(c) How far does a body fall from a state of rest in of a second? (d) On the surface of the moon, how far does a body fall from a state of rest in 3 seconds, if g = 5.4 ft. ? 8. If F denotes the number of degrees of temperature indicated on the Fahrenheit scale, the equivalent reading C on the Centigrade scale may be found by the formula C=5(F— 32). Change the following readings to Centigrade readings: (a) 100° F. (b) 32° F. (c) 5° F. CHAPTER II ADDITION, SUBTRACTION, AND PARENTHESES ADDITION OF MONOMIALS 31. While in arithmetic the word sum refers only to the result obtained by adding positive numbers, in algebra this word includes also the results obtained by adding negative, or positive and negative numbers. In arithmetic we add a gain of $6 and a gain of $4, but we cannot add a gain of $6 and a loss of $4. In algebra, however, we call the aggregate value of a gain of 6 and a loss of 4 the sum of the two. Thus a gain of $2 is considered the sum of a gain of $6 and a loss of $4. Or in the symbols of algebra (+$6) + (− $4) = + $2. Similarly, the fact that a loss of $6 and a gain of $4 equals a loss of $2, may be represented thus (− $6) + (+$4) = ( − $ 2). In a corresponding manner we have for a loss of $6 and a loss of $4 (− $6) + (− $ 4) = (— $ 10). Since similar operations with different units always produce analogous results, we define the sum of two numbers in such a way that these results become general, or that and 6 + (−4) = +2, 1 (+6) + (+ 4) = +10. 32. These considerations lead to the definition of addition: If two numbers have the same sign, add their absolute values; if they have opposite signs, subtract their absolute values and (always) prefix the sign of the greater. In Exs. 23-26, find the numerical value of a+b+c+d, if: 23. a=1, b=-2, c=-4, d = 6. 27. What number must be added to 3 to give 7? 28. What number must be added to 7 to give 3? 30. What number must be added to -3 to give - 7? 31. Add 4 yards, 7 yards, and 3 yards. 32. Add 4 a, 7 a, and 3 a. 33. Add 4 a bx, 7 a2bx, and 3 a2bx. 33. Similar or like terms are terms which have the same literal factors, affected by the same exponents. Dissimilar or unlike terms are terms which are not similar. 34. The sum of two similar terms is another similar term. The sum of 3 x2 and – 1⁄2 x2 is § x2. The Dissimilar terms cannot be united into a single term. sum of two such terms can only be indicated by connecting them with the + sign. 35. Algebraic sum. In algebra the word sum is used in a wider sense than in arithmetic. While in arithmetic a — b denotes a difference only, in algebra it may be considered either the difference of a and b or the sum of a and — b. |