Long Measure.-When is this measure used? Recite the table. How many barley-corns in 11 inches? How many' inches in 9 feet? How many inches in 2 yards? How many rods in 3 furlongs? How many miles in 8 furlongs? How many inches in 4 feet? In 8 inches how many barley-corns In 12 inches? Land or Square Measure.-When is this measure applied? Recite the table. How many square feet in 5 square yards? How many square inches in 2 square feet? How many rods in 3 roods? How many acres in 24 roods? In 28 acres? Cubic Measure.-What is the use of this measure? Recite the table. How many feet in half a cord of wood? In a quarter of a cord? In three quarters of a cord? In of a cord? Motion or Circle Measure.-By whom is this measure used? Recite the table. How many seconds in 2 minutes? How many degrees in 3 signs? How many signs in 2 degrees ? In 3 degrees? Time.-How is time naturally divided? Recite the table. How many hours in 3 days? How many days in 6 weeks? How many weeks in 5 months? How many months in 8 years? In 11 months how many weeks? In 48 weeks now many months? In 42 days how many weeks? In 56 days? How many months in a year? Name them, and the number of days in each month? How many days has leap-year? Paper. Recite the table. How many sheets in 3 quires? Particulars.-Recite the table. How many in 5 dozen? REDUCTION. 1. REDUCTION is of two kinds, termed Simple and Compound, by which we can change or reduce a sum or quantity of one kind or denomination, to another, whether it be greater or less, still retaining the same value. 2. When the sum consists of only one denomination to be reduced to another, it is called Simple Reduction. 3. The operations are all performed either by Multiplication or Division, for this reason-when a large denomina tion is to be reduced to a less, as pounds to drams, or dollars to mills, the operation is by Multiplication, and is called descending; but when drams are to be reduced to pounds, or mills to dollars, the operation is by Division, and called ascending. 4. Thus, to reduce 2 pounds avoirdupois to drams, multiply the pounds by the number of ounces in a pound, and this will reduce it to ounces; then by the number of drams in an ounce, and this will reduce it to drams: 2lbs. 16oz. =32oz.; 32 × 16=512 drams in 2 pounds. 5. Then, to reduce the 512 drams to pounds, divide by 16, and it will give the ounces; then by 16 again, and it will give the pounds: thus, 512-16=32 ounces; 32÷16=2 pounds. 6. By the above process, sums in Reduction will reciprocally prove each other; and it should be generally practised. SIMPLE REDUCTION. RULE. 1. Multiply the sum or quantity by that number of the next lower denomination which it requires to make one of its own. 2. If there be one or more denominations between that and that to which it is to be reduced, first reduce it to the next lower than its own, aud then to the next lower, and so continue. 3. When low denominations are to be brought to higher, as drams to pounds, cents to dollars, inches to miles, &c., divide by as many of the lower as make one of the higher, and set down what remains (if any) on the right, and so continue. Explanation. First multiply the 2 cwt. by 4, and this will reduce it to quarters, because 4 quarters make 1 cwt.; then multiply the quarter by 28, and this will reduce it to pounds, because 28 pounds make 1 quarter; then multiply by 16, which will reduce it to ounces, because 16 ounces make 1 pound; then multiply the ounces by 16, and it will reduce it to drams, because 16 drams make 1 ounce. Then, to prove it, divide the sum of the drams by the same denominations by which you multiplied, and this will reduce it to 2 cwt. 2. Reduce 1 year to seconds. Thus : REVIEW. Reduction.-1. What do you understand by Reduction? 2. When the sum consists of only one denomination? 3. How are all the operations to be performed? 4. How will you reduce 2 pounds to drams? 5. How will you reduce drams to pounds? 6. Proof. Rule. 1. How do you multiply? 2. If there be one or more denominations? 3. When low denominations are to be reduced to higher? AVOIRDUPOIS WEIGHT. (1.) Bring 80 pounds to ounces. TROY WEIGHT. (9.) Bring 12 pounds to ounces. (10.) Bring 15 pounds to grains. (11.) Bring 20 pounds to grains. (12.) Bring 738 ounces to pounds. (13.) Bring 1296 grains to ounces. APOTHECARIes' weight. (14.) Bring 144 ounces to drams. CLOTH MEASURE. (19.) Bring 6 yards to quarters. (20.) Bring 5 yards to nails. Ans. 1280. 5376. 8960. 172032. 80. 3 lbs., 12 oz. 21504. Ans. 144. 86400. 115200. 61 lbs., 6 oz. Ans. 1152. 46080. 168. 18432. Ans. 24. 80. 256. 688. (21.) Bring 64 quarters to nails, (27.) Bring 2 barrels to pints. Ans. 504. (28.) Bring 6794 gills to gallons. 212 galls., 1 qt., 2 gills. (29.) Bring 872 pints to barrels. (30.) Bring 4984 pints to hogsheads. DRY MEASURE. (31.) Bring 12 bushels to pecks. (36.) Bring 30 yards to feet. 3 bbls., 14 galls., 2 qts. Ans. 48. 26. 36. 2400. LONG MEASURE. Ans. 90. 990. 3200. 120. (37.) Bring 60 poles to feet. LAND OR SQUARE MEASURE. (41.) Bring 15 roods to poles. SOLID OR CUBIC MEASURE. (46.) Bring 9 feet to inches. (47.) Bring 12 feet of round timber to inches. (48.) Bring 7984 inches to feet. MOTION or CIRCLE MEASURE. (49.) Bring 40 degrees to minutes. (50.) Bring 27 degrees to seconds. TIME. (51.) Bring 10 years to weeks. Ans. 600. 3200. 810. 5760. Ans. 15552. 20736. 4 ft., 1072 in. Ans. 2400. 97200. Ans. 520. 6. 672. 2160. (55.) Bring 20 days to minutes. 28800. (56.) Bring 18 hours to seconds. 64800. (57.) Bring 20 years to days. 7300. (58.) Bring 9 days to seconds. (59.) Bring 7898600 seconds to days. (60.) Bring 648 months to years. |