EXAMPLES FOR ILLUSTRATION. 1. If 1lb. of butter cost 1s. 9d. what cost 39lbs? 21 39 189 63 1819 12/819 20 68 3 3 8 3 £. S. d. Ans. 3£. 8s. 3d. It will be for the benefit of the learner to examine every part with care and attention. Stated by the first rule. You will perceive that, in this question, two of the terms are of the same name; these I placed one for the first, and the other for the third terms, minding to place the demanding term, (or the one the question required the value of,) in the third place, and the other, being one of the supposition, in the first place, (that is, for the first term,) and the remaining one, (which was of the same kind with the answer,) for the second. Having stated the question, I proceeded, according to rule, to examine the first and third terms, and found that they were of the same name, and neither of them of different denominations. I next examined the second term, which I found to consist of more than one denomination; this, as directed, I reduced to the lowest name mentioned, which was pence; after I had reduced this to pence, I,(according to rule,) multiplied the second and third terms together, and divided the product by the first term. (Here observe, that when either of the terms consists of an unit, you may omit to multiply or divide by it, as the question will stand the same.) In this example I divided by 1, the first term, and it brought 819, the same figures I had before I divided; which shows that I might have omitted dividing by it. Now the question arose, what is the name of this quotient 819; the rule tells me that, whatever name the second term is left in, the quotient or fourth term will come in the same name; by examining, I found that my second term was left in pence; consequently, my fourth term is pence; which according to the rules of Reduction, I brought into pounds, by dividing by 12, the pence in a shilling, aud 20, the shillings in a pound; this brought he answer. 2. If 39lbs. of butter cost 3£. 8s. 3d. what cost 1lb? lbs. £. S. d. lb. 39 3 8 3 :: 1 20 2182 68 39)819(12)21 78 I 9 39 S. d. 39 Ans. 1s. 9d. Here I proceeded according to rule, placing the demanding term in the third place, and the other of the same kind, in the first, and the remaining one in the second. By examining the first and third terms, I found that they were alike in name, but the second, I found to consist of pounds shillings and pence; and, as the lowest name was pence, I reduced this term to pence. The next to be done was, to multiply the second and third terms together; but the third term being one, I omitted multiplying by it, as it would not have altered the question; I now proceeded to divide by the first term 39, this brought 21. Now what was the name of this quotient? the second term was reduced to pence; then this according to rule, is pence, which I brought into shillings; the result was 1s. 9d. the answer which proves the last example. The same question as above, stated by rule 2d. 2. If 39lbs. of butter cost 3£. 8s. 3d. what cost 1lb? lbs. lb. £. S. d. Ans. 1s. 9d. I began, placing that term in the third place, which is of the same kind with the answer. I then considered whether, from the nature of the question, the answer must be more or less than the third term, which I 39)819(12)21 found to be less; according to 12 78 39 39 rule, I placed the 39lbs. the 1 9 greater of the two, for the first s. d. term, and the other for the second. By examining the first and second terms, I found that they were alike in name; but the third, I found to consist of pounds, shillings, and pence; and, as the lowest name was pence, I reduced this term to pence. The next to be done was to multiply the second and third terms together; but, the second term being one, I omitted it, as it would not alter the question. I now proceeded to divide by the first term 39; this brought 21, (as in th last example,) which I brought into shillings by dividing by 12, the pence in a shilling, the result was 1s. 9d. the answer. 3. Suppose 14lbs. of sugar cost 1D. 75cts. what cost 2C. 1qr. 19lbs. at that rate? Ans. 33D.87cts. 5m. In this question, the two terms that are of a kind are the 14lbs. and the 2C. 1qr. 19lbs. and as the C. &c. is the demanding term, or the one the question required the value of, I placed that for the third term; and the 14lbs. for the first, and the price for having stated the question, I examined the first and third terms, and found that the third consisted of different denominations; and as pounds were the lowest mentioned, I reduced it to pounds by the rules of reduction; this brought the third term to the same name or denomination of the first; I now proceeded to examine the second term, and found this to consist of two denominations, viz. dollars and cents; I reduced this term to cents, multiplying by 100, the cents in a dollar; then, according to the rule, I multiplied my second and third terms together, and divided that product by the first term, (the 14lbs.) this brought 3387. Here the question arose, what is the name of this quotient? By observing my second term, I perceived that I had reduced that to cents; consequently, my quotient, or fourth term, is cents; this I brought into dollars, by pointing off two figures from right to left for cents, (as heretofore taught,) after having done this, I observed that I had 7 remainder, after dividing. Here was another question; what must be done with this? The rule is the guide; it says, if there happens to be a remainder, &c. reduce it to the next denomination, below the last quotient, and divide by the same divisor again, &c. The quotient was cents and mills, being the next denomination below; I reduced the remainder to mills, and divided again by the divisor 14; this brought 5 mills, which I placed to the right of the quotient, which was the answer, viz. 33D. 87cts. 5m. The last question stated by rule 2. 3. Suppose 14lbs. of sugar cost 1D. 75cts. what cost 2C. 1qr. 19lbs. at that rate? 1 Term. Ans. 33D. 87cts. 5 m. &c. To state this question by rule 2, I placed that term in the third place which was of the same kind with the answer, viz. $1.75cts. Then, as I found, from the nature of the question, that the answer must be more than the third term, accordingly I placed the greater of the two, for the second term. After having stated the question, I examined my first and second terms, and found that the second consisted of different denominations, and as pounds were the lowest mentioned. I reduced this term to pounds by the rules of reduction; this brought the second term to the same name or denomination of the first; I now proceeded to examine the third term, and found it to consist of two denominations, viz. dollars and cents; this I reduced to cents, multiplying by 100, the cents in a dollar; then, according to rule, I multiplied my second and third terms together, and divided that product by the first term, (the 14lb.) NOTE. After multiplying the second and third terms together, the same observations apply to this question that were given in the last. 4. Suppose you purchase 3C. 2qr. 14lbs. of lead for 13£. 10s. 8d. what is 1lb. 8oz. worth at that rate? Ans. 1 shilling. 3 Term. 16. ning the question, I perceived that the 1lb. 8oz. was Ing term; this I placed for the third term, and the |