Eaton's Elementary Algebra: Designed for the Use of High Schools and Academies

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Thompson, Brown, 1868 - Algebra - 252 pages
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Page 71 - To reduce a mixed number to an improper fraction, — RULE : Multiply the whole number by the denominator of the fraction, to the product add the numerator, and write the result over the denominator.
Page 40 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Page 207 - Batio is the relation of one quantity to another of the same kind ; or it is the quotient which arises from dividing one quantity by another of the same kind.
Page 100 - D. The distance from A to D is 34 miles ; the distance from A to B is to the distance from C to D as 2 to 3 ; and of the distance from A to B, added to one half the distance from C to D, is three times the distance from .B to C.
Page 45 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.
Page 44 - ... the square of the second. In the second case, we have (a — &)2 = a2 — 2 ab + b2. (2) That is, the square of the difference of two quantities is equal to the square of the first, minus twice the product of the two, plus the square of the second.
Page 44 - The square of the sum of two quantities is equal to the square of the first, plus twice the product of the first multiplied by the second, plus the square of the second.
Page 207 - The first term of a ratio is called the antecedent, and the other the consequent ; and the two terms together are called a couplet.
Page 227 - Multiply the last term by the ratio, from the product subtract the first term, and divide the remainder by the ratio, less 1 ; the quotient will be the sum of the series required.
Page 251 - Springfield in 5f days. How far from Boston did they meet ? Ans. 42 miles. 163. The product of two numbers is 90; and the difference of their cubes is to the cube of their difference as 13 : 3. What are the numbers? •***' 164. A and B start together from the same place and travel in the same direction. A travels the first day 25 kilometers, the second 22, and so on, travelling each day 3 kilometers less than on the preceding day, while B travels 14 kilometers each day. In what time will the two...

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