From these illustrations we derive the following RULE. Q. How do you obtain the numerator? A. Bring the given denominations to the lowes! denomination mentioned, for a numerator. Q. How do you obtain the denominator? A. Bring 1 (or an integer) of that higher denomination into the same denomination, for a denominator. 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. 1 gill 7. What part of 15 pipes is 25 galls.? 9. What part of 1 month is 19 days? 10. What part of 1 month is 25 days, 13 hours? A. 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 VALUE OF A FRACTION. 1. How much is of a shilling? How much of a lb. › Operation by Slate illustrated. 1 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 a 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? More Exercises for the Slate. 2. What is the value of 3. What is the value of 4. What is the value of pwts. 1619. of a cwt.? A. 3 qrs. of an acre? A. 1 rood, 133 rds. of a pound Troy? A. 10 oz. 8 5. What is the value of 24 of a hogshead? A. 49 gallon 1972 qts. 6. What is the value of of a pound avoirdupois? A. 1lb 14378 oz. 7. What is the value of 8. What is the value of 551's sec. 8 of a hogshead? A. 50 gallons. of a day? A. 16 hours, 36 min 1 L. 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. In this example, we multi ply the 1, in 0, as in Re duction of whole numbers viz., pounds by what makes a pound, shillings by what makes a shilling, &c. But this operation may be express ed differently, thus; 70× 20 × 12-18=d.; or, by dividing the denominators, thus; 80÷20=24÷12= d., Ans., as before, in its lowest terms. RULE. Q. How, then, would you proceed? A. Multiply the fraction, as in Reduction of whole numbers. More Exercises for the Slate. 2. Reduce o of a pound to the fraction of a shilling. A. T 3. Reduce 1920 of a pound to the fraction of a farthing. A. qi 4. Reduce Tobs of a hogshead to the fraction of a gallon. A. 16 gai 5. Reduce TT of a bushel to the fraction of a quart. 6. Reduce TT of a day to the fraction of a minute. 7. Reduce Tog of a cwt. to the fraction of a pound. 8. Reduce 9. Reduce 1 o of a hhd. to the fraction of a pint. A. pt. of a pound to the fraction of a shilling: ¶ LI. TO REDUCE FRACTIONS OF A LOWER DEN @MKD TION INTO A HIGHER. We have seen, that, to divide a fraction T XL, we und multiply the denominator, or divide the xumentoz. This rule is the reverse of the last, T Ly and proves it. 1. Reduce of a penny to the fraction of a pound. More Exercises for the Slate. 2. Reduce of a shilling to the fraction of a pound. 3. Reduce of a farthing to the fraction of a pound. 4. Reduce of a gallon to the fraction of a hogshead. 4. Toos hhd. 5. Reduce of a quart to the fraction of a bushel. A. TЯT bu. 6. Reduce of a minute to the fraction of a day. A. TIIT· 7. Reduce of a pound to the fraction of a hundred weight. A. TOOF. 8. Reduce of a pint to the fraction of a hogshead. A. 2620=810. 9. Reduce of a shilling to the fraction of a pound. A. T DECIMAL FRACTIONS. ¶ LII. Q. When such fractions as these occur, viz. O, 187, 1000, how is a unit supposed to be divided? 250 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. 65 Let me see you write down, in this manner, o,, 100. Q. What name do you give to fractions written in this manner? A. Decimal Fractions. Q. Why called decimal? A. From the Latin word decem, signifying ten; because they increase and decrease in a tenfold proportion, like whole numbers. Q. What are all other fractions called? A. Vulgar, or Common Fractions. Q. In whole numbers, we are accustomed to call the right-hand figure, units, from which we begin to reckon o sumerate; hence it was found convenient to make the same piace 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? 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? Q. What is the second, third, fourth, &e. 1 A. The second is hundredths, the third thou |