(56.) Reduce 15s. 11d. to the fraction of a pound. (57.) Reduce 54d. to the fraction of a shilling. (58.) Reduce 1cwt. 2qr. 6lb. 3oz. 83dr. to the fraction of a cwt. ell. (59.) Reduce 5oz. 33dr. to the fraction of a lb. Troy, (60.) Reduce 3qr. 33n. to the fraction of an English (61.) Reduce 147 days 15hrs. to the fraction of a year. (62.) What part of a pound is 158. 9 d.? (63.) What part of a groat is of three half-pence? (64.) What part of 10cwt. 1qr. 12lb. is 8cwt. 1qr. 25lb. 1oz. 7drs? (65.) Reduce 4bush. 2 pecks of corn to the fraction of a quarter. (66.) Reduce 1qr. 3n. to the fraction of a yard. (67.) Reduce 2 roods 15per. to the fraction of an acre. Examples to Prop. 10. 7 (68.) Reduce 2880 of a farthing to the fraction of a pound. Here a small name is brought into a great, Therefore 2880×××6=2330 of a £. of a £. 7 (69.) Reduce of a pound to the fraction of a farthing. Here a great name is to be brought into a small, Hence × 2 × 12 x = 250 of a farthing. (70.) Reduce (71.) Reduce dwt. (74.) What part (75.) Reduce 2880 of a penny to the fraction of a pound. of a pound to the fraction of a penny. of lb. Troy is § of a dwt.? of a lb. Troy to the fraction of a of a cwt. is of a lb. Avoirdupois? of a owt. to the fraction of a lb. of a week to the fraction of a second. (77.) What part of a hhd. of wine is of a gallon. (76.) Reduce Examples to Prop. 11. (78.) Find the least number that can be divided by 4, 7, 12, 21, and 34, without a remainder. By Rule 1. Here 4 and 7 may be rejected, because 12 and 21 are multiples of them. The common measure to 4 and 7 is 1; hence Note. 4 is the common measure to 28 and 12; 21 is the common measure to 84 and 21; and 2 is the common measure to 84 and 34, (79.) What is the least number that can be divided by 4, 6, and 10, without a remainder? (80.) Find the least number that can be divided by 2, 3, 4, 5, 6, and 7, without a remainder. 12. (81.) Find the least common multiple of 3, 4, 8, and (82.) Find the least number that can be divided by 1, 2, 3, 4, 5, 6, 7, 8, and 9, without a remainder. (83.) Find the least number that can be divided by 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, and 20, without a remainder. Examples to Prop. 12. 2 2 (84.) Reduce, 1, 2, 3, and 4, to a common denomi nator. Hence the new fractions are 360, 420, 520, 228, and 120, as above, Hence,=18, &=15,328, 18, fractions of the same valne as above, only in their lowest terms (85.) Reduce,,, and, to a common denomi nator. (86.) Reduce of 3 of § and 2 of 7 of 3 to a common denominator. (87.) Reduce 51, 3, 4, and 6, to improper fractions, having a common denominator. (88.) Reduce 1, 2137 33 9 5 to simple fractions, and having a common denominator. (89.) Reduce 3, 3, 4, and 1, to a common denomi nator. (90.) Reduce 4, §, 1, 7, and 19, to a common denominator. ADDITION OF VULGAR FRACTIONS. RULE. Reduce mixed numbers to improper fractions; complex and compound fractions to simple ones; and fractions of different denominators to a common denominator. Then the sum of the numerators written, over the common denominator, will be the sum of the fractions required. Note 1. If the fractions are of different denominations, reduce them to their proper quantities, (by Prop. 8th in Reduction, or reduce them to the same denomination by Prop. 10th) and then add them together. 2. When several fractions are to be added together, it is commonly the best to add those two together which may most easily be reduced to a common denominator, then their sum, and a third, &c. 3. When several mixed numbers, as 42, &c. are to be collected into one sum, first add the fractions to the fractions, and, to the left-hand of the sum, join the sum of the whole numbers. First, 35 = 29, 45 = 7. Then the fractions become 26, 7, and fi, A Or thus, The sum of,, and, when reduced to a common denominator, is,. 01488. Then 3+4+1488888, as before. (See the third note.) (2.) Add,, and 2, together. (3.) Add of, and 53, together. 47 947772 3143 together. (5.) Add of 3, 4 of 19, and g of 12, together. (6.) Add and of of 15 together. (7.) Add of a pound, of a shilling, and of a penny, together. (8.) What is the sum of 2 of 17. 10s. 4 of 37. 10s. and of a hundred guineas? of a cwt. of an ounce. of a yard. (9.) Add 1⁄2 of a lb. troy to together. of a foot, and of a mile, (13.) Add & cf an acre, 3 of nineteen square feet, and of a square inch, together. (14.) What is the sum of 2 of a tun of wine, and 3 of a hhd.? (15.) Add of a chaldron to of a bushel. (16.) Add of a week, 3 of a day, and of an hour, together. (17.) Add of of a year, of of a day, and of 3 of 19 hours, together. SUBTRACTION OF VULGAR FRACTIONS. RULE. Reduce mixed numbers to improper fractions; complex and compound fractions to simple ones; and fractions of different denominators to a common denominator. Then the difference of the numerators, written above the common denominator, will give the difference of the fractions required. |