#$&* course Mth158 6/18/13 11:14 amI just received my book, and will try to catch up as soon as I can. If your solution to stated problem does not match the given solution, you should self-critique per instructions at http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm.
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Given Solution: * * ** Counting numbers are the numbers 1, 2, 3, .... . None of the given numbers are counting numbers Rational numbers are numbers which can be expressed as the ratio of two integers. 1/2+10.3 are rational numbers. Irrational numbers are numbers which can be expressed as the ratio of two integers. {-sqrt(2)}, pi+sqrt(2) are irrational numbers.. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* Question: * R.1.44 \ 32 (was R.1.24) Write in symbols: The product of 2 and x is the product of 4 and 6 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: ( ""Product"" indicates multiplication while ""is"" indicates the expressions are equal ) The result is: 2x = 4 * 6 confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: * * ** The product of 2 and x is 2 * x and the product of 4 and 6 is 4 * 6. To say that these are identical is to say that 2*x=4*6. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I did not write out the multiplication sign between the 2 and the x; I do not think it is necessary, but it adds more clarification. ------------------------------------------------ Self-critique Rating: 3 ********************************************* Question: * R.1.62 \ 50 (was R.1.42) Explain how you evaluate the expression 2 - 5 * 4 - [ 6 * ( 3 - 4) ] YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 2 - 5 * 4 - [ 6 * ( 3 - 4 ) ] = 2 - 5 * 4 - [ 6 * (-1) ] = (You must begin with the grouped expressions, starting with the innermost and working your way out) 2 - 5 * 4 - (-6) = (Multiplication is worked next) 2 - 20 - (-6) = 2- 20 + 6 = (subtraction of a negative number is the same as adding it as a positive number) -18 + 6 = -12 confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: * * **Starting with 2-5*4-[6*(3-4)]. First you evaluate the innermost group to get 2-5*4-[6*-1] . Then multiply inside brackets to get 2-5*4+6. Then do the multiplication to get 2-20+6. Then add and subtract in order, obtaining -12. ** ********************************************* Question: * R.1.98 \ 80 (was R.1.72) Explain how you use the distributive property to remove the parentheses from the express (x-2)(x-4). YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: (x-2)(x-4) First you multiply the beginning elements making the first element in the product x^2 Next you multiply the outer elements (x*-4) making the second element in the product -4x You also multiply the inner elements (-2*x) making the third element in the product -2x Then the last elements in each expression are multiplied (-2*-4) resulting in -8 This leaves the product = x^2 - 4x -2x -8 = x^2 -6x -8 confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: * * ** COMMON ERROR: Using FOIL. FOIL is not the Distributive Law. FOIL works for binomial expressions. FOIL follows from the distributive law but is of extremely limited usefulness and the instructor does not recommend relying on FOIL. Starting with (x-2)(x-4) ; one application of the Distributive Property gives you x(x-4) - 2(x-4) . Applying the property to both of the other terms we get x^2 - 4x - (2x -8). Simplifying: x^2 - 4x - 2x + 8 or x^2 - 6x + 8. * &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I understand how you distributed it this way. ???? This is basically what FOIL does though, right? Is it okay if we think of it with the FOIL method on binomial problems? It seems to simplify the process for me mentally to be able to think of it that way. I do see that it is limited with the multiplication of larger expressions, however. ------------------------------------------------ Self-critique Rating: 2
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Given Solution: * * ** Good answer but at an even more fundamental level it comes down to order of operations: (4+3)/(2+5) means 7/7 which is equal to 1. By order of operations, in which multiplications and divisions precede additions and subtractions, 4/2+3/5 means (4/2) + (3/5), which gives us 2+3/5 = 2 3/5 * Add comments on any surprises or insights you experienced as a result of this assignment. " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: ********************************************* Question: * R.1.102 \ 86 (was R.1.78) Explain why (4+3) / (2+5) is not equal to 4/2 + 3/5. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: Although they appear to be very similar, they are not. The first problem is dominantly a division problem, where the 4+3 and the 2+5 must be worked first. The problem becomes 7 over 7 = 1. This is very different from the other problem. There are no groupings to be worked out first, but the denominators must be changed in order to add. The common denominator is found to be ten. When changing the problem to reflect this we are left with 8/10 + 6/10 =(8 + 6)/10 = 14/10 = 7/5 1 is not equal to 7/5. Working out these problems helps to more clearly define their differences, although they may at first appear to be nearly identical. confidence rating #$&*: 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: * * ** Good answer but at an even more fundamental level it comes down to order of operations: (4+3)/(2+5) means 7/7 which is equal to 1. By order of operations, in which multiplications and divisions precede additions and subtractions, 4/2+3/5 means (4/2) + (3/5), which gives us 2+3/5 = 2 3/5 * Add comments on any surprises or insights you experienced as a result of this assignment. " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!