#$&* course Mth 158 1/25/13 4:45PM????? I have a question. On the assignments page :
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Given Solution: * * ** Counting numbers are the numbers 1, 2, 3, .... . None of the given numbers are counting numbers Rational numbers are numbers which can be expressed as the ratio of two integers. 1/2+10.3 are rational numbers. Irrational numbers are numbers which can be expressed as the ratio of two integers. {-sqrt(2)}, pi+sqrt(2) are irrational numbers.. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* Question: * R.1.44 \ 32 (was R.1.24) Write in symbols: The product of 2 and x is the product of 4 and 6 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 2x = 4 * 6 2x = 24 2x/2 = 24/2 x = 12 confidence rating #$&*: 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 know I didn't need to solve it, but I felt weird just leaving it like that.
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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) x (x - 4) - 2 (x - 4) x^2 - 4x - 2x - 8 x^2 - 6x - 8 confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: * * ** COMMON ERROR: Using FOIL. FOIL is not the Distributive Law. FOIL works for binomial expressions. FOIL follows from the distributive law but is of extremely limited usefulness and the instructor does not recommend relying on FOIL. Starting with (x-2)(x-4) ; one application of the Distributive Property gives you x(x-4) - 2(x-4) . Applying the property to both of the other terms we get x^2 - 4x - (2x -8). Simplifying: x^2 - 4x - 2x + 8 or x^2 - 6x + 8. * &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* Question: * R.1.102 \ 86 (was R.1.78) Explain why (4+3) / (2+5) is not equal to 4/2 + 3/5. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: When there is a division bar between two expressions like (4+3) / (2+5) is is understood that you act as if there are parentheses around them and solve the addition first, before dividing. 4/2 and 3/5 are not connected by a division bar, the two rational numbers are separated by a plus sign, signifying the addition of both fractions. They both require different orders to solve them. One is dividing the sums of two expressions, the other is adding the quotients of two expressions. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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. I'm looking forward to memorizing/learning all the orders of operations and principles and properties and whatnot better than I do now, so I don't get so confused when people try to explain why something does what it does. I kind of feels good to be doing math again. I didn't do any last semester. (my first semester at the college.)" 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: When there is a division bar between two expressions like (4+3) / (2+5) is is understood that you act as if there are parentheses around them and solve the addition first, before dividing. 4/2 and 3/5 are not connected by a division bar, the two rational numbers are separated by a plus sign, signifying the addition of both fractions. They both require different orders to solve them. One is dividing the sums of two expressions, the other is adding the quotients of two expressions. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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. I'm looking forward to memorizing/learning all the orders of operations and principles and properties and whatnot better than I do now, so I don't get so confused when people try to explain why something does what it does. I kind of feels good to be doing math again. I didn't do any last semester. (my first semester at the college.)" Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!