A new practical and theoretical arithemtic: in which, in addition to the usual modes of operation, the science of numbers, the Prussian canceling system, and other important abbreviations, hold a prominent place

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J. Ernst, 1854 - Mathematics - 288 pages
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Page 160 - The rule for casting interest, when partial payments have been made, is to apply the payment, in the first place, to the discharge of the interest then due. If the payment exceeds the interest, the surplus goes towards discharging the principal, and the subsequent interest is to be computed on the balance of principal remaining due. If the payment be less than the interest, the surplus of interest must not be taken to augment the principal; but interest continues on the former principal until the...
Page 134 - If 8 men can build a wall 20 feet long, 6 feet high and 4 feet thick, in 12 days ; in what time...
Page 208 - Multiply each man's stock by the time he continues it in trade ; then say, as the sum of the products is to each particular product, so is the whole gain or loss to each man's share of the gain or loss. EXAMPLES. 1. A and B...
Page 133 - It is evident that the terms of a proportion may undergo any change which will not destroy the equality of the ratios ; or which will leave the product of the means equal to the product of the extremes.
Page 136 - For, if we have given ab' = a'b, then, dividing by bb', we obtain Corollary. The terms of a proportion may be written In any order which will make the product of the extremes equal to the product of the means.
Page 238 - ... broad; what length must a ladder be to reach from the outside of the ditch to the top of the castle?
Page 258 - To the remainder, bring down the first figure in the next period, and call it the dividend. 4. Involve the root to the next inferior power to that which is given, and multiply it by the number denoting the given power for a divisor.
Page 88 - ... thing remains, multiply it by the next inferior denomination, and divide by the denominator as before, and so on as far as necessary, and the quotient will be the answer.
Page 79 - OPERATIONS WITH FRACTIONS A) To change a mixed number to an improper fraction, simply multiply the whole number by the denominator of the fraction and add the numerator.
Page 182 - Multiply each payment by the time at which it is due ; then divide the sum of the products by the sum of the payments, and the quotient will be the time required.

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