WRITTEN EXERCISES. 1. Reduce of a ton to the fraction of a pound. ANALYSIS.-In this example 5000 × 20 × 100 lb. we multiply, as in reduction descending, by the numbers required to reduce tons to pounds, = applying the rule for the multiplication of common fractions. 2. Reduce .0002 T. to the decimal of a pound. .0002 20 .0040 100 .4000 lb. ANALYSIS.-We multiply by the same numbers in this as in the preceding example, applying the rule for the multiplication of decimals. RULE. Multiply the given fraction, as in reduction of denominate numbers, by the numbers required to reduce it to the proper denomination. 3. Reduce of a pound to the fraction of a penny. 4. .015 bu. is what decimal of a pint? 5. What fraction of a pint is of a gallon? 6. Reduce sq. rd. to the fraction of a sq. ft. 7. Reduce .0005 hr. to the decimal of a second. 8. of a rod is what fraction of an inch? 9. 48003 is what fraction of a grain? 10. What decimal of a sq. ft. is .035 sq. yd.? 11. Reduce of a degree to the fraction of a second. 12. What decimal of a cubic foot is 120 of a cord? 13. Change 7 of a pound Troy to the decimal of a grain. 14. Change of a ton to the fraction of an ounce. 15. Reduce of a leap year to the fraction of an hour. 25 CASE II. To reduce a denominate fraction to an equivalent fraction of a higher denomination. ORAL EXERCISES. 1. What part of a foot is of an inch? ANALYSIS.—One inch is of a foot, and of an inch is of of a foot; or÷12 of a foot. = = 2. What part of a foot is .6 of an inch? ANALYSIS.-.6 ÷ 12 = .05 of a foot. of a shilling? .24 qt.? 3. What fraction of a pound is 6. 7. of a day? of a dime is what fraction of a dollar? 8. .9 of a dime is what decimal of a dollar? 9. Half a peck of oats is what fraction of a bushel? 10. What fraction of an eagle is a quarter of a dollar? WRITTEN EXERCISES. 1. of a lb. is what fraction of a ton? ANALYSIS.-In this example we divide, as in reduction ascending, by the numbers required to reduce pounds to tons, applying the rule for the division of common fractions. 2. .4 of a lb. is what decimal of a ton? 100).4000 20).0040 .0002 tons. ANALYSIS.-We divide by the same numbers in this as in the preceding example, applying the rule for the division of decimals. RULE. Divide the given fraction, as in reduction of denominate numbers, by the numbers required to reduce it to the proper denomination. 3. 12 of a penny is what fraction of a pound? 4. Reduce .5 of a pint to the decimal of a gallon. 5. Reduce of an inch to the fraction of a rod. 6. Reduce 36 half inches to the fraction of a yard. 7. .480 of a sq. rod is what decimal of an acre? 8. 2700 of a second is what fraction of an hour? 9. 1 of a cent is what part of an eagle? 10. What part of an eagle is .1 of a cent? CASE III. To find the value of a denominate fraction in whole numbers of a lower denomination. ORAL EXERCISES. 1. Reduce of a bushel to pecks. ANALYSIS.-In one bushel there are 4 pecks, and in of a bushel there are of 4 pecks of 4 pecks=2 pecks. 2. Reduce .5 of a bushel to pecks. ANALYSIS.-.5 x 4= 2.0 pecks. 3. How many inches in of a yard? 4. How many cents in of a dollar? 5. In .8 of a dollar there are how many cents? 6. How many seconds in of a minute? 7. In .01 of a cwt. there are how many pounds? 8. Reduce of a pound to shillings. 9. How many glasses, each containing 3 gills, can be filled from of a gallon of water? WRITTEN EXERCISES. 1. Reduce of a gallon to quarts and pints. × 4=1211 qt. = Ans. 1 qt. 1 pt. 1 pt. ANALYSIS.-We reduce gallons to quarts by multiplying by 4. 8×4=12qt.=11qt. We then reduce the plying by 2. qt. to pints, by multi × 2=1 pint; and the entire result is 1 qt. 1 pt. 2. Reduce .375 of a gallon to quarts and pints. .375 4 11.500 2 1.000 Ans. 1 qt. 1 pt. ANALYSIS.-We multiply the gallons by 4, as in the preceding operation. .375X4 1.500 qt. We then reduce the .500 qt. to pints, by multiplying by 2. .500 × 2=1.000 pt.; and the entire result is 1 qt. 1 pt. RULE. Multiply the given fraction by the number required to reduce it to the next lower denomination. When the product is greater than a unit, change to a whole or mixed number, multiply the fractional part, if any, by the number required to reduce it to the next lower denomination, and proceed as before, until the reduction is completed. 3. Reduce of a ton to pounds and ounces. 4. What is the value of of a rod in yards, feet, and inches? 5. Reduce .8534 bu. to pecks, quarts, and pints. 6. Add of a day and 4 of an hour, and give the result in hours, minutes, and seconds. 7. From £.3805 subtract .3805 s., giving the result in shillings, pence, and farthings. 8. Three farms contain respectively 120g A., 160 A., and 185 A.; how many acres and square rods are there in all? 9. If I buy 12 cwt. of flour from one man, 16.25 cwt. from another, and 183 cwt. from a third, and then sell 19.75 cwt., how many cwt. and lb. do I have left? 10. Find the sum of 5 of a day, & of an hour, § of an hour, and of a minute. 11. From of an oz. of gold I sold of a pwt.; how much had I remaining? 12. Find the sum of 18.546°, 15.314°, and 1.09°, in degrees, minutes, and seconds. 13. Reduce 128 pints to the fraction of a bushel, add of a bushel to the result, and give the answer in bushels. 14. Reduce of a bushel to the fraction of a pint, add 128 pt., and change the result to bushels. CASE IV. To reduce one denominate number to the fractional part of another. = ORAL EXERCISES. 1. What fraction of an hour is 15 minutes? ANALYSIS.-In one hour there are 60 minutes, and 15 minutes = 15 or 4 of an hour. 2. What decimal of an hour is 15 minutes? = ANALYSIS-15 minutes of an hour. of an hour=.25 of an hour. 3. What fraction of a gallon is 3 quarts? What decimal of a gallon? 4. Reduce 50 cents to the decimal of a dollar. |