In the same way we will now find the answer to the following QUESTIONS FOR EXERCISE. 1. Reduce .876 to an equivalent denominate number. 2. What is the denominate value of .9684 of a lb. Troy? 3. Give the value of .865 of a ton in its proper denominations? 4. What denominate number is equal to .16804 of a cwt.? 5. Reduce .8965 of a . to its proper denominations. 6. What is the denominate value of .864 of a bushel? .00964 of a bushel? 7. Give the denominate value of .9 of a tun of wine; .0086 of a tierce; .0009 of a hhd. 8. Reduce .05 of a circle to an equivalent denominate number. 9. What is the denominate value of .008 of a square mile? 10. What denominate number equals .8 of a cubic yard? .05 of a cord? 11. Reduce .8 of a yard to an equivalent denominate number; also, .9 of an ell E. 12. Reduce .0864 of a revolution to an equivalent denominate number. 13. What is the denominate value .073 of a year? of .005 of a lunar month? NOTE.-Vulgar fractions of any particular denomination, are reduced to an equivalent denominate number in the same manner as decimals, i. e., by multiplying the numerator, and dividing by the denominator, according to the following RULE. MULTIPLY the numerator of the FRACTION by the quantity required of the next lower denomination, to make a unit in ITS (the FRACTION'S) OWN denomination, and divide the product by the denominator, the QUOTIENT (if any,) will be the ANSWER for the NEXT lower denomination, and if a fraction yet remains, proceed as before till no fraction remains, or till you have arrived at the lowest denomination, the several QUOTIENTS, taken in order, will give the ANSWER sought. 168 EXAMPLES. 1. Reduce of a pound sterling to a proper denominate number. Here the numerator (Thus : is regarded as 9£., to be divided by 168, and hence, the process is the same as division of denominate numbers, (Example 2, page 164,) and gives 1s. 1d. 11⁄2fars. for ANSWER. £ 2. What denominate number is equivalent to of a pound Troy? Here the numerator is re- Thus : garded as 1lb. to be divided by 63, (the denominator.) Now, 1lb. 12ozs., which contain 63, 0 time; hence, we have Ooz. ; but 12ozs.= 240dwts., which contain 63, 3 times, giving 3dwts, and 51 remainder, which (51) we reduce to grs., making 1224 grains, which contain 63, 19 times, and 27 over, giving 193 193 grains. Hence, lb. 3dwts. 194 grains. ANSWER. = = The preceding EXAMPLES are believed to be sufficient to show the learner how a vulgar fraction of a higher denomination may be reduced to an equivalent denominate number. On the same principle we may find the ANSWER to the following 1. Reduce QUESTIONS FOR EXERCISE. of an Eagle to an equivalent denominate number containing dollars, dimes, cents, and mills. 2. Reduce of a pound sterling, to an equivalent denominate number. 3. What denominate number equals 1 of a pound Troy? 4. Give the equivalent denominate number of 5. Find the denominate value of 1 of a . of a ton. 6. Reduce 33 of a bushel to a proper denominate number. 7. Give the value of of a tun of wine in the lower denominations of wine measure. 8. What is the denominate value of of a circle? 9. Reduce of a square mile to its proper denominations. 10. What denominate number can you foot of square timber? from of a cord? 11. Reduce to a denominate number an ell E.; of a yard; of an ell Fl.; burg. form from & of a of a cubic yard? 3 16 of an Aune; of of an ell Ham 12. What is the denominate value of of a revolution. 13. Reduce 49 T73 of a year to an equivalent denominate number. 14. What is the value of of a bundle of paper, when reduced to its proper denominations? ARTICLE XVII. PROFIT AND LOSS. 1. PROFIT signifies what is RECEIVED, whether for labor, the use of money or advantage in trade. PROFIT 2. Loss signifies what is given without an equivalent, and may be sustained on labor, money, or merchandize. and Loss are generally reckoned at so much per cent. 3. MERCHANDIZE, is that which is transferred in trade either for labor, money, or other merchandize. 4. PER CENT. is a contraction of per centum, (Lat. PER, for, CENTUM, a hundred,) meaning, for a hundred. 1. If I buy goods for 350 dollars, and sell them again for 400 dollars, what do I gain per cent.? i. e., what do I gain on EACH hundred dollars paid out? In the first place, it is plain that I gain 50 dollars on 350 dollars, i. e., on the cost. Now, if $350 gain $50, then 1 dollar will gain of $50 = 350-33 to of a dollar, and hence, $100 will gain 100 times $1 = to $190 = to 142 dollars. Answer-which may be done by equations, thus: $350 GIVEN to $50 gain, and $100 REQUIRED. Therefore, = to 50 It is, therefore, plain, that my gain on each $100, is $143; and, hence, it is 14 per cent. ANSWER. 2. If I buy goods for $975, and sell them again for $850, do I gain or lose, and how much per cent.? In this case, it is plain, that I must lose $125, on an expenditure of $975. Now, if $975 lose $125, then $1, will lose of $125 hence, $100 will lose 100 times $3 = to 125 975 = to 39 of a dollar; and, to 500 = to 123 39 dollars = to 12 per cent., nearly. ANSWER. The same may be done by equations; thus, $975 are GIVEN to $125 loss, and $100 REQUIRED; therefore, 3. Sold a piece of cloth for $45 more than it cost me, and thereby gained 15 per cent., what was the cost? 100 Now, If the cloth was sold for $45 more than it cost, it is plain there must have been a gain of $45 on the first cost; but the gain was 15 per cent., i. e., it was 15 of the cost. if 15 100 of the cost = $45, then the whole cost (1), must be 100 of $45 = to 100 × 45 to $300. ANSWER. Or, by EQUATIONS, we have 15 of the cost GIVEN to $45, and (the whole cost) REQUIRED. 15 15 4. If I sell tea for 60 cents per pound, and thereby lose 20 per cent., what did the tea cost me per pound? By the conditions of the question, I must have sold the tea for 80 per cent. of the cost, i. e., the price (60 cents,) for which I sold it, must have been less than the whole (100), of the cost. Now, 108-100=100, which gives of the cost to 60 cents, or 100 60 of a dollar. Now, if 80% of the 100 20 100 80 100 16 of a dollar, then the whole cost (1), must be 100 cost = to 100 of 80 662 cents. 60 100 80 × 100 = dollars to of a dollar = 60 80 of the cost is GIVEN to $10, and (the Here, whole cost,) REQUIRED. |