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? 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. of a cwt.? A. 3 qrs. of an acre? A. 1 rood, 134 rds. of a pound Troy? A. 10 oz. 8 5. What is the value of 24 of a hogshead? A. 49 gallons 12 qts. 6. What is the value of † of a pound avoirdupois? A. 1lb. 1437 oz. 7. What is the value of 8. What is the value of 551 sec. 80 of a hogshead? A. 50 gallons. of a day? A. 16 hours, 36 miɛ 1 L. TO REDUCE FRACTIONS OF A HIGHER DENOMINA. TION INTO A LOWER. We have seen (T XXXVIII.) that fraccions are multiplied by multiplying their numerators, or dividing their denominators. 1. Reduce £. to the fraction of a penny. OPERATION. In this example, we multi ply the 1, in 40, as in Reduction of whole numbers, viz., pounds by what makes a pound, shillings by what inakes a shilling, &c. But this operation may be expressed differently, thus; 20 × 12-18=d.; or, by dividing the denominators, thus; Denom. 480 RULE. 20-A÷12— d., Ans., as before, in its lowest terms. Q. How, then, would you proceed?” A. Multiply the fraction, as in Reduction of whole numbers. More Exercises for the Slate. 2 Reduce 26 of a pound to the fraction of a shilling. A. S. 4 3 Reduce 1920 of a pound to the fraction of a farthing. A. qr. 4. Reduce Toog of a hogshead to the fraction of a gallon A. 1 gal. 5. Reduce TT of a bushel to the fraction of a quart. 160 A. 191 qt. 6. Reduce 144 of a day to the fraction of a minute. 7. Reduce 10% of a cwt. to the fraction of a pound. 8. Reduce 2 9. Reduce A. lb. of a hhd. to the fraction of a pint. A. pt. ʊ of a pound to the fraction of a shilling. shilling, ✈ s ILI. TO REDUCE FRACTIONS OF A LOWER DENOMINA◄ TION 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. Q. How do you proceed? RULE. A. Divide as in Reduction of whole numbers. 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. A. TIZO L. 4. Reduce of a gallon to the fraction of a hogshead. A. TOOg hhd. 5. Reduce of a quart to the fraction of a bushel. A. 1 bu. 6. Reduce 14 of a minute to the fraction of a day. A. TIT 7. Reduce of a pound to the fraction of a hundred weight. 8. Reduce of a pint to the fraction of a hogshead. A. 2820=630. 9. Reduce of a shilling to the fraction of a pound. A. To. DECIMAL FRACTIONS. LII. Q. When such fractions as these occur, viz., TOO, 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, fo, foo, too, 525 1000 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, 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? I 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, &c. ? A. The second is hundredths the third thou sandths, the fourth ten thousandths, and so on, as in the numeration of whole numbers. Let me see you write down again in the form of a decimal. Q. As the first figure at the right of the separatrix is tenths, in writing down To, then, where must a cipher be placed? Let me see you write down in the form of a decimal • Write down Toʊ, TổO, T8O. Q. How would you write down in decimals Too? A. By placing 2 ciphers at the right of the separatrix, that is, before the 7. Let me see you write it down. A. ,007. Let me see you write down TOO. Q. Why do you write 2 down with 2 ciphers before it? A. Because in T, the 2 is thousandths; consequently, the 2 must be thousandths when written down in decimals. Q. Now, as , and as multiplying 15 by 10 produces o, which is also equal to, how much less in valuc is,05 than,5? A. Ten times. Q. Why? A. Because the parts in are ten times smaller than in ; and, as the numerator is the same in both expressions, consequently, the value is lessened 10 times. 1 Q. How, then, do decimal figures decrease in value from the le towards the right? A. In a tenfold proportion. Q. What does ,50 mean? A. 5 tenths, and no hundredths. Q. What, then, is the value of a cipher at the right of decimals? |