To reduce a compound fraction to a single one. Multiply all the numerators together, for the required numerator, and all the denominators together for the required denominator, and the fraction so found will be the answer. EXAMPLE. Reduce of of to a single fraction. Answer=1. PROBLEM VI. To find the value of a vulgar fraction in known parts of a whole number, I. Multiply the numerator by as many as will make one of the next inferior denomination, and divide the product by the denominator of the fraction. II. If there is any remainder, multiply it by the next inferior denomination, and divide by the same denominator as before, and proceed in this manner with each, till you come to the lowest denomination, and the several quotients put together will show the known parts of integer, or whole pumbers. EXAMPLE. What is the value of of a pound sterling? Answer 4s. 7 d. and parts of a farthing. Note. If the fraction is an improper one, divide the nume rator by the denominator, and the quotient will be the highest denomination; and proceed with the remainder as before. PROBLEM VII. To reduce a fraction of one denomination to the fraction of another. I. If the fraction is to be reduced from a less denomination to a greater, multiply the denominator by all the denominations, minations, from the given one to that which is sought; then place the numerator over the product, and it will be the fraction required. IL. But if from a greater to a less, multiply the numerator by all the denominations, as before, and place the given denominator under their product, and you will have the frac tion required. EXAMPLE I. What part of a hundred weight is of a pound? Answer 3 5X28X4560 3 of an hundred weight. EXAMPLE II. What part of a pound weight is of an hundred weight? What part of a penny is of a pound sterling? I. Reduce compound fractions to single ones, and mixed numbers to improper fractions; then reduce each fraction to the same denomination, and a common denominator. II. Add all their numerators together, under the sum write the common denominator, and the fraction so represented will be their sum. What is the sum of of a pound, and of a shilling, in parts of a penny? 2 × 20×12 3 of a pound reduced to parts of a penny, is =40=140=0, and of a shilling reduced to parts of What is the sum of 4 of a foot, and of an inch, in parts of a foot? 43 reduced to an improper fraction, is of a foot, and of an inch, reduced to parts of a foot, is , and 5 5 SX12 96 reduced to a common denominator, is 448 - and; then 4+5=953 parts of a foot the answer. 96 96 PROBLEM VIII. To subtract one vulgar fraction from another. Prepare the fractions as in addition, then subtract the numerators; write the common denominator under the dif ference, and you will have the difference required. sum. EXAMPLE I. What is the difference between and } ? and reduced, are 19 and; then 10 the EXAMPLE II. What is the difference between of a foot, and of an inch, in parts of a foot? of an inch reduced to parts of a foot, is 3 5 × 12 60 thenand, reduced to a common denominator, is 48 and therefore 48 ference. parts of a foot is the dif PROBLEM X. To multiply fractions or mixed numbers together. I. Reduce mixed numbers to fractions, and each fraction to the same denomination. II. Multiply their numerators together for the numerator of the fraction required; and their denominators together, for the required denominator; and the fraction so found will be the answer. EXAMPLE I. What is the product of, multiplied by ? Answer == |