## 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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added addition algebraic apples arithmetical becomes bought bushels called cents changed coefficient consists containing cost denominator denotes difference distance Divide dividend division dollars elimination entire equal equation evident exactly example exponent expressed factors figures Find Find the square Find the sum find the value four fourth fraction given gives greater greatest common divisor half Hence hour illustrate increased James lemons less letter manner means method miles minus monomial Multiply necessary negative obtained operation oranges perfect square person piece polynomial positive pound preceding prime principle problem proportion pupil question quotient radical ratio Reduce remainder represent required to find result rule second degree separated share shows sides similar solution solving square root substitution subtracted suppose taken third tion twice units unknown quantity whole 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.