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 25. A. 15o=214. 7. How many times is contained in? A. 1. 8. How many times is contained in ? A. 2134. 9. What number multiplied by 4 will make ? A. 21. T3 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 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 gru.? 13. What part of 1 s. is 1 d.? Is 2d.? 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. 30 2. What part of 1£ is 2s. 6d. ? A. 20=1. 3. What part of 1 cwt. is 3 qrs. 15 lbs. 14 oz.? A. 88. 4. What part of 1 yd. is 3 q3 na.? A. 1. 5. What part of 1 bu. is 3 pecks, 7 qts. 1 pt.? 6. What part of 1 tun is 1 gal. O qts. 2 pts. 1 gil.? 7. What part of 15 pipes is 25 gals.? A. gg. 8. What part of 2 m. is 7 fur. 11 in. 2 b. c.?A. 9. What part of 1 mo. is 19 days? A. 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. ¶ XLIX. A. $23. Z. 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. T6 ? an hour? ?? ' of 1 qr Operation by Slate illustrated. 1. What is the value of of a pound? I. 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. TL. To reduce Fractions of a higher Denomination into lower. We have seen (¶ XXXVIII.) that fractions are multiplied by multiplying their numerators, or dividing their denominators. 1. Reduce o £ to the fraction of a penny. OPERATION. Numer. 1 20 s. 20 New numer. 240 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 shilling, &c. But this operation may be expressed differently, thus; 480 × 20 × 12 = 4 4 8 = 1 d. ; or, by dividing the denominators thus; ÷ 2011÷ 12=d., Ans., as before, in 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 of a pound to the fraction of a shilling. A. 28. 3. Reduce 1920 of a pound to the fraction of a farthing. A. qr. 4. Reduce Tous of a hogshead to the fraction of a gallon. A. Te gal. 5. Reducer of a bushel to the fraction of a quart. A. fff gt. 6. Reduce of a day to the fraction of a minute. A. tttf m. 7. Reduce Toog of a cwt. to the fraction of a pound. 8. Reduce of a hhd. to the fraction of a pint. A. lb. A. pt. 9. Reduce Tʊ of a pound to the fraction of a shilling. A. 8. TLI. To reduce Fractions of a lower Denomination into a higher. We have seen, that, to divide a fraction, (¶ XL.) we must multiply the denominator, or divide the numerator. This rule is the reverse of the last, (¶ L.), and proves it. 1. Reduce of a penny to the fraction of a pound. OPERATION. 12 24 20 New denom. 480 Then, o, Ans. In this example, we divide as in Reduction, (¶ XXÍX), viz. pence by pence, shillings by shillings; but, in order for this, we must either multiply the denominator or divide the numerator by the same numbers that we should di vide by in Reduction of whole numbers. The same result will be obtained d. if performed thus: Tģo £, Ans. Hence the following RULE. 8. × 12 × 20 1. How do you proceed? A. Divide as in Reduction of whole numbers. More Exercises for the Slate. 2. Reduce of a shilling to the fraction of a pound. A. złō £. 3. Reduce of a farthing to the fraction of a pound. A. 1920 £. 4. Reduce of a gallon to the fraction of a hogshead. A. Toog hhd. 5. Reduce ff of a quart to the fraction of a bushel. A. 1 bu. 171 6. Reduce 144 of a minute to the fraction of a day. A. TITT. 7. Reduce of a pound to the fraction of a cwt. A. TO08. 8. Reduce of a pint to the fraction of a hhd. A. 2520=630. 9. Reduce } of a shilling to the fraction of a pound. |