## Eaton's Elementary Algebra, Designed for the Use of High Schools and AcademiesThompson, Brown, and Company, 1875 |

### From inside the book

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Page 60

... ties is divided by their greatest common divisor , the

... ties is divided by their greatest common divisor , the

**quotient**will be their least common multiple . Hence , to find the least common multiple of any two quantities , 4 RULE . Divide one of the quantities by their 60 ELEMENTARY ALGEBRA . Page 61

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**quotient**by the other quantity , and the product will be their least common multiple . - NOTE 1. If the least common multiple of more than two quanti- ties is required , find the least common multiple of two of them , then of this ... Page 63

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**quotient**arising from dividing the numerator by the denominator . xy y Thus , is a fraction whose numerator is xy and denominator y , and whose value is x . 83. The principles upon which the operations in frac- tions are carried on are ... Page 65

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**quotients**by any factor common to them ; and so proceed till the terms are mutually prime . Or , Divide both terms by their greatest common divisor . axy to its lowest terms . xys a Ans . 2. Reduce xy 2 x 272 a2 x2 y2 3. Reduce to its ... Page 66

... nominator , by multiplying its numerator and denominator by the

... nominator , by multiplying its numerator and denominator by the

**quotient**arising from dividing this multiple by its denominator . Hence , RULE . Multiply all the denominators together for a common 66 ELEMENTARY ALGEBRA .### Other editions - View all

### Common terms and phrases

2ab+b² a b c a²x² added Algebra arithmetical mean arithmetical progression binomial cents coefficient cologarithm common difference completing the square cube root Divide dividend division dollars elimination equal examples Expand exponent extracting the square fifth figures Find the cube Find the factors Find the fourth Find the greatest Find the least Find the square Find the sum Find the value Find two numbers geometrical progression greatest common divisor Hence horse improper fraction integral quantity least common multiple less logarithm mantissa minus monomial Multiply negative NOTE number of terms obtain OPERATION polynomial proportion quadratic equation quan quotient radical sign ratio reduced gives remainder second term square root Substituting this value subtracted Theorem third tities Transposing trial divisor twice unknown quantity x² y²

### Popular passages

Page 207 - An INVERSE, or RECIPROCAL RATIO, of any two quantities is the ratio of their reciprocals. Thus, the direct ratio of a to b is a : b...

Page 10 - In reducing the equation so as to find the value of the unknown quantities. EXAMPLES FOR PRACTICE. 1. The sum of the ages of a father and his son is 60 years, and the age of the father is double that of the son ; what is the age of each...

Page 44 - ... the square of the second. In the second case, we have (a — &)2 = a2 — 2 ab + b2. (2) That is, the square of the difference of two quantities is equal to the square of the first, minus twice the product of the two, plus the square of the second.

Page 83 - ... quantity. 4. If one member is divided by any quantity, the other member must be divided by an equal quantity. 5. If one member is involved or evolved, the other must be involved or evolved to the same degree. TRANSPOSITION. 100. TRANSPOSITION is the changing of terms from one member of an equation to the other, without destroying the equality.

Page 155 - Resolve the quantity under the radical sign into two factors, one of which is the greatest perfect power of the same degree as the radical.

Page 45 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — b) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.

Page 207 - PROPORTION when the ratio of the first to the second is equal to the ratio of the second to the third.

Page 87 - Four quantities are proportional when the ratio of the first to the second is equal to the ratio of the third to the fourth.

Page 43 - I. The square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second.

Page 251 - How far from Boston did they meet ? Ans. 42 miles. 163. The product of two numbers is 90 ; and the difference of their cubes is to the cube of their difference as 13 : 3. What are the numbers? 164. A and B start together from the same place and travel in the same direction. A travels the first day 25 kilometers, the second 22, and so on, travelling each day 3 kilometers less than on the preceding day, while B travels 14£ kilometers each day. In what time will the two be together again ? Ans. 8 days.