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acre added algebraic quantities apples arithmetical progression arithmetical series ascer binomial Binomial Theorem bought bushels common difference complete equation Completing the square cost denotes Divide the number dividend division dollars entire quantity equal equation containing exactly divide exponent expressed extract the square Extracting the root Find a number Find the cube Find the product Find the square Find the sum find the value following examples geometrical series Give an example given number greater greatest common divisor Hence least common multiple lemons less number letter minus monomial negative quantity number of places number of terms oranges peaches perfect square polynomial positive quantity principle proportion pupil quan question quotient radical sign ratio reduced remainder represent the number required the numbers required to find result rule second degree second power sheep solving square root three numbers tities Transposing twice unknown quantity whole number yards
Page 178 - Multiply the divisor, thus increased, by the last figure of the root; subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Page 232 - Ratio is the quotient which arises from dividing one quantity by another of the same kind. Thus, the ratio of 2 to 6 is 3; the ratio of a to ma is m. REMARKS. — 1st In comparing two numbers or quantities by their quotient, the number expressing the ratio which the first bears to the second, will depend on which is made the standard of comparison.
Page 102 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Page 106 - ... by dividing the numerator of the dividend by the numerator of the divisor, and the denominator of the dividend by the denominator of the divisor.
Page 81 - The least Common Multiple of two or more quantities is the least quantity that will contain them exactly. Thus, 6 is the least common multiple of 2 and 3 ; and lOxy is the least common multiple of 2x and by. NOTE. — LCM stands for least common multiple.
Page 203 - The square of any polynomial is equal to the square of the first term, plus twice the product of the first term by the second, plus the square of the second...
Page 235 - In any proportion the product of the means is equal to the product of the extremes.
Page 217 - If, then, any problem furnishes an equation in which the known term is negative, and greater than the square of half the coefficient of the first power of the unknown quantity, we infer, that the conditions of the problem are incompatible with each other.
Page 149 - How much has each ? Ans. A $980, B $1540, and C $2380. 11. A certain number is expressed by three figures, and the sum of the figures is 1 1 ; the figure in the place of units, is double that in the place of hundreds ; and if 297 be added to the number, its figures will be inverted ; required the number. Ans. 326.