. In 27 fathoms, how many inches? 13. John Smith's horse is 15 hands high; how many inches high is he? 14. In 7m. 3fur. 7ch. 2rd. how many links? 15. Reduce 3a. 2r. 27sq. rd. 127 sq. ft. 126sq. in. to square inches. 16. How many cu. in. in 17 cords? 17. Reduce 76493c. in. to cords, etc. 18. How many gills in 27gal. 3qt. 1pt. 3gi. ? 19. Reduce 643gi. to gallons, etc. 20. Change 46bu. 3pk. 6qt. 1pt. to pints. 21. In 874qt. how many bushels ? 22. Reduce 17h. 56m. 43 sec. to seconds. 23. Reduce 178cwt. 2qr. 10lb. to ounces. 24. Reduce 10yd. 2na. to nails. 25. Reduce 726890 inches to miles. DEFINITIONS AND GENERAL PRINCIPLES. 120. All numbers are even or odd. An EVEN NUMBER is a number that is divisible by 2; as 2, 4, 8, 12. An ODD NUMBER is a number that is not divisible by 2; as 1, 3, 5, 11, 19. 121. All numbers are prime or composite. A PRIME NUMBER is a number that is divisible by no whole number except itself and one; as 1, 2, 3, 5, 7, 11, 19. A COMPOSITE NUMBER is a number that is divisible by other numbers besides itself and 1; thus, 6 is composite, because it is divisible by 2 and by 3; 12 is composite, because it is divisible by 2, 3, 4, and 6; 25 is composite, because it is divisible by 5 and 5. FACTORING NUMBERS. 122. The FACTORS of a number are those numbers whose continued product is the number; thus, 3 and 7 are the factors of 21; 3 and 6, or 3, 3, and 2 are the factors of 18; etc. The prime factors of a number are those prime numbers whose continued product is the number; thus, the prime factors of 12 are 2, 2, and 3; the prime factors of 36 are 2, 2, 3, and 3; etc. NOTE. Since 1, as a factor is useless, it is not here enumerated. 120. What is an Even Number? An Odd Number? 121. A Prime Number? What is the only even prime number? What is a Composite Number? 122. What are the Factors of a number? What are the prime factors of a number? |