An Elementary Treatise on Algebra: Theoretical and Practical ... |
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Page 25
... divisor . If a multiplied by b give the product ab , then ab divided by a must give b for a quotient , and if divided by b , give a . In short , if one simple quantity is to be divided by another simple quantity , the quotient must be ...
... divisor . If a multiplied by b give the product ab , then ab divided by a must give b for a quotient , and if divided by b , give a . In short , if one simple quantity is to be divided by another simple quantity , the quotient must be ...
Page 26
... divisor from that of the dividend . Divide 2a by a * . Ans . 2a2 . Divide -a by a . Ans . -a . Divide 16x3 by 4x . Ans . 4x2 . Divide 15axy3 by -3ay . Ans . -5xy2 Divide 63am by 7an . Ans . 9 am-n Divide 12ax by -3ax . Ans . -42-1 ...
... divisor from that of the dividend . Divide 2a by a * . Ans . 2a2 . Divide -a by a . Ans . -a . Divide 16x3 by 4x . Ans . 4x2 . Divide 15axy3 by -3ay . Ans . -5xy2 Divide 63am by 7an . Ans . 9 am-n Divide 12ax by -3ax . Ans . -42-1 ...
Page 27
... divisor . EXAMPLES . 1. Divide 3ax - 15x by 3x . 2. Divide 8x3 + 12x2 by 4x2 . Ans . a - 5 . Ans . 2x + 3 . 3. Divide 3bcd + 12bcx - 9b2c by 3bc . Ans . d + 4x - 36 . 4. Divide 7ax + 3ay - 7bd . by -7ad . x By b Ans . a Tata 5. Divide ...
... divisor . EXAMPLES . 1. Divide 3ax - 15x by 3x . 2. Divide 8x3 + 12x2 by 4x2 . Ans . a - 5 . Ans . 2x + 3 . 3. Divide 3bcd + 12bcx - 9b2c by 3bc . Ans . d + 4x - 36 . 4. Divide 7ax + 3ay - 7bd . by -7ad . x By b Ans . a Tata 5. Divide ...
Page 28
... divisor into the yet unknown factor , the quotient ; and the highest power of any letter in the product , or the now called divi- dend , must be conceived to have been formed by the highest power of the same letter in the divisor into ...
... divisor into the yet unknown factor , the quotient ; and the highest power of any letter in the product , or the now called divi- dend , must be conceived to have been formed by the highest power of the same letter in the divisor into ...
Page 29
... divisor is a2 + ab , and the first term of the remainder is ab , in which a is contained b times . We then multiply the divisor by b , and there being no remainder a + b is the whole quotient . Divide a3 + 3a2x + 3ax2 + x3 by х + а . As ...
... divisor is a2 + ab , and the first term of the remainder is ab , in which a is contained b times . We then multiply the divisor by b , and there being no remainder a + b is the whole quotient . Divide a3 + 3a2x + 3ax2 + x3 by х + а . As ...
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An Elementary Treatise on Algebra: Theoretical and Practical Horatio Nelson Robinson No preview available - 2016 |
Common terms and phrases
2d power 3d term 4th power added algebraic arithmetical arithmetical mean arithmetical series assumed binomial square cent Clearing of fractions coefficients common difference Completing the square compound interest compound quantity cube root cubic equation distance Divide the number dividend division divisor dollars equa equal roots equation becomes EXAMPLES Expand exponents factors find the values following rule four numbers fourth fraction will produce geometrical progression geometrical series give greater greatest common measure Hence improper fraction last term least common multiple less letter logarithm lowest terms method miles mixed quantity moon number of terms numbers in geometrical Observe operation primitive equation principle problem produce the series quadratic equations quotient remainder represent Required resolved second power shillings simple equations solution square root substitute subtract suppose Theorem third three numbers tion Transpose unknown quantity unknown term whole numbers
Popular passages
Page 11 - If equal quantities be divided by the same, or by equal quantities, the quotients will be equal. 5. If the same quantity be both added to and subtracted from another, the value of the latter will not be altered.
Page 33 - To reduce a mixed quantity to an improper fraction, multiply the integer by the denominator of...
Page 195 - There are four numbers in geometrical progression, the second of which is less than the fourth by 24 ; and the sum of the extremes is to the sum of the means as 7 to 3. What are the numbers?
Page 184 - If the sum of an arithmetical series is 567, the first term 7, and the common difference 2; what is the number of terms?
Page 202 - There are two numbers, which are to each other, as 16' to 9, and 24 is a mean proportional between them. What are the numbers ? Ans. 32 and 18. 13. The sum of two numbers is to their difference as 4 to 1, and the sum of their squares is to the greater as 102 to 5. What are the numbers 1 Ans.
Page 145 - Prob. 9. It is required to divide the number 18 into two such parts, that the squares of those parts may be to each other as 25 to 16.
Page 42 - Multiply each numerator into all the denominators except its own for a new numerator, and all the denominators together for a common denominator.
Page 155 - Any trinomial can be separated into two binomial factors, when the extremes are squares and positive, and the middle term is twice the product of the square roots of the extremes.
Page 191 - When three magnitudes, a, b, c, have the relation of a: c: : a—b : b—c ; that is, the first is to the third as the difference between the first and second is to the difference between the second and third, the quantities a, b, c, are said to be in harmonical proportion.
Page 143 - A and B, set out to meet each other; A leaving the town C at the same time that B left D. They travelled the direct road...