Algebra for Beginners |
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Page 2
... sometimes convenient to consider any factor , or factors , of a product as the coefficient of the remaining factors . Thus in the product 6ube , 6a may be appropriately called the coefficient of bc . A coefficient which is not merely ...
... sometimes convenient to consider any factor , or factors , of a product as the coefficient of the remaining factors . Thus in the product 6ube , 6a may be appropriately called the coefficient of bc . A coefficient which is not merely ...
Page 6
... sometimes be advisable to add short verbal explanations ; the importance of this will be seen later . EXAMPLES I. c . If a = 4 , b = 1 , c = 3 , ƒ = 5 , g = 7 , h = 0 , find the value of 1. 3f + 5h - 7b . 4. 3g - 4h + 7c . 2. 7c - 9h + ...
... sometimes be advisable to add short verbal explanations ; the importance of this will be seen later . EXAMPLES I. c . If a = 4 , b = 1 , c = 3 , ƒ = 5 , g = 7 , h = 0 , find the value of 1. 3f + 5h - 7b . 4. 3g - 4h + 7c . 2. 7c - 9h + ...
Page 31
... sometimes better to express this last result as a frac- tion ; thus dividend = quotient . Example 1 . divisor Since the product of 4 and x is 4x , it follows that when 4x is divided by x the quotient is 4 , or otherwise , 4x ÷÷ x = 4 ...
... sometimes better to express this last result as a frac- tion ; thus dividend = quotient . Example 1 . divisor Since the product of 4 and x is 4x , it follows that when 4x is divided by x the quotient is 4 , or otherwise , 4x ÷÷ x = 4 ...
Page 38
... sometimes enclosed within brackets to indicate that they must all be operated upon in the same way . Thus in the expression 2a - 3b- ( 4a - 2b ) the brackets indicate that the expression 4a - 2b treated as a whole has to be sub- tracted ...
... sometimes enclosed within brackets to indicate that they must all be operated upon in the same way . Thus in the expression 2a - 3b- ( 4a - 2b ) the brackets indicate that the expression 4a - 2b treated as a whole has to be sub- tracted ...
Page 39
... -2 . Then before multiply- ing by 3 , the expression within its bracket is simplified . The other steps will be easily seen . 58. Sometimes a line called a vinculum is drawn over CHAP . VII . ] 39 REMOVAL OF BRACKETS .
... -2 . Then before multiply- ing by 3 , the expression within its bracket is simplified . The other steps will be easily seen . 58. Sometimes a line called a vinculum is drawn over CHAP . VII . ] 39 REMOVAL OF BRACKETS .
Common terms and phrases
a²+b² acres algebraical sum Arithmetic arranged beginner cents CHAPTER coefficient Completing the square compound expressions convenient cube root descending powers difference digits dimes Divide division divisor Elementary Algebra equal examples see Elementary EXAMPLES XVII exceeds Find the highest Find the lowest find the number Find the product Find the square Find the sum find the value following expressions given expressions half-dollars Hence highest common factor lowest common denominator lowest common multiple lowest terms miles an hour miles per hour minute-hand Multiply negative numerator and denominator obtain quadratic equation quotient Reduce to lowest remainder removing brackets Resolve into factors result rule of signs side simple equation simultaneous equations Solve the equations square root Subtract Transposing trinomial unknown quantities walk whence write yards α α
Popular passages
Page 91 - The product is a2+2a6-}-62; from which it appears, that 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 107 - Conversely, the difference of the squares of any two quantities is equal to the product of the sum and the difference of the two quantities.
Page 89 - It is evident from the Rule of Signs that (1) no even power of any quantity can be negative; (2) any odd power of a quantity will have the same sign as the quantity itself. NOTE. It is especially worthy of notice that the square of every expression, whether positive or negative, is positive.
Page 54 - Transpose all the terms containing the unknown quantity to one side of the equation, and the "known quantities to the other.