14 How many sq. rods in 1210 sq. yards? A. 40 sq. roda. 15. How many barrels in 1260 gallons? A. 40 barrels. ↑ XLVII. To divide one Fraction by another. 1. At of a cent an apple, how many apples may be bought for of a cent? How many times in? How many times in ? 2. William gave of a dollar for one orange; how many oranges, at that rate, can he buy for § of a dollar How many for of a dollar? For 2? For 2? For 27? For ? Hence we see that fractions, having a common denominator, may be divided by dividing their numerators, as well as subtracted and added, and for the same reason. 1. At of a dollar a yard, how many yards of cloth may be bought for of a dollar? In this example, as the common denominator is not used, it is plain that we need not find it, but only multi ply the numerators by the same numbers as before. This will be found to consist in multiplying the nu merator of the divisor into the denominator of the dividend, and the denominator of the divisor into the numerator of the dividend. But it will be found to be more convenient, in practice, to invert the divisor, then multiply the upper terms together for a numerator, and the lower terms for a denominator; thus, taking the last example; PROOF., the quotient, mul tiplied by the divisor, thus, the divisor. , gives From these illustrations we derive the following RULE. 1. How do you proceed to divide one A. I invert the divisor, then multiply the for a new numerator, and the lower for a action by another per terms togethe ww denominator Note. Mixed numbers must be reduced to improper frac tions, and compound to simple terms. PROOF. It would be well for the pupil to prove cach result as in Simple Multiplication, by multiplying the divisor and quotient together, to obtain the dividend. More Exercises for the Slate. 2. At of a dollar a peck, how many pecks of salt may be bought for of a dollar? A. 4 pecks. 3. Divide by 4. A. 14=2 4. Divide by15. A. 14o=214. 5. Divide 1 by fr. A. 3%. 6. Divide 9 by of. A. 37. 7. How many times is 8. How many times is contained in ? A. 12. 9. What number multiplied by will make ? 9. 2154. ? A. 21. 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? 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? 2 qrs.? Is 3 qra ? 13. What part of 1s is 1d.? Is 2 d.? Is 3d. ? Is 1. What part of a bushel is 3 pks. 4 qts.? I. How do you obtain the numerator? A. Bring the given denominations to the lowest denomination mentioned for a numerator. II. 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 2s. 6d.? A. 2%=1. 24 3. What part of 1 cwt. is 3 qrs. 15 lbs. 14 oz.? A. JIE. 4. What part of 1 yd. is 3 qrs. 3 na.? A. 18. 5. What part of 1 bu. is 3 pecks, 7 qts. 1 pt.? A. . 6. What part of 1 tun is 1 gal. 0 qts. 2 pts. 1 gil.? A. zôtī 7. What part of 15 pipes is 25 gals.? A. 398. 8. What part of 2 m. is 7 fur. 11 in. 2 b. c.? 9. What part of 1 mo. is 19 days? A. 18. 10. What part of 1 mo. is 25 days, 13 hours? $13. 11. What part of 1 mo. is 22 days, 15 h. 1 min. .9. 1358) 1 XLIX. To reduce a Fraction to Whole Numbers of less Denominations, OR, To find the Value of a Fraction. 1. How much is of a shilling? How much of a lh of a lb.? of a lb. ? of a cwt.??? 18? of a lb.? 1 of a lb.? of 1 qr 27? 1 an hour??? Operation by Slate illustrated. 1 What is the value of of a pound RULE. 1. 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 a pound, ounces by what makes an ounce, as in reduction of whole numbers. II. What do you divide the product by? A. By the denomi nator. III. 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 plots. 1619. 5. What is the value of qts. 6. What is the value of 14378 oz. of a cwt.? A. 3 qrs. of an acre? A. rood, 13 rds of a hhd.? A. 49 gallons 1 of a pound avoirdupois? A. 1lb. 7. What is the value of 898 of a hogshead? A. 50 gallons 8. What is the value of of a day? A. 16 h. 36 m. 55 sec. ¶ L. To reduce Fractions of a higher Denomlilation into 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 In this example, we multiply the 1, in as in Reduction of whole numbers, viz., pounds by what makes a pound, shillings by what makes a shiling, &c. But this operation may be expressed differently, thus, 40 × 20 × 12=448 = 1 d.; or, by dividing the denominators thus; o÷20=24÷ =jd. Anś., | 12=d., Ans., us before, in New numer. 240 Then, 240 Denom. 480 its lowest terms. RULE. 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. 12 3. Reduce 1920 of a pound to the fraction of a farthing. A. qr. 4. Reduce Toos of a hogshead to the fraction of a gallon. A. gal. 5. Reduce of a bushel to the fraction of a quart. A. f f f qt. 6. Reduce of a day to the fraction of a minute. 7. Reduce Too of a cwt. to the fraction of a pound. 8 Reduce 2520 of a hhd. to the fraction of a pint. A. lb 4. tpt 9. Reduce To of a pound to the fraction of a shilling. |