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 11
... remainder divided by z . The same thing may be expressed by drawing a hori- zontal line , or bar , over the compound quantity , which line or bar is called a vinculum . Thus , x + yxz , de- notes that the sum of x and y is to be ...
... remainder divided by z . The same thing may be expressed by drawing a hori- zontal line , or bar , over the compound quantity , which line or bar is called a vinculum . Thus , x + yxz , de- notes that the sum of x and y is to be ...
Σελίδα 24
... Remainder Saby - 5xy Remainder 27b - 15a 4 . 5 . From x2 + 2xy + y2 From 13x2y - 4xy2 + y3 Take ̄x2 - 2xy + y2 Take 6x2y + xy2— y3 Rem . 4xy Rem . 7xy - 5xy2 + 2y3 6. From 17abc + 63-3bc , subtract abc - 663-4bc . Ans . 16abc + 7b3 + bc ...
... Remainder Saby - 5xy Remainder 27b - 15a 4 . 5 . From x2 + 2xy + y2 From 13x2y - 4xy2 + y3 Take ̄x2 - 2xy + y2 Take 6x2y + xy2— y3 Rem . 4xy Rem . 7xy - 5xy2 + 2y3 6. From 17abc + 63-3bc , subtract abc - 663-4bc . Ans . 16abc + 7b3 + bc ...
Σελίδα 38
... remainder , which we find to be b , we then multiply the divisor by b , and again subtracting , there remains nothing , so that a + b is the complete quotient . ( 39. ) That the operation may be the most simple , it will be necessary to ...
... remainder , which we find to be b , we then multiply the divisor by b , and again subtracting , there remains nothing , so that a + b is the complete quotient . ( 39. ) That the operation may be the most simple , it will be necessary to ...
Σελίδα 39
... remainder . In this example , we find 2 for remainder , which , be- ing placed over the divisor 2x - 3 , gives the fraction 2 to be added to our quotient . 2x - 3 3. Divide a1 + a2z2 + z1 by a2 + DIVISION . 39.
... remainder . In this example , we find 2 for remainder , which , be- ing placed over the divisor 2x - 3 , gives the fraction 2 to be added to our quotient . 2x - 3 3. Divide a1 + a2z2 + z1 by a2 + DIVISION . 39.
Σελίδα 47
... remainder , place it over the denominator for the fractional part . EXAMPLES . 9a - 6x2 - 8c4 1. Reduce to a mixed quantity . Dividing the numerator by the denominator , we find this FIRST OPERATION . 9a - 6x2 - 8c1la - x2 9a - 9x2 | 9 ...
... remainder , place it over the denominator for the fractional part . EXAMPLES . 9a - 6x2 - 8c4 1. Reduce to a mixed quantity . Dividing the numerator by the denominator , we find this FIRST OPERATION . 9a - 6x2 - 8c1la - x2 9a - 9x2 | 9 ...
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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.