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 denomi nation 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. &. 4. What part of 1 yd. is 3 qrs. 3 na.? A.†g. A. ta 8064 5. What part of 1 bu. is 3 pocks, 7 qts. 1 pt.? A. §. 6. What part of 1 tun is 1 gal. 0 qts. 2 pts. 1 gil.? 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.? A. 9. What part of 1 mo. is 19 days? A. 18. 10. What part of 1 mo. is 25 days, 13 hours? 11. What part of 1 mo. is 22 days, 15 h. 1 min. $13. ↑ 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 b 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 of a cwt.? A. 3 qrs. 3. What is the value of of an acre?,A. Í rood, 13} rds 4. What is the value of 3 pwts. 161§. 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 pound Troy? A. 10 oz. 8 TL. To reduce Fractions of a higher Denomination into lower. We have seen (T 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 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; 0 × 20 × 12=4 4 8 = 1d.; or, by dividing the denominators thus;÷20=24÷ d., Ans., as before, in its lowest terms. 12 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. 3. Reduce To of a pound to the fraction of a farthing. A. qr. 4. Reduce Tobs of a hogshead to the fraction of a gallon. A. gal. 5. Reduce of a bushel to the fraction of a quart. Ꭿ. ᏐᏐ { qt. 6. Reduce TT of day to the fraction of a minute. A. 111 m. 7. Reduce Tog of a cwt. to the fraction of a pound. Reduce of a hhd. to the fraction of a pint. A. lb. A. pt. A. s. 9. Reduce 1 of a pound to the fraction of a shilling. 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. 1. How do you proceed? A. Divide as in Reduction of whole numbers. More Exercises for the Slate. 2. Reduce 2 of a shilling to the fraction of a pound. A. to £. 3. Reduce of a farthing to the fraction of a pound. 4. Reduce of a gallon to the fraction of a hogshead. A. Toos hhd. 5. Reduce of a quart to the fraction of a bushel. A. TT bu 6. Reduce of a minute to the fraction of a day. A. TET 7. Reduce of a pound to the fraction of a cwt. A. TOOB 8. Reduce of a pint to the fraction of a hhd. 1. 2520=630. 9 Reduce of a shilling to the fraction of a pound. 250 DECIMAL FRACTIONS. ¶ LII. Q. When such fractions as these occur, viz. To, TOO, 1000, how is a unit supposed to be divided? A. Into 10 equal parts, called tenths; and each tenth into 10 other equal parts, called hundredths; and each hundredth into 10 more equal parts, called thousandths, &c. Q. How is it customary to write such expressions? A. By taking away the denominator, and placing a comma before the numerator. 25 65 Let me see you write down, in this manner, 10, 100, 100, 525 1000 Q. What name do you give to fractions written in this man ner? A. Decimal Fractions. Q. Why called decimal? A. From the Latin word decem, signifying ten; because they increase and decrease in a ten fold proportion, like whole numbers. Q. What are all other fractions called? A. Vulgar, or com mon fractions. Q. In whole numbers, we are accustomed to call the right hand figure, units, from which we begin to reckon, or numerate; hence it was found convenient to make the same place a starting point in decimals; and, to do this, we make use of a comma; what, then, is the use of this comma? A. It merely shows where the units' place is. Q. What are the figures on the left of the comma called? A. Whole numbers. Q. What are the figures on the right of the comma called? A. Decimals. Q. What, then, may the comma properly be called? A. Separatrix. Q. Why? A. Because it separates the decimals from the whole numbers. Q. What is the first figure at the right of the separatrix called? A. 10ths. Q. What is the second, third, fourth, &c.? A. The second is hundredths, the third thousandths, the fourth ten thousandths, and so on, as in the numeration of whole numbers. Let me see you write down again fo in the form of a deci mal. Q. As the first figure at the right of the separatrix is tenths, in writing down To, then, where must a cipher be placed? A. In the tenths' place. Let me see you write down in the form of a decimal T 7.05. |