#$&* course Mth 158 8/29 1 001. `* 1
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Given Solution: * * ** Counting numbers are the numbers 1, 2, 3, .... . None of the given numbers are counting numbers Rational numbers are numbers which can be expressed as the ratio of two integers. 1/2+10.3 are rational numbers. Irrational numbers are numbers which can be expressed as the ratio of two integers. {-sqrt(2)}, pi+sqrt(2) are irrational numbers.. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ok ------------------------------------------------ Self-critique Rating: ok ********************************************* Question: * R.1.44 \ 32 (was R.1.24) Write in symbols: The product of 2 and x is the product of 4 and 6 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 2*x=4*6 confidence rating #$&*: 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): ok ------------------------------------------------ Self-critique Rating: ok ********************************************* Question: *R.1.62 \ 50 (was R.1.42) Explain how you evaluate the expression 2 - 5 * 4 - [ 6 * ( 3 - 4) ] YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: start with 2 - 5 * 4 - [ 6 * ( 3 - 4) ] and solve the parentheses within the brackets first (don't even bother with even looking at the part outside the brackets yet) you get 2 - 5 * 4 - [ 6 * -1 ] then solve what's left in the brackets so 2 - 5 * 4 - -6 the double negative becomes a positive, so the equation becomes 2 - 5 * 4 +6. Then you start with the multiplication part, so 2 - 20+6 and that will = -12 confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: * * **Starting with 2-5*4-[6*(3-4)]. First you evaluate the innermost group to get 2-5*4-[6*-1] . Then multiply inside brackets to get 2-5*4+6. Then do the multiplication to get 2-20+6. Then add and subtract in order, obtaining -12. ** * R.1.98 \ 80 (was R.1.72) Explain how you use the distributive property to remove the parentheses from the express (x-2)(x-4). YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: (x-2)(x-4) you will multiply (x-4) by x as well as -2 so it'll look like x(x-4)-2(x-4). Then you basically have two easier distributive problems. So x(x-4)=x^2-4x and -2(x-4)=-2x+8 though the problems aren't actually separate so after you do that, the equation looks like x^2-4x-2x+8, and then you can simplify that to x^2-6x+8 confidence rating #$&*: 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: the 1st version of the problem you do what's in the parentheses before you can do anything else. So (4+3)/(2+5) would = 7/7 = 1 so in a way you were dealing with or simplifying one fraction 2nd version is done by order of operations, so (4/2)+ (3/5) = 2+.6= 2.6 confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: * * ** Good answer but at an even more fundamental level it comes down to order of operations: (4+3)/(2+5) means 7/7 which is equal to 1. By order of operations, in which multiplications and divisions precede additions and subtractions, 4/2+3/5 means (4/2) + (3/5), which gives us 2+3/5 = 2 3/5 * Add comments on any surprises or insights you experienced as a result of this assignment. " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: ********************************************* Question: * R.1.102 \ 86 (was R.1.78) Explain why (4+3) / (2+5) is not equal to 4/2 + 3/5. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: the 1st version of the problem you do what's in the parentheses before you can do anything else. So (4+3)/(2+5) would = 7/7 = 1 so in a way you were dealing with or simplifying one fraction 2nd version is done by order of operations, so (4/2)+ (3/5) = 2+.6= 2.6 confidence rating #$&*: 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. " 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: the 1st version of the problem you do what's in the parentheses before you can do anything else. So (4+3)/(2+5) would = 7/7 = 1 so in a way you were dealing with or simplifying one fraction 2nd version is done by order of operations, so (4/2)+ (3/5) = 2+.6= 2.6 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. " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!#*&!