# The First Part of the United States Arithmetic: Designed for Schools

E.C. & J. Biddle, 1849
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Page 49 - Multiply the last remainder by the preceding divisor, or last but one, and to the product add the preceding remainder ; multiply this sum by the next preceding divisor, and to the product add the next preceding remainder ; and so on, till you have gone backward through all the divisors and remainders to the first.
Page 17 - ... any number divided by 9, will leave the same remainder as the sum of its figures, or digits, divided by 9, which may be thus demonstrated.
Page 91 - Proceed in this way through all the denominations to the highest, and the quotient last found, together with the several remainders, if any, will give the value sought.
Page 36 - The reason of this method is obvious ; for any number multiplied by the component parts of another, must give the same product as if it were multiplied by that number...
Page 47 - ... and it is evident, that as often as the whole divisor is contained in the whole dividend, so often must any part of the former be contained in a like part of the latter. * This follows from the second contraction in Multiplication...
Page 14 - Los números cardinales 0: zero 1: one 2: two 3: three 4: four 5: five 6: six 7: seven 8: eight 9: nine 10: ten 11: eleven 12: twelve 13: thirteen 14: fourteen 15: fifteen 16: sixteen 17: seventeen 18: eighteen 19: nineteen 20: twenty 21: twenty-one 22: twenty-two...
Page 57 - Troy Weight. 24 grains (gr.) — 1 pennyweight (dwt). 20 pennyweights — 1 ounce (oz.) 12 ounces — 1 pound (Ib.).
Page 31 - Place the least number under the greatest, so that units may stand under units, tens under tens, &c. .and draw a line under them. 2. Begin at the right hand, and take each figure in the lower line from the figure above it, and set down the remainder.
Page 24 - Subtract the subtrahend from the dividend, and to the remainder bring down the next period for a new dividend, with which proceed as before ; and so on, till the whole is finished.
Page 44 - When the divisor is large, the pupil will find assistance in determining the quotient figure, by finding how many times the first figure of the divisor is contained in the first figure, or if necessary, the first two figures of the dividend.