8. How many times is contained in ? A. 21. 9. What number multiplied by will make? A. 2. REDUCTION OF FRACTIONS. It will be recollected, that in Reduction (¶ 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. 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? Is2 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? 11. What part of 19 cents is 11 cents? 12. What part of 1 d. is 1 farthing? Is 13. What part of 1 s. is 1 d.? Is 2 d.? 1. What part of a bushel is 3. pks. 4 qts.? 2 Is 21 minutes? 1 ba.: = 32 qts., and 3 pks. 4 qts.28 qts. Then, as 32 qts. make 1 bushel, 1 qt. is a of a bushel, and 25 qis. 28 times 24 4 28 Numer. as before. = bu. Ans., the same Then, Ans. From these illustrations we derive the following RULE. Q. How do you obtain the numerator? 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 de nomination into the same denomination, for a denominator. More Exercises for the Slate. 2. What part of 1 £. is 2 s. 6 d. A. 201 A. 188. 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.? 6. What part of 1 tun is 1 gallon, 0 qts. 2 pts. A. 18. pt.? 7 What part of 15 pipes is 25 galls.? 9. What part of 1 month is 19 days? A. 82. 1 gill? A. 8861. A. 378: 11. What part of 1 month is 22 days, 15 h. 1 min.? 1 XLIX. TO REDUCE A FRACTION TO WHOLE NUM BERS OF LESS DENOMINATIONS, OR, TO FIND THE Operation by Slate illustrated. What is the value of of a pound? Q. What do you multiply the numerator by? A. By as many of the next denomination as make one of that; that is, pounds by what makes pound, ounces by what makes an ounce, as in Reduction of whole numbers. Q. What do you divide the product by? Q. If there be a remainder, how do you proceed! A. Multiply and divide as before. More Exercises for the Slate. 2. What is the value of 3. What is the value of 4. What is the value of pwts. 1612. of a cwt.? A. 3 qrs. of an acre? A. 1'rood, 13} rds. 5. What is the value of 24 of a hogshead? A. 49 gallons 125 qts. 6. What is the value of H of a pound avoirdupois? A. 1 D. 14379 oz. 1L. TO REDUCE FRACTIONS OF A HIGHER DENOMINA TION INTO A LOWER. We have seen (¶ XXXVIII.) that fractions are multiplied by multiplying their numerators, or dividing their denominators. 1. Reduce £. to the fraction of a penny. OPERATION. Numer. 1 20 s. 20 12 d. New numer. 240 Then, 24 0 Denom. 480 In this example, we multiply the 1, in 0, as in Re duction of whole numbers viz., pounds by what makes pound, shillings by what makes a shilling, &c. But this operation may be express. ed differently, thus ; 0X 20 x 12-18=d.; or, by dividing the denominators, =d. Ans. thus; 80÷20=4÷12¬ d., Ins., as before, in its lowest terms. RULE. QHow, then, would you proceed? A. Multiply the fraction, as in Reduction of whole numbers. More Exercises for the Slate. Reduce to of a pound to the fraction of a shilling. % Reduce 1920 of a pound to the fraction of a farthing. A. જે વ 4. Reduce Toby of a hogshead to the fraction of a gallon. A. To gal 5. Reduce TT of a bushel to the fraction of a quart. Reduce TT of a day to the fraction of a minute. A. tttfm 1. Reduce Too of a cwt. to the fraction of a pound. A. b. Reduce go of a hhd. to the fraction of a pint. A. † pl LI. TO REDUCE FRACTIONS OF A LOWER DENOMINA TION INTO A HIGHER. . We have seen, that, to divide a fraction, (T XL.) we must multiply the denominator, or divide the numerator. This rule is the reverse of the last, (T L.) and proves it. 1. Reduce of a penny to the fraction of a pound. More Exercises for the Slate. Reduce of a shilling to the fraction of a pound. Reduce of a farthing to the fraction of a pound. A. TIZO £ 4 Reduce of a gallon to the fraction of a hogshead. A. Toog hhd. Reduce 19 of a quart to the fraction of a bushel. 6. Reduce of a minute to the fraction of a day. 7. Reduce of a pound to the fraction of a hundred weight A. TOOD. 8. Reduce of a pint to the fraction of a hogshead. Reduce of a shilling to the fraction of a pound. |