In the foregoing example, the 6 was first brought into 4ths, or quarters, by multiplying it by the denominator of the divisor, thereby reducing it to parts of equal size with the divisor; hence we derive the following RULE. I How do you proceed to divide a whole number by a fraction? A. Multiply the dividend by the denominator of the dividing fraction, and divide the product by the numerator. 2. At Exercises for the Slate. of a dollar a bushel, how many bushels of rye can I have for 80 dollars? OPERATION. 80 dividend. 480 Numer. 5) 1280 Quotient, 256 bushels, Ans. 3. If a family consume of a quarter of flour in one week, how many weeks will 48 quarters last the same family? A. 128 weeks. 4. If you borrow of your neighbour of a bushel of meal at one time, how many times would it take you to borrow 96 pushels? A. 960 times. 5. How many yards of cloth, at of a dollar a yard, may be bought for 200 dollars? A. 1000 yards. 6. How many times is 36 contained in 720? A. 140. 7. How many times is 83 contained in 300 improper fraction. A. 36. 8. Divide 620 by 81 9. Divide 84 by 128. 10. Divide 92 by 42. A. 757. A. 160. A. 20§. Reduce 8§ to un 11. Divide 100 by 22 Ꭿ. 364. A. 5127. 12. Divide 86 by 157. 13. How many rods in 220 yards? A. 40 rods. 14. How many sq. rods in 1210 sq. yards? A. 40 sq. rods. 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? 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? OPERATION. Reducing the fractions and to a common denominator, thus :— In this example, as the common denominator is not used, it is plain that we need not find it, but only multiply the numerators by the same numbers as before. This will be found to consist in multiplying the numerator of the divisor into the denominator of the dividend, and the denominato" 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; Then is contained in as many times as 4 is contained in 9,= 24. A. 21 yards. 1. How do you proceed to divide one fraction by another? A. I invert the divisor, then multiply the upper terms togethe: for a new numerator, and the lower for a new denominator. Note. Mixed numbers must be reduced to improper fractions, and compound to simple terms. PROOF. It would be well for the pupil to prove each 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 14. A. 14=2 4. Divide by 215. A. 14o=214. 5. Divide 1 by f1. A. 3. 6. Divide 94 by ≥ of §. A. 37. 7. How many times is contained in ? A. 12. 8. How many times is contained in? A. 215. 9. What number multiplied by will make? A. 218. 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? Is 2 qrs.? Is 3 qrs.? 13. What part of 1 s. is 1 d.? Is 2 d.? Is 3d.? 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. 24%. 3. What part of 1 cwt. is 3 qrs. 15 lbs. 14 oz.? A. ZIE. 4. What part of 1 yd. is 3 qrs. 3 na.? A. 1. 5. What part of 1 bu. is 3 pecks, 7 qts. 1 pt.? A. 6. 6. What part of 1 tun is 1 gal. 0 qts. 2 pts. 1 gil.? A. 864 7. What part of 15 pipes is 25 gals.? A. 343. 8. What part of 2 m. is 7 fur. 11 in. 2 b. c.? A. 883 2 9. What part of 1 mo. is 19 days? A. 18. $13. 10. What part of 1 mo. is 25 days, 13 hours? 11. What part of 1 mo. is 22 days, 15 h. 1 min. A. 12581 ↑ 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 lb fe of a lb.? of a lb. ? of a lb.? 1 of a lb.? z's of 1qr of a cwt.??? 18? 37? 1 an hour?? ? Operation by Slate illustrated. 1. What is the value of of a pound? 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 pwts. 1618. 5. What is the value of qts. 6. What is the value of 1437 oz. 7. What is the value of 8. What is the value of of a cwt.? A. 3 qrs. of an acre? A. Í rood, 133} rds of a hhd.? A. 49 gallons 1 of a pound avoirdupois? A. 1lb. 88 of a hogshead? A. 50 gallons. of a day? A. 16 h. 36 m. 553 sec |