The Elements of Algebra: Designed for the Use of Common Schools, Also Serving as an Introduction to the "Treatise on Algebra"H.H. Hawley & Company, 1848 - 251 σελίδες |
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Σελίδα 7
... . Conversion of compound repetends to vulgar fractions , . Inequalities , ..... Permutations , Combinations , Probabilities , 213 228 232 234 235 239 ... 243 246 ELEMENTS OF ALGEBRA . CHAPTER I. DEFINITIONS AND PRELIMINARY RULES CONTENTS .
... . Conversion of compound repetends to vulgar fractions , . Inequalities , ..... Permutations , Combinations , Probabilities , 213 228 232 234 235 239 ... 243 246 ELEMENTS OF ALGEBRA . CHAPTER I. DEFINITIONS AND PRELIMINARY RULES CONTENTS .
Σελίδα 235
... INEQUALITIES . ( 169. ) When two quantities or expressions are equal , as the two members of an equation , this equality is de- noted by the symbol = . In a similar way the symbol > , placed between two quantities or expressions ...
... INEQUALITIES . ( 169. ) When two quantities or expressions are equal , as the two members of an equation , this equality is de- noted by the symbol = . In a similar way the symbol > , placed between two quantities or expressions ...
Σελίδα 236
... inequalities existing in opposite senses . I. The same quantity may be added or subtracted from both members of an inequality , and the inequality will remain in the same sense as before . Thus , if 6 > 2 , and we add 3 to both members ...
... inequalities existing in opposite senses . I. The same quantity may be added or subtracted from both members of an inequality , and the inequality will remain in the same sense as before . Thus , if 6 > 2 , and we add 3 to both members ...
Σελίδα 237
... inequality will exist in the same sense as the given inequalities . III . But if the corresponding members of two inequali- ties , existing in the same sense , be subtracted from each other , the resulting inequality will not always ...
... inequality will exist in the same sense as the given inequalities . III . But if the corresponding members of two inequali- ties , existing in the same sense , be subtracted from each other , the resulting inequality will not always ...
Σελίδα 238
... inequality 4x - 2 > 10 . 2. Find the limit of x in the inequality 3x + 2 < 12 + x . Ans . x > 3 . Ans . x < 5 . ~ + bx — ab > : ax m 3. Given bx n -ax + ab < · Ans . a2 m b2 -- N to find the value of x . x > a , and x < b . That is ...
... inequality 4x - 2 > 10 . 2. Find the limit of x in the inequality 3x + 2 < 12 + x . Ans . x > 3 . Ans . x < 5 . ~ + bx — ab > : ax m 3. Given bx n -ax + ab < · Ans . a2 m b2 -- N to find the value of x . x > a , and x < b . That is ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
added algebraic algebraic quantities antecedent arithmetical progression bx-ab change the signs Clear the equation cleared of fractions coefficient common denominator Consequently decimal denote digits Divide the number divisor equal equation of fractions EXAMPLES exponent expression Extracting the square favorable Find a number find the values find x formula four quantities fourth geometrical geometrical progression gives Hence inequality least common multiple left-hand term letters metical mixed quantity NEGATIVE PRODUCTS negative quantities nth root number of combinations number of permutations number of terms number sought numerator and denominator obtain OPERATION placed polynomial POSITIVE PRODUCTS pression proportion quadratic equation quotient rate per cent reciprocal Reduce remainder repetend Rule under Art second term simple chance simple equations solved square root subscript numbers substituted subtract things taken third tions Transposing and uniting twice uniting terms unknown quantity values of x VULGAR FRACTIONS
Δημοφιλή αποσπάσματα
Σελίδα 54 - Subtract the numerator of the subtrahend from the numerator of the minuend, and place the difference over the common denominator.
Σελίδα 77 - Two persons, A and B, lay out equal sums of money in trade ; A gains $126, and B loses $87, and A's money is now double of B's : what did each lay out ? Ans. $300.
Σελίδα 69 - What number is that whose third part exceeds its fourth part by 16 ? Let x= the number required, Then its — part will be —x, and its — part —a;.
Σελίδα 181 - One hundred stones being placed on the ground, in a straight line, at the distance of a yard from each other, how far will a person travel who shall bring them one by one to a basket, which is placed one yard from the first Stone ? Ans.
Σελίδα 99 - Then divide the first term of the remainder by the first term of the divisor...
Σελίδα 38 - ... the first term of the quotient ; multiply the• divisor by this term, and subtract the product from the dividend.
Σελίδα 44 - To reduce a mixed quantity to the form of a fraction. RULE. Multiply the entire part by the denominator of the fraction...
Σελίδα 134 - Since the square of a binomial 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...
Σελίδα 10 - It denotes that the quantities between which it is placed, are to be multiplied together.
Σελίδα 47 - To reduce an improper fraction to a whole or mixed number, — RULE : Divide the numerator by the denominator ; the quotient will be the whole or mixed number. EXAMPLES FOR PRACTICE.