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.
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 by the second, plus the square of the second.
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 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 87 - RATIO 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 206 - Hence -,- = -76" dn that is a" : b" = c" : dn THEOREM IX. 23 1 If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d...
Page 87 - Thus, the ratio of a to b is written, a : b, or v ; read, a is to b, or a divided by b. 105. PROPORTION is an equality of ratios. Four quantities are proportional when the ratio of the first to the second is equal to the ratio of the third to the fourth.
Page 78 - Now .} of f- is a compound fraction, whose value is found by multiplying the numerators together for a new numerator, and the denominators for a new denominator.
Page 217 - The sum of three numbers in arithmetical progression is 15, and the sum of their squares is 83. What are the numbers...

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