Common School AlgebraF.A. Brown, 1862 |
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Αποτελέσματα 1 - 5 από τα 5.
Σελίδα 96
... nator . Remark . As the resulting fractions should be simpli- fied , it is best to represent the operation , then strike out the common factors , previous to the actual performance 2 am 6 ( a + b ) 2.6am ( a + b ) of the multiplication ...
... nator . Remark . As the resulting fractions should be simpli- fied , it is best to represent the operation , then strike out the common factors , previous to the actual performance 2 am 6 ( a + b ) 2.6am ( a + b ) of the multiplication ...
Σελίδα 101
... nator , the fractions become 12 a2 b3 c ' 12 a2 b3 c ' ART . 69. Hence we have the following and 10 a2 m 12 a2 b3 c RULE ΤΟ REDUCE FRACTIONS ΤΟ THE LEAST COMMON DENOMINATOR . Find the least common multiple of all the given denomi ...
... nator , the fractions become 12 a2 b3 c ' 12 a2 b3 c ' ART . 69. Hence we have the following and 10 a2 m 12 a2 b3 c RULE ΤΟ REDUCE FRACTIONS ΤΟ THE LEAST COMMON DENOMINATOR . Find the least common multiple of all the given denomi ...
Σελίδα 177
... nator , the third power of a fraction is found by raising both numerator and denominator to the third power . 3 3 Thus , ( ) = 27 343 ' and ( - ) 3 = = = 3 a3 63 Conversely , the third root of a fraction is found 12 $ 32. ] 177 THIRD ...
... nator , the third power of a fraction is found by raising both numerator and denominator to the third power . 3 3 Thus , ( ) = 27 343 ' and ( - ) 3 = = = 3 a3 63 Conversely , the third root of a fraction is found 12 $ 32. ] 177 THIRD ...
Σελίδα 178
... nator . For example , the third root of is , that of m3 is m n · Find the third roots of the following fractions . 1. 125 1331 2 . 343 1728 . 3. 9261 12167 4. 2375 . 5 . 19683 24389 6. 1,462 . 1728 ART . 101. But if either numerator or ...
... nator . For example , the third root of is , that of m3 is m n · Find the third roots of the following fractions . 1. 125 1331 2 . 343 1728 . 3. 9261 12167 4. 2375 . 5 . 19683 24389 6. 1,462 . 1728 ART . 101. But if either numerator or ...
Σελίδα 208
... nator . This is manifestly the case , since reducing to a common denominator does not change the value of frac- tions , but only their form . Hence , we may reduce the exponents of all the factors in an irrational quantity to a common ...
... nator . This is manifestly the case , since reducing to a common denominator does not change the value of frac- tions , but only their form . Hence , we may reduce the exponents of all the factors in an irrational quantity to a common ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
2d power a² b² a² b³ a³ b² algebra ALGEBRAIC QUANTITIES B's age B's money barrel bushel cents chaise changing the signs coefficient common denominator corn cows difference Divide dividend division divisor equal equation example expressions extract the root factors Find the 3d following RULE formula fractional exponents geometrical progression gives greater Hence horse integral quantity irrational quantities least common multiple less Let the learner Let x represent letter manner merator miles monomial Multiply nator number of dollars number of terms numerator and denominator polynomial preceding proportion radical sign ratio reduce remainder represent the number represent the price Required the age Required the number Required the price result second member second power second root separate sheep Substitute subtract tens third power third root transpose unknown quantity whole number x2 y³ yard zeros
Δημοφιλή αποσπάσματα
Σελίδα 96 - Multiply all the numerators together for a new numerator, and all the denominators together for a new denominator.
Σελίδα 73 - ANOTHER. 1. Divide the coefficient of the dividend by the coefficient of the divisor. 2.
Σελίδα 79 - 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 168 - There will be as many figures in the root as there are periods in the given number.
Σελίδα 144 - Which proves that the square of a number composed of tens and units contains, the square of the tens plus twice the product of the tens by the units, plus the square of the units.
Σελίδα 223 - In any proportion the terms are in proportion by Composition and Division; that is, the sum of the first two terms is to their difference, as the sum of the last two terms is to their difference.
Σελίδα 2 - Algebraic operations are based upon definitions and the following axioms : — 1. If the same quantity, or equal quantities, be added to equal quantities, the sums will be equal. 2. If the same quantity, or equal quantities, be subtracted from equal quantities, the remainders will be equal. 3. If equal quantities be multiplied by the same quantity, or equal quantities, the products will be equal. 4. If equal quantities be divided by the same quantity, or equal quantities, the quotients will be equal....
Σελίδα 235 - ... multiply the last term by the ratio, subtract the first term from this product, and divide the remainder by the ratio diminished by unity.
Σελίδα 219 - In any proportion, the product of the means is equal to the product of the extremes.
Σελίδα 3 - If the same quantity be both added to and subtracted from another, the value of the latter will not be changed. 6. If a quantity be both multiplied and divided by another, its value will not be changed.