What is the value of of a guinea ?-Anf. 95. 4d. 2. 3. What is the value of 4. What is the value of Anf. 30z. 5pwt. 22111gr. 5. poles. What is the value of § of an acre?—Ans. 2 roods 20 Cafe 6. To reduce a compound fraction to a fimple one of the fame value. Rule. Multiply all the numerators together for a new numerator, and all the denominators together for a new denominator; and that will be the fraction required. Example 1. Reduce of of 2 of a pound sterling to a fimple fraction. the foregoing cafe, and the value of this fimple fraction; and the two values will be found to be equal. 30 2. Reduce of of to a fimple fraction.Anfwer 20 or 4. 3. Reduce of of 7 of to-a fimple fraction.-Anf 168 or 21 1800 223 If any part of the compound fraction be a whole or mixed number, it must be reduced to a fraction by one of the foregoing cafes, before the compound fraction can be reduced to a fimple one. Cafe 7. To reduce fractions having different denominators to fractions of the fame value having a common denomi nator. Rule. Multiply each numerator into all the denominators, except its own; and the product is the numerator of that fraction; fraction; and multiply all the denominators continually together, and the product is the common denominator. 2 Example 1. Reduce, 3, and 4 to fractions of the fame value, and having the fame denominators. 6: 7 24 the numerator for 4, 7 28 the numerator for 3. 21 the numerator for 1. 42 cominon denominator. Therefore the new fractions equal to the former ones are, 2 equal to 1, 2 equal to 3, 24 equal to 4. 2. Reduce, of, 5, and to a common denominator! Anf. 00, B426, 12540, 2400. 60 In this cafe, as well as the former, if any of the parts be a whole or mixed number, or a compound fraction, they must be reduced to fimple fractions, as in the laft example. Cafe 8. To reduce a fraction of one denomination to that of another, without changing its value. This is either afcending or defcending; afcending is when a fraction of a lefs denomination is brought into a fraction of a greater; and defcending, when a fraction is brought from a greater to a less denomination. · · Rule. When a fraction is to be brought from a lefs to a greater denomination, bring the fraction from a simple to a compound one, by comparing it with the intermediate denominations, which are between the given fraction and the denomination required; and then, by the rule in Case 6, bring the compound fraction to a fimple one. وردية Example 1. Bring of a penny to the fraction of a pound. of 20 A penny is of a thilling, and a fhiliing is of a pound, therefore of a penny is of Ereduced to a fimple fraction, is Dd 2 600 of a pound, which, of a pound, as follows: Numerators. Rule. When a fraction is to be brought from a greater to a lefs denomination, multiply the numerator of the fraction by the number of parts of the next inferior denomination, and that product by the number of parts of the next denomination; and fo on till it be brought to the denomination required; and the product is the numerator of the fraction required. Example 2. Reduce of a pound fterling to the fraction of a penny. Here I multiply the numerator by 20, as that is 2 the number of fhillings contained in a pound, and _20 that product by 12, as there are so many pence in 40 a fhilling; and the product gives a numerator to the fraction required. 12 480 Thus, if in this cafe the reduction be ascending, the denominator only of the fraction need be multiplied; and, if defcending, the numerator only... 3. Reduce -Anf. 1200. of a pound troy to the fraction of a pwt. 4. Reduce of a day to the fraction of a minute.— Anf. $260 or 640. 5760 5. Reduce of a guinea to the fraction of a penny.Anf. 736. Addition of Vulgar Fractions. Before vulgar fractions can be added together, it is neceffary that they be brought into a proper form, for which, Rule. Reduce the compound fractions to fimple ones,. and whole and mixed numbers to improper fractions, and fractions A fractions of different denominations to fractions of the fame denomination. Then reduce all the fractions to fractions of the fame common denominator. Add all the numerators together, and place the fum over the common denominator; and this fraction will be equal to the fum of all the given fractions, The total thus found, if it be an improper fraction, may be reduced to a whole or mixed number. Example 1. Add, and together. In this example, as in the former, I first (after having reduced the mixed number 3 and the compound fraction of to fimple fractions) reduce all the fractions to a common denominator, by multiplying the numerator of each into all the the denominators except its own, for a numerator to each fraction, and all the denominators into each other for a common denominator, as taught in reduction of fractions; the numerators of thefe newly-difcovered fractions are then added together, and their fum 3455 placed over the common denominator 875 is the anfwer or fraction equal to the fum of all the given fractions, which, divided by 5, gives, and reduced to a mixed number is 3195 166 The proof of addition of fractions is wrought by finding the value of each of the given fractions, and adding them together, and then finding the value of the whole fraction or fum of the fractions, and if these two values be equal the work is right. Qu. 3. What is the fum of of a pound and 3 of a fhilling?-Anf. 73% of a pound. 1 In this example the fraction of a filling must be reduced to the fraction of a pound before the work can be wrought, as before directed. Q. 4. What is the fum of, g, and 7 of ¿?—Answer 278 Qu. 5. What is the sum of of a week, 4 of a day, and an hour?-Anf. 2 days 14 hours. Subtraction of Vulgar Fractions. Rule. Reduce the fractions in the fame manner as for addition; then the lefs numerator is to be fubtracted from the greater, and the difference placed over the common denominator will form the fraction required. Example 1. Subtract 3 from §. |