207. To divide a fraction by a whole number. LE. Multiply the denominator of the fraction by the whole er, and over it set the numerator. 8. When the whole number will divide the numerator of the ion without remainder, then divide the numerator by it, under the quotient set the denominator'. Place 1 as a denominator to the whole number, and this rule will coincide the first, in the same manner as the preceding rule has been shewn to coe with it. The truth of this rule is evident from ex. 30; for the one fourth part of ve thirteenths is evidently three thirteenths: and the like will appear from examples. 3. Which is greatest, the sum of 5 11 and or the difference 7 12' 7. 29 of 1- and and how much? Answer, the sum, by 10 30' 377 420 2 7 or their 9' 4. Which is the greater, the product of by 5 quotient, and how much? Answer, the quotient, by 64 315 est, the product or the quotient, and how much? Answer, the 27 quotient, by 7 112 8. If 2 be added to, and also divided by it, which is 8 greatest, the sum or the quotient, and how much? Answer, the 9. What sum will arise by adding the sum and difference of 2 3 of 3 guineas and of 4 pounds together? Ans. 51. 6s. 8d. 3 4 5 4 10. If the quotient of 2— by of 2 be multiplied by the 4 sum, what is the product? Answer 7– 5 61 128 210. PROPORTION, OR, THE RULE OF THREE RULE I. Examine the question so as to be able to determine how the stating is to be made, then reduce the first and third terms to fractions of the same denomination, if they are not so already, and the second to a fraction of the greatest denomination contained in it, or of a greater denomination if convenient. II. With the fractions to which the given numbers are reduced state the question, and examine whether the answer will be greater or less than the second term; if greater, mark the less extreme for a divisor, but if less, mark the greater. III. Invert the marked term, and then multiply the three terms continually together; the product will be a fraction of the same denomination with that which the second term was reduced to, and must be reduced to its proper quantity for the answer m. *This rule is founded on the same principles with the Rule of Three in whole numbers, (Art. 126,) and under it are included both the direct and inverse rules, which in effect are only branches of one and the same general rule. 1 EXAMPLES. 1. If 2cwt. of cheese cost 10l. 2s. 6d. what cost lcwt. 1qr. Explanation. I first reduce the terms which will be the first and third to fractions of an to cwt., and Icwt. 1qr. 14lb. to 5 5 8 81 +107. 2s. 6d., the second, to L.: I then state the question, from the nature 8 of which I find that the answer ought to be less than the second term; I therefore mark the greater extreme for a divisor; having inverted I put the 11 5 three terms down with signs of multiplication between, and multiply them to gether; the product is next reduced to its proper terms, which gives the 405 64 answer. In the multiplication, the elevens cancel each other. Here as the terms require no reducing, I first state the question, and find that the answer will be less than the second term; I therefore mark the greater 4 term for a divisor, which being inverted, and multiplied by the two other 9 terms, produces the fraction 189 320 L.; this reduced to its proper quantity is the answer. 3. If my friend lends me 10 guineas for 10 weeks and 3 days, how long ought I to lend him 5l. 4s. 6d. to acquit myself of the obligation? I find that the answer will be greater than the second term, consequently I mark the less extreme, and proceed as before. 4. If by walking 2 miles an hour I can perform a journey in 8 days, how many days will another who can walk 33 miles an hour require to go the same distance, allowing 12 hours to 7. If 3 ounces of gold cost 171. 15s. 6d. what sum will purchase 44 ounces? Ans. 211. 11s, 8d... |