REDUCTION OF FRACTIONAL COMPOUND NUMBERS. CASE I. ART. 160. To reduce a fraction of a higher denominatim, to a fraction of a lower. 1. Reduce of a peck to the fraction of a pint. SOLUTION.-To reduce pecks to pints, we multiply by 8 to reduce them to quarts, then by 2 to reduce them to pints. In like manner, multiply the fraction pk. OPERATION. pt. qt. qt. X8=1; 1X2=}: or, of a peck by 8, to reduce it to the frac-x8x2= pt. Ans. tion of a quart, then by 2, to reduce it to the fraction of a pint. Hence, fractional numbers may be reduced from a higher to a lower denomination, (Art. 81), by multiplying by that number of the next lower order which makes a unit of the higher. *2. Reduce of a bu. to the fraction of a qt. Ans. . 0 Rule for Case I.-Multiply as in Reduction of Whole Numbers, Art. 81, according to the rules for the multiplication of fractions. REM. The work in Cases I and II may often be shortened by Cancellation. 3. Reduce lb. Av. to the fraction of an oz. Ans. 4. of a lb. Troy, to the fraction of an oz. Ans. 3. of a yd. to the fraction of a na. Ans. of an A. to the fraction of a P. Ans. . 7. 3 of a dollar to the fraction of a ct. Ans. . REVIEW.-160. How reduce pecks to pints? How the fraction of a peck to the fraction of a pint? How are fractional numbers reduced from a higher to a lower denomination? CASE II. ART. 161. To reduce a fraction of a lower denomination, to a fraction of a higher. 1. Reduce of a pint to the fraction of a peck. SOLUTION. To reduce pints to pecks, we first divide by 2 to reduce them pt. OPERATION. qt. qt. pk. to quarts, and then by 8 to reduce ÷÷2=1; 1÷8=24 them to pecks. In like manner, divide the fraction by 2, to reduce it to the fraction of a or, 4 pk. Ans, quart, and then by 8, to reduce it to the fraction of a peck. Hence, fractional numbers may be reduced from a lower to a higher denomination (Art. 81), by dividing the given fraction by that number of its own denomination which makes a unit of the next higher. *2. Reduce of a qt. to the fraction of a bu. Ans. '0• Rule for Case II.-Divide, as in Reduction of Whole Numbers, Art. 81, according to the rules for the division of fractions. 3. Reduce of a na. to the fraction of a yd. Ans. 4. of a gr. T. to the fraction of a lb. Ans. 600. Ans. 15. Ans. 30. Ans. 2800. 7. 4 of an oz. to the fraction of a cwt. 8. g of an in. to the fraction of an E. En. of a min. to the fraction of a da. 9. 10. of a dr. to the fraction of a qr. Ans. 7'5. Ans. 60. REVIEW.-160. What is Case 1? What is the rule for Case 1? 161. How reduce pints to pecks? How the fraction of a pint to the fraction of a peck? How are fractional numbers reduced from a lower to a higher denomination? What is Case 2? The Rule for Case 2? CASE III. ART. 162. To find the value of a fraction in integers (whole numbers) of a lower denomination. 1. Find the value of of a day in integers. SOLUTION.- of a da., are of 24 hr.; and of 24 hr. are found by multiplying by 2 and dividing by 5 (Art. 152). This gives 93 hr. Again, of an hour are the same as 3 of 60 minutes, which are 36 min. Hence, of a day=9hr. 36 min. OPERATION. 24 hr. 2 60 min. 3 5)180 93 hr. 36 min. 5)48 Ans. 9 hr. 36 min. *2. Value of of a mi. in integers. Ans. 6 fur. 16 rd. Rule for Case III.-Take the number of units of the next lower denomination which forms a unit of the denomination of the fraction; multiply it by the numerator, and divide the product by the denominator. If this division produce a fraction, find its value in the same manner, and so on: the several quotients will be the answer. 3. What is the value of of a dollar? 4. Of of a mile? 5. Of of a lb. Troy? 6. Of 4 of a lb. Av.? 7. Of of an acre? 8. Of of a T. of wine? Ans. 60 cts. Ans. 3fur. 8rd. . Ans. 9oz. 12 pwt. Ans. 9oz. 2 dr. Ans. 2 R. 20 P. . Ans. 3hhd. 31 gal. 2 qt. CASE IV. ART. 163. To reduce a quantity having one or more denominations, to the fraction of another quantity composed of one or more denominations. 1. Reduce 2 feet 3 inches to the fraction of a yard: that is, 2ft. 3 in. is what part of 1 yard? SOLUTION.-2 ft. 3 in. 27 inches: 1 yd.=36 inches; and since 1 inch is of 36 inches, 27 inches are 373. Ans. 3 yd. 36 2. Find what part 2ft. 6 in. is of 6ft. 8 in. SOLUTION.-Reducing both quantities to the same denomination, the first is 30, and the second 80 in. Since 1 in. is g of 80 in., 30 in. will be 30=3. OPERATION. 2 ft. 6 in.= = 6 ft. 8 in. 80 in. Ans. 38=3. *3. Reduce 2 pk. 4 qt. to the fraction of a bu. *4. What part is 2yd. 1qr. of 8 yd. 3 qr.? Rule for Case IV.-Reduce both quantities to the lowest denomination in either; the less will be the numerator, and the greater the denominator of the required fraction, which reduce to its lowest terms. 5. Reduce 13 hr. 30 min. to the frac. of a da. Ans. 1% 6. 3 fur. 25 rd. to the fraction of a mile. 7. 2 ft. 8in. to the fraction of a yard. 8. What part is 96 pages of 432 pages? 9. 15 mi. 3 fur. 3rd. of 35 mi. 7 fur. 7rd.? 10. A man has a farm of 168 A. 28 P.: if he sell 37 A. 2R. 14P., what part will he sell? Ans. 97 434 NOTE. If one or both quantities contain a fraction, reduce them to a common denominator, and compare their numerators. 11. What part is 7 oz. 17 dr. of 1 lb. Av.? 12. 13. 2qt. 13 pt. of 1 bu. 1 qt. 13 pt.? Ans.. ADDITION AND SUBTRACTION OF FRACTIONAL COMPOUND NUMBERS. ART. 164. 1. Add 3 of a yard, to 1⁄2 of a foot. SOLUTION. Find the value of each of the quantities in integers (Art. 162), and then obtain their sum by the rule for addition in Art. 101. If their difference be required, subtract according to the Rule in Art. 102. 5423 OPERATION. in. Rule for Addition or Subtraction.-First, find the value of each fraction in integers (Art. 162): Then add or subtract, as may be required, according to the rules for the addition and subtraction of compound numbers. NOTE. If fractions occur in the lowest denomination, add or subtract by the rules for addition and subtraction of fractions. 18 7. of a da., less of an hr., equals what? Ans. 18 hr. 36 min. 40 sec. 1. Reduce 32989 to its lowest terms. . 2. Find the sum of 3 and; of of 2, 3, 4, and 8. 5 and; of 3 and 1}; Ans. to last, 619. and ?? and? Ans. to last, 211. two-fifths of what? How find What is the Rule? NOTE. If one or both quan REVIEW.-162. Two-fifths of a day, are two-fifths of 24 hours? What is Case 3? 163. What is Case 4? What the Rule? tities contain a fraction, how proceed? 164. What is the rule for the addition or subtraction of fractional compound numbers? |