REDUCTION. To change a Compound Number to a Simple Number. 350. ILLUSTRATIVE EXAMPLE. Change 2 bu. 3 pk. 4 qt. to quarts. WRITTEN WORK. 4 pecks, in 2 bushels there are 2 times 4, or 8 2 bu. 3 pk. 4 qt. pecks, which with 3 pecks added are 11 pecks. 4 11 pk. 8 92 qt. Ans. Since in 1 peck there are 8 quarts, in 11 pecks there are 11 times 8 quarts, etc. Rule. 351. To change a compound number to a simple number of a lower denomination: Multiply the number of the highest denomination by the number of units it takes of the next lower denomination to make one of that higher, and to the product add the given number of the next lower denomination. Multiply this sum in like manner, and so proceed till the given number is changed to units of the required denomination. 352. Examples for the Slate. 1. Change 4 T. 350 lb. 8 oz. to ounces. 2. What is the value of 2 lb. 8 oz. of gold at $ 20 an ounce? 3. Change 3 rd. 4 yd. 1 ft. to feet. 4. What will it cost to fence both sides of a road 26 rd. 6 ft. long, at 22 a foot? 5. How many square feet are there in an acre? 6. Change 3 sq. m. 35 A. to acres. 7. In a cubic yard, how many cubic inches? 8. What shall I receive for 25 gal. 3 qt. of milk at 7 cents a quart? 9. Mr. Russell sold 4 bu. 1 pk. 2 qt. of cherries at 12 cents a qt.; what did he receive for them? 10. If the pulse beats 80 times in 1 minute, how many times will it beat in a common year? 11. If a child sleeps of his time, how many hours will he sleep in 5 years, allowing for 1 leap year? 12. How many minutes were there in the first century? 13. The Tropic of Cancer is 23° 30′ north of the equator. What is the distance in geographical miles? in common miles? 353. Changing numbers to numbers of lower denominations is called reduction descending. For other examples in reduction descending, see page 171. To change a Simple Number to a Compound Number. 354. ILLUSTRATIVE EXAMPLE. Change 4354 feet to rods, yards, etc. Explanation. Since 3 ft. make a yard, in 4354 ft. there are as many yards as there are 3's in 4354, which are 1451, and 1 ft. remains. Since 5 yards make a rod, in 1451 yards there are as many rods as there are times 5 in 1451, which are 263, and yd., or 4 yd.. remain, etc. Rule. 355. To change a simple number to a compound number of higher denominations: Divide the given number by the number of units it takes of its denomination to make one of the next higher. Set aside the remainder, and divide, as before, the quotient thus obtained; and so proceed till the required denomination is reached. The last quotient with the several remainders is the number sought. 356. Examples for the Slate. Change to compound numbers: (14.) 3268 yards. (20.) 9328 lb. of soap. 26. What will 20 old silver dollars weigh in oz. pwt. etc., each dollar weighing 412 grains? 27. The trade-dollar weighs 420 grains. What will 20 trade-dollars weigh? 28. How many miles is it through the earth from pole to pole, the distance being 41707308 feet? 29. In a certain pasture 973 quarts of berries were picked in one week. How many bushels were picked ? 357. Changing numbers to numbers of higher denominations is called reduction ascending. For other examples in reduction ascending, see page 171. REDUCTION OF DENOMINATE FRACTIONS. To change a Denominate Fraction to Integers of Lower Denominations. 358. ILLUSTRATIVE EXAMPLE I. Change ğ rd. to yards, feet, and inches. To change a fraction of one denomination to integers of lower denominations: Change the fraction, as far as possible, to an integer of the next lower denomination. If a fraction occurs in the result, proceed with it as with the first fraction, and so continue as far as required. 361. Examples for the Slate. Change to units of lower denominations: 44. How many planks 8 inches wide will cover the roadway of a bridge of a mile long, each plank reaching from side to side? To change Integers of Lower Denominations to a Fraction of a Higher. 362. ILLUSTRATIVE EXAMPLES. (I.) Change 5 oz. 6 pwt. 16 gr. to the fraction of a pound. (II.) Change 2 pk. 6 qt. to the decimal of a bushel. Explanation (I.). — Since 24 grains make a pennyweight, 16 gr. are pwt., or pwt., which, added to the 6 pwt. given, are 63 pwt. 20 pwt. Since 20 pwt. make an ounce, 20 pwt. equals as large a part of an ounce, or oz., etc. 63 pwt. = Explanation (II.).— Since 8 qts. make a peck, 6 qts. are equal to 0.75 pk., which, added to the 2 pecks given, are 2.75 pecks. Since 4 pks. make a bushel, 2.75 pk. are equal to 0.6875 bu. Ans. 0.6875 bu. 363. From the preceding operations we derive the following Rule. To change integers of lower denominations to a fraction of a higher denomination: Change the number of the lowest given denomination to a fraction of the next higher. Unite this fraction with the number of that higher denomination. Change, in like manner, the number thus formed, and so continue as far as required. 45. Change 1 qt. O pt. 1 gi. to the fraction of a gallon. 47. What part of a rod is 4 yd. 0 ft. 4 in.? |