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acº added algebraic arithmetical binomial cents changed coefficient common denominator complete consequently containing cube root decimal Define denote Divide dividend division equal equation equivalent ExAMPLEs Explain the operation exponent expression factors figures find the values formulas four fourth fraction Given gives greatest common divisor Hence indicated known last term least common multiple less letter logarithm means method Multiply negative Note number of terms obtain OPERATION perfect polynomial positive Problem proportion quadratic equation quotient radical Raise ratio Reduce remainder Repeat the Rule represent Required Resolve result Rule simple solution Solve square root Substituting subtract taken Theorem third tion transposing twice units unknown quantity Whence write
Σελίδα 95 - Reduce compound fractions to simple ones, and mixt numbers to improper fractions ; then multiply the numerators together for a new numerator, and the denominators for. a new denominator.
Σελίδα 267 - 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 = e :f Now ab = ab (1) and by Theorem I.
Σελίδα 280 - ... that is, Any term of a geometric series is equal to the product of the first term, by the ratio raised to a power, whose exponent is one less than the number of terms. EXAMPLES. 1.
Σελίδα 51 - 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.
Σελίδα 259 - It is required to divide the number 40 into two such parts, that the sum of their squares shall be 818. Ans. 23 and 17.
Σελίδα 54 - ... the square of the second. _ Again, (a — by = (a — 5) (a — 5) = a2 — 2a6 + 52. (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 first by the second, plus the square of the second.
Σελίδα 259 - Divide the number 60 into two such parts, that their product shall be to the sum of their squares in the ratio of 2 to 5. Ans. 20 and 40.
Σελίδα 270 - ... two triangles are to each other as the products of their bases by their altitudes.