5. Divide 14 by fi: A. 33. REDUCTION OF FRACTIONS. It will be recollected, that in Reduction (9 XXIX.) whole numbers were brought from higher to lower denominations by multiplication, and from lower to higher denominations by division; hence, fractions of one denomination may be reduced to another after the same manner, and by the same rules. 1 XLVIII. TO REDUCE WHOLE NUMBERS TO THE FRACTION OF A GREATER DENOMINATION. 1. What part of 2 miles is 1 mile? 2. What part of 4 miles is 1 mile? Is 2 miles ? Is 3 miles? 3. What part of 1 yd. is 1 qr.? Is 2 qrs.? Is 3 qrs.? 4. What part of 8 gallons is 1 gallon? Is 3 gallons ? 5. What part of 9 oz. is 1 oz.? Is 2 oz.? Is 5 oz. ? 6. What part of 7 yds. is 1 yd.? Is 6 yds.? Is 7 yds. ? 7. What part of $21 is $17? Is $11? Is $13 ? 8. What part of 271 inches is 11 in.? Is 251 in. ? 9. What part of 1 month is 1 day? Is 2 days? 10. What part of 1 hour is 11 minutes ? Is 21 minutes ? 11. What part of 19 cents is 11 cents ? Is 3 cents ? 12. What part of 1 d. is 1 farthing? Is 2 qrs.? Is 3 qrs.? 13. What part of 1 s. is 1 d.? Is 2 d.? Is 3 d.? 1. What part of a bushel is 3 pks. 4 qts.? 1 bu.= 32 qts., and 3 pks. 4 qts.=28 qts. 4 Then, as 32 qts. make 1 bushel, 1 qt. is 32 24 of a bushel, and 28 qts. 8 4 28 times =) 32 Denom. 28 Numer. Abu: Ans., the same as before. Then =, Ans. mark From these illustrations we derive the following RULE. A. Bring the given denominations to the lowest denomination mentioned, for a numerator. Q. How do you obtain the denominator ? A. Bring 1 (or an integer) of that higher denomination into the same denomination, for a denominator. More Exercises for the Slate. 2. What part of 1 £. is 2 s. Cd. A. =$ 3. What part of 1 hundred weight is 3 qrs. 15 lbs. 14 oz.? 4. What part of 1 yard is 3 qrs. 3 na. ? A. 16 5. What part of 1 bushel is 3 pecks, 7 qts. 1 pt. ? A. 6. What part of 1 tun is 1 gallon, 0 qts. 2 pts. I gill? 4. gr. 17. What part of 15 pipes is 25 galls.? A. 38 8. What part of 2 miles is 7 fur. 11 in. 2 b. c.? A. 483370 9. What part of 1 month is 19 days? A. 18. 10. What part of 1 month is 25 days, 13 hours ? A. 413. 11. What part of 1 month is 22 days, 15 h. 1 min.? A. 1387. T XLIX. TO REDUCE A FRACTION TO WHOLE NUM BERS OF LESS DENOMINATIONS, or, TO FIND THE 1. How much is 1 of a shilling? How much I of a lb. ? Po of a lb.? 16 of a lb.? H of a lb.? 19 of a lb.? as of 1 qr. of a cwt.? ? ? 15? ? an hour ? ? ? Operation by Slate illustrated. 20 s. OPERATION. Q. How do you proNumer. 5 ceed in this example ? A. As 1 £. of one pound iš the 6 same as of 20 s., and, to get & of 20, we mul40 tiply the numerator 5 36 and 20 together, mak ing 100; which, divid16 s. 8 d. Ans. 4 ed by the denominator 12 6, gives 16 s. and of another shilling re6) 48 (8 d. maining. This =* 48 of 12 d.; then, of 12 d.=8 d. RULE. A. By as many of the next denomination as make one of that; that is, pounds by what makes a pound, ounces by what makes an ounce, as in Reduction of whole numbers. Q. What do you divide the product by ? More Exercises for the Slate. 2. What is the value of of a cwt. ? A. 3 qrs. 3. What is the value of j of an acre ? A. 1 rood, 134 rds. 4. What is the value of 2% of a pound Troy? A. 10 oz. 8 pwts. 1619. 5. What is the value of 213 of a hogshead ? A. 49 gallons 12973 qts. 6. What is the value of 37 i of a pound avoirdupois ? A. 1 lb. 14971 oz. 7. What is the value of 530 of a hogshead? A. 50 gallons. 8. What is the value of 13 of a day? A. 16 hours, 36 min. 553 sec. I L. TO REDUCE FRACTIONS OF A HIGHER DENOMINA TION INTO A LOWER. We have seen (1 XXXVIII.) that fractions are multiplied by multiplying their numerators, or dividing their denominators. 1. Reduce 450 £. to the fraction of a penny. In this example, we multi OPERATION. ply the 1, in do, as in ReNumer. 1 duction of whole numbers, 20 s. viz., pounds by what makes á pound, shillings by what 20 makes a shilling, &c. But 12 d. this operation may be express ed differently, thus ; 450 X New numer. 240 20 X 12=4=fd; or, by dividing the denominators, Then, 240 thus; Ito-20=212 =fd. Ans. Denom. 480 d., Ans., as before, in its lowest terms. RULE. Q. How, then, would you proceed ? A. Multiply the fraction, as in Reduction of whole numbers.' More Exercises for the Slate. 2. Reduce to of a pound to the fraction of a shilling. A. s. 3. Reduce 1927 of a pound to the fraction of a farthing. A. gr. 4. Reduce Tody of a hogshead to the fraction of a gallon. A. Te gal. 6. Reduce Th of a bushel to the fraction of a quart. A. 141 qt. 6. Reduce 144T of a day to the fraction of a minute. A. 144 m. 7. Reduce to y of a cwt. to the fraction of a pound. A. 1b. 8. Reduce zoo of a hhd. to the fraction of a pint. A. $ pt. 9. Reduce Igo of a pound to the fraction of a shilling. Ă. Ja FLI. TO REDUCE FRACTIONS OF A LOWER DENOMINA TION INTO A HIGIER. We have seen, that, to divide a fraction, (TT XL.) we must multiply the denominator, or divide the numerator. This rule is the reverse of the last, (1 L.) and proves it. duction, (1 XXIX.) viz., pence by pence, shillings by 'shillings; but, in 12 order for this, we must either multiply the denominator or divide the numera24 tor by the same numbers that we should 20 divide by in Reduction of whole num bers. The same result will be obtainNew denom. 480 ed if performed thus : d. Then, to, Ans. 3 x 12 x 20=45o £., Ans. Hence the following RULE. Q. How do A. Divide as in Reduction of whole numbers. you procitor? More Exercises for the Slate. 2. Reduce I of a shilling to the fraction of a pound. A. ato £. 3. Reduce 1 of a farthing to the fraction of a pound. A. 1927 £. 4. Reduce It of a gallon to the fraction of a hogshead. A. Toto hhd. 5. Reduce 14 i of a quart to the fraction of a bushel. A. I bu. 6. Reduce 1441 of a minute to the fraction of a day. A. 1441 7. Reduce of a pound to the fraction of a hundred weight. A. Toor: 8. Reduce of a pint to the fraction of a hogshead. A. 2520=630 9. Reduce of a shilling to the fraction of a pound, A. . |