#$&* course Mth 158 Tues, Jan 27th, 700pm If your solution to stated problem does not match the given solution, you should self-critique per instructions at http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm.
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Given Solution: * * ** Counting numbers are the numbers 1, 2, 3, .... . None of the given numbers are counting numbers Rational numbers are numbers which can be expressed as the ratio of two integers. 1/2+10.3 are rational numbers. Irrational numbers are numbers which can be expressed as the ratio of two integers. {-sqrt(2)}, pi+sqrt(2) are irrational numbers.. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique Rating: ********************************************* Question: * R.1.44 \ 32 (was R.1.24) Write in symbols: The product of 2 and x is the product of 4 and 6 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 2x=4x6 confidence rating #$&*: I was confident with this, but is it ok to write 2x instead of 2*x ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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): ------------------------------------------------ Self-critique Rating: ********************************************* Question: * R.1.62 \ 50 (was R.1.42) Explain how you evaluate the expression 2 - 5 * 4 - [ 6 * ( 3 - 4) ] YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: Order of operations, Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction. In this case you would start with the inner most parenthesis even though you are subtracting. 3-4 = -1 6*-1 = -6 2-20-(-6) -12 confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: * * **Starting with 2-5*4-[6*(3-4)]. First you evaluate the innermost group to get 2-5*4-[6*-1] . Then multiply inside brackets to get 2-5*4+6. Then do the multiplication to get 2-20+6. Then add and subtract in order, obtaining -12. ** ********************************************* Question: * R.1.98 \ 80 (was R.1.72) Explain how you use the distributive property to remove the parentheses from the express (x-2)(x-4). YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: With the distributive property, you take the first set of parenthesis and multiply then by the second set. x(x-4)-2(x-4), then multiply x^2-4x-2x-8; then combine like terms. Giving an answer of x^2-6x+8 confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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): ------------------------------------------------ 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: Because of the order of operations, the first problem you would complete the addition first because they are in parenthesis 4+3= 7, and 2+5=7 7/7=1; The second problem is a fraction 4/2 + 3/5 = 7/10 confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ I am confused on the second question, I am not sure if it is because of the way it is written on the computer or what. To me it looks like a fraction but I see in the solution it was put in parenthesis. So my answer was incorrect. Also, in your answer one says 2+3/4 Can you explain this to me. Thanks.
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Given Solution: * * ** Good answer but at an even more fundamental level it comes down to order of operations: (4+3)/(2+5) means 7/7 which is equal to 1. By order of operations, in which multiplications and divisions precede additions and subtractions, 4/2+3/5 means (4/2) + (3/5), which gives us 2+3/5 = 2 3/5 * Add comments on any surprises or insights you experienced as a result of this assignment. I am surprised at how much of this came back to me as I was reviewing this material. " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: ********************************************* Question: * R.1.102 \ 86 (was R.1.78) Explain why (4+3) / (2+5) is not equal to 4/2 + 3/5. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: Because of the order of operations, the first problem you would complete the addition first because they are in parenthesis 4+3= 7, and 2+5=7 7/7=1; The second problem is a fraction 4/2 + 3/5 = 7/10 confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ I am confused on the second question, I am not sure if it is because of the way it is written on the computer or what. To me it looks like a fraction but I see in the solution it was put in parenthesis. So my answer was incorrect. Also, in your answer one says 2+3/4 Can you explain this to me. Thanks.
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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 am surprised at how much of this came back to me as I was reviewing this material. " 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: Because of the order of operations, the first problem you would complete the addition first because they are in parenthesis 4+3= 7, and 2+5=7 7/7=1; The second problem is a fraction 4/2 + 3/5 = 7/10 confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ I am confused on the second question, I am not sure if it is because of the way it is written on the computer or what. To me it looks like a fraction but I see in the solution it was put in parenthesis. So my answer was incorrect. Also, in your answer one says 2+3/4 Can you explain this to me. Thanks.
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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 am surprised at how much of this came back to me as I was reviewing this material. " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!#*&!