Second. When the Fraction to be subtracted is the greater. Borrow one unit from the number annexed to the smallest fraction, then adding that unit to this fraction, you make the Subtraction. from 3 take 1 difference. Be a Mixed Number to multiply by a Fraction; -or, a Mixed Number by another Mixed Number. The shortest way in the two cases, is to add together the two parts of each mixed number, and then the question is reduced to multiply one fraction by another. EXAMPLES. 1st. Multiply 72 the product = 36 2nd. Multiply 9 2 261. or, 3 by, which gives for or, 49 by, which gives DIVISION. The same observation for Division as for Multipli-cation, with regard to the mixed numbers. EXAMPLES. 1st. Divide 5 or, by, which gives for result or, 3 by 102, which gives for FRACTIONS OF FRACTIONS. QUESTIONS. First. A Merchant buys the of the cargo of a vessel; then he makes over to one of his friends the of his purchase. What proportion has each of them of the total cargo of the Vessel ? Ans. 1& 45 Second. Nine persons are to divide equally among themselves the sum of 8283 £. One of these persons dying, leaves a widow and four children; he be queaths to his widow the third part of his claim, and his children must divide the rest in equal shares. Query How much will the widow and each of the children receive. Ans. The widow, 306, and each of the children, 153. : Third. Peter and Paul are in partnership, but Peter, who owns the of the capital, dies, leaving a wife and 3 children; he wills to his widow the of his estate, to the eldest of his children one third “and a half of the third of what remains, and the other two children must divide equally the remainder. It is supposed that the whole capital in partnership is 54327£. What are the shares of the widow and of each of the children? Ans. The widow 10348, the eldest 12:35, each of the others 64671. REDUCTION OF FRACTIONS. By the way of the Greatest Common Divisor. In order to exercise the scholars in this kind of Reduction, Examples may be given to them in this manner. Make them multiply two fractions by each other, then to make the proof of this multiplication, let them divide the product by one of the factors, the quotient of this division, after the reductions made, will be the other factor. APPLICATION. + × 1 = 7%; then 7 div. += 1; this last fraction being reduced to its lowest terms by the way of the greatest common divisor, gives, as if must be. To Reduce a Vulgar Fraction into Decimals. Write 1, 2, 3, &c. cyphers at the right of the numerator of the fraction; then divide this number, thus increased, by the denominator; the quotient will contain as many decimals, as cyphers you will have written at the right of the numerator. APPLICATION. It is required to express the value of the fraction within one thousandth part. Since the quotient must contain thousandths, you must write three cyphers at the right of the numerator which gives 5000 to be divided by 7, the quotient of which is 714, and consequently the value of the frac tion within a thousandth, will be 0,714. |