Ray's Algebra, Part First: On the Analytic and Inductive Methods of Instruction, with Numerous Practical Exercises, Designed for Common Schools and Academies, Part 1 |
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Page 7
... equal to 15 , then 1x or x is equal to 5 . The learner will see that the two methods of solving this ques- tion are the same in principle ; but that it is more convenient to represent the quantity we wish to find , by a single letter ...
... equal to 15 , then 1x or x is equal to 5 . The learner will see that the two methods of solving this ques- tion are the same in principle ; but that it is more convenient to represent the quantity we wish to find , by a single letter ...
Page 8
... equal to 12 ; hence if 2x is equal to 12 , one x , which is the half of 2x , is equal to the half of 12 , which is 6 . VERIFICATION . - 6 added to 6 makes 12 . 3. What number added to itself will make 16 ? If a represents the number ...
... equal to 12 ; hence if 2x is equal to 12 , one x , which is the half of 2x , is equal to the half of 12 , which is 6 . VERIFICATION . - 6 added to 6 makes 12 . 3. What number added to itself will make 16 ? If a represents the number ...
Page 9
... equal to 18 , what is x equal to ? Why ? NOTE . If the pupil does not readily perceive how to solve a question , let the instructor ask questions similar to the preceding . 2. A travels a certain distance one day , and twice as far the ...
... equal to 18 , what is x equal to ? Why ? NOTE . If the pupil does not readily perceive how to solve a question , let the instructor ask questions similar to the preceding . 2. A travels a certain distance one day , and twice as far the ...
Page 10
... equal to 24 , what is the value of x ? What is the share of the second ? Of the third ? VERIFICATION . - The first ... equal to twice the first , and the third is equal to three times the first ; what are the numbers ? 3. There are three ...
... equal to 24 , what is the value of x ? What is the share of the second ? Of the third ? VERIFICATION . - The first ... equal to twice the first , and the third is equal to three times the first ; what are the numbers ? 3. There are three ...
Page 12
... equal to twice the smaller , and the sum of the larger and twice the smaller is equal to 28 ; what are the numbers ? 3. Thomas bought 5 apples and 3 peaches for 22 cents ; each peach cost twice as much as an apple ; what was the cost of ...
... equal to twice the smaller , and the sum of the larger and twice the smaller is equal to 28 ; what are the numbers ? 3. Thomas bought 5 apples and 3 peaches for 22 cents ; each peach cost twice as much as an apple ; what was the cost of ...
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Common terms and phrases
acre added algebraic quantities apples arithmetical progression arithmetical series binomial Binomial Theorem bought bushels coefficient common difference complete equation Completing the square cost Divide the number dividend division dollars entire quantity equal EQUATIONS CONTAINING exactly divide exponent expressed extract the square Find a number Find the cube Find the product Find the square Find the sum find the value following examples fraction geometrical progression geometrical series Give an example greater greatest common divisor Hence least common multiple lemons less number letter minus monomial negative quantity number of places number of terms oranges perfect square polynomial positive quantity preceding principle proportion pupil quan question quotient radical sign ratio reduced remainder represent the number required the numbers required to find result second degree second power solution solving square root three numbers tities Transposing twice unknown quantity whole number yards
Popular passages
Page 60 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Page 106 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Page 178 - Multiply the divisor, thus increased, by the last figure of the root; subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Page 235 - In any proportion the product of the means is equal to the product of the extremes.
Page 124 - A hare is 50 leaps before a greyhound, and takes 4 leaps to the greyhound's 3 ; but 2 of the greyhound's leaps are equal to 3 of the hare's ; how many leaps must the greyhound take to catch the hare ? Let x be the number of leaps taken by the hound.
Page 217 - If, then, any problem furnishes an equation in which the known term is negative, and greater than the square of half the coefficient of the first power of the unknown quantity, we infer, that the conditions of the problem are incompatible with each other.
Page 64 - That is, 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 81 - The least Common Multiple of two or more quantities is the least quantity that will contain them exactly. Thus, 6 is the least common multiple of 2 and 3 ; and lOxy is the least common multiple of 2x and by. NOTE. — LCM stands for least common multiple.
Page 232 - If we compare the numbers 2 and 6, by the first method, we say that 2 is 4 less than 6, or that 6 is 4 greater than 2. If we compare 2 and 6 by the second method, we say that 6 is equal to three times 2, or that 2 is one third of 6.