The student's algebra |
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Page 14
... in common Arithmetic , is the reverse of Multiplication , and is commonly divided into three cases . CASE I. When the quantities are both simple . RULE . - Divide the coefficient of the dividend , 14 MULTIPLICATION . Division.
... in common Arithmetic , is the reverse of Multiplication , and is commonly divided into three cases . CASE I. When the quantities are both simple . RULE . - Divide the coefficient of the dividend , 14 MULTIPLICATION . Division.
Page 15
... Divide 12axy by 4x . 4x ) 12axy 3ay 3. Divide x by -x . x 12axy or -3ay . 4.x 4. Divide -X -1 . 2a2x2 4x by бах ах Here бах ах 2a2x2 4x2a2x2 ах 2a3x3 a2x X = бах 4x 20ax2 10 2x 4x2 5. Divide - by 3 5a 2x 5a 10ах ба Here = ( as in ...
... Divide 12axy by 4x . 4x ) 12axy 3ay 3. Divide x by -x . x 12axy or -3ay . 4.x 4. Divide -X -1 . 2a2x2 4x by бах ах Here бах ах 2a2x2 4x2a2x2 ах 2a3x3 a2x X = бах 4x 20ax2 10 2x 4x2 5. Divide - by 3 5a 2x 5a 10ах ба Here = ( as in ...
Page 16
... Divide 15xyz by 3xyzễ . 3. Divide -27a2x3 by 9ax2 . 4. Divide 56ax by -8ax . 2a 3.x 5. Divide by 4x 4a CASE II . 1 Ans . 3r . Ans . 5+ Ans . - 3ax . Ans . —7a * x * 2a2 Ans . 3x2 When the dividend is a compound quantity , and the ...
... Divide 15xyz by 3xyzễ . 3. Divide -27a2x3 by 9ax2 . 4. Divide 56ax by -8ax . 2a 3.x 5. Divide by 4x 4a CASE II . 1 Ans . 3r . Ans . 5+ Ans . - 3ax . Ans . —7a * x * 2a2 Ans . 3x2 When the dividend is a compound quantity , and the ...
Page 17
... Divide x by a + z . Here ( by note ) x a + z the quotient . EXAMPLES FOR PRACTICE . 1. Divide 4x2 + 6xy by 2x . Ans . 2x + 3y . - Ans . 2y + xy — 5z . 2. Divide 12xy2- 6x2y2 + 30xyz by - 6xy . 6ax - 3a2x2 - 15a3x3 by -3ax . 3. Divide x ...
... Divide x by a + z . Here ( by note ) x a + z the quotient . EXAMPLES FOR PRACTICE . 1. Divide 4x2 + 6xy by 2x . Ans . 2x + 3y . - Ans . 2y + xy — 5z . 2. Divide 12xy2- 6x2y2 + 30xyz by - 6xy . 6ax - 3a2x2 - 15a3x3 by -3ax . 3. Divide x ...
Page 18
... Divide x3 - 3x2y + 3xy2 — y3 by x - y . x — y ) x3 - 3x2y + 3xy2 — y3 ( x2 — 2xy + y2 x3- x2y -2x2y + 3xy2 -2xy + 2xy xy2 - y3 xy2 y3 In this example the terms are arranged according to the rule , beginning with x3 . 1. The first term ...
... Divide x3 - 3x2y + 3xy2 — y3 by x - y . x — y ) x3 - 3x2y + 3xy2 — y3 ( x2 — 2xy + y2 x3- x2y -2x2y + 3xy2 -2xy + 2xy xy2 - y3 xy2 y3 In this example the terms are arranged according to the rule , beginning with x3 . 1. The first term ...
Common terms and phrases
5th power added Algebra Algebraist answer the conditions arithmetical progression axiom bushels coefficient completing the square compound quantity cube root denominator difference digits dividend divisor equa EXAMPLES FOR PRACTICE extracting the root extracting the square find the values Find two numbers four numbers four quantities fourth power gained gallons geometrical progression given equation hence least common multiple lues miles multiplying this equation number of yards Pure Quadratics QUADRATIC EQUATIONS quan quantities be proportionals question quired quotient radical sign ratio remainder Required each person's Required the cube Required the length Required the number Required the price Required the sides Required the square second equation second term shillings Simple Equations simple quantity sold solution square root squaring each side substituting this value subtracted surd quantity Theorem third three numbers transposing transposition unknown quantity values of x vulgar fraction whence whole number yards of silk
Popular passages
Page 13 - If four magnitudes are in proportion, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.
Page 11 - Ratio is the relation which one quantity bears to another in respect of magnitude, the comparison being made by considering what multiple, part, or parts, one is of the other.
Page 14 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.
Page 79 - Prob. 3. Find two numbers, the greater of which shall be to the less, as their sum to 42 ; and as their difference to 6.
Page 13 - If the first magnitude be the same multiple of the second that the third is of the fourth, and the fifth the same multiple of the second that the sixth is of the fourth...
Page 40 - Sib., his head weighs as much as his tail and half his body, and his body weighs as much as his head and his tail ; what is the whole weight of the fish ? . Aas.
Page 13 - In any proportion, the product of the means is equal to the product of the extremes.
Page 13 - Composition, when the sum of the first and second is to the second as the sum of...
Page 80 - A farmer with 28 bushels of barley at 2s. 4d. per bushel, would mix rye at 3 shillings per bushel, and wheat at 4 shillings per bushel, so that the whole mixture may consist of 100 bushels, and be worth 3s. 4d. per bushel. How many bushels of rye, and how many of wheat must he mix with the barley ? Ans.