# Introduction to Arithmetic

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1860 edition. Excerpt: ...guineas, give away two-fifths of it to one man, two-fifths of the remainder to a second, and the rest to a third, how much money does each of them receive? Ans. The first, 10,10s.; Second, 6, 6.; Third, 9, 9s. 35. If one cock empty a cistern in five, and another in four hours, in what time will they empty it if used together? Ans. 2 hours. 36. If a greyhound's leap is one-fourth longer than a hare's, in what time will it overtake the hare that is fifty leaps before it, and that they both take one leap in a second? Ans. 3 min. 20 sec. 87. Two men set out at the same time, the one from London to York, and the other from York to London; the one travels at the rate of 5 miles an hour, and the other 6J; in how many hours will they meet, the distance between the two places being 197 miles? Ans. 16jr hours. DECIMAL FRACTIONS. Decimal Fractions are those which are written decimally in the same way as integers--the only difference being that a point is placed before the figures for distinction. They express tenths or combinations of tenths: thus--.3, three-tenths;.47, forty-seven hundredths. The term is derived from the Latin word decem, signifying ten. In Decimal Fractions, instead of both numerator and denominator being expressed, as in Vulgar Fractions, the numerator only is written down, and the denominator is always understood to be either 10,100, 1000, or some other combination of tenths, according to the number of figures in the numerator. If the numerator consists of 1 figure, tenths are meant, and the understood denominator is 10; if of 2 figures, hundredths are meant, and the denominator understood is 100, and so on; the denominator being always 1, with as many nothings annexed as there are figures in the numerator: ...