course Mth 158 5/28 6 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 #$&* ********************************************* Question: * R.1.44 \ 32 (was R.1.24) Write in symbols: The product of 2 and x is the product of 4 and 6 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 2 * X = 4 * 6 confidence rating #$&* 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 #$&* ********************************************* Question: * R.1.62 \ 50 (was R.1.42) Explain how you evaluate the expression 2 - 5 * 4 - [ 6 * ( 3 - 4) ] YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: I refreshed my memory of this particular assignment during orientation. The way I recall how to perform the order of operations is Please Excuse My Dear Aunt Sally. Though this method may seem elementary, it never fails to work and I’m always able to recall it. Basically, one would follow the steps. P- parenthesis, E- exponents, M- multiplication, D- division, A- addition, S- subtraction. Therefore, in the following expression 2 - 5 * 4 - [ 6 * ( 3 - 4) ], the first step would be (3-4) which yields -1. Then -1*6 which yields -6. Then 5*4, which is 20, and then it is important to work from left to right. 2-20 + 6 is our remaining expression. Working left from right, 2 – 20 = -18 + 6 which is -12 as the final answer. confidence rating #$&* 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: The more patronized way of removing parenthesis by distribution is probably FOIL- first, outer, inner, last. However, I always seem to make an error while doing that process- therefore, I remove the parentheses by simply multiplying out the problems (which, in its own way is FOIL, ((I just don’t like to recognize it)) ) (x-2)(x-4) First, multiply the first x by the second x, which yields x squared. Then multiply x by -4, which is -4x, then multiply -2 by x, which is -2x, and finally multiply -2 by -4, which is +8. Altogether our problem is= x squared -4x + -2x + 8. Simplified we have= x squared -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): Looks like my fear of FOIL paid off!!!
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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. "