#$&*
course Mth 151
Question: `q001. If you are earning money at the rate of 8 dollars / hour and work for 4 hours, how much money do you make during this time? Answer in such a way as to explain your reasoning as fully as possible. A solution to this problem appears several lines below, but enter your own solution before you look at the given solution.YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: (type in your solution starting in the next line)
The answer is $32. Multiplication allows a formula that lets us determine what the resulting amount would be if one were to make $8/hr every hour for four times. This adds up, or multiplies to, the answer which is 32 dollars.
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self-Critique: OK
------------------------------------------------
Self-Critique Rating: OK
*********************************************
Question: `q002. If you work 12 hours and earn $168, then at what rate, in dollars / hour, were you making money?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: (type in your solution starting in the next line)
The answer is $14 and is found using the exact reverse of the previous question. By dividing 168 equally into 12 parts we are able to determine that in order to come to the final sum of a $168 paycheck the rate of money made would have to equal $14/hr
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self-Critique: OK
------------------------------------------------
Self-Critique Rating: OK
*********************************************
Question: `q003. If you are earning 8 dollars / hour, how long will it take you to earn $72? The answer may well be obvious, but explain as best you can how you reasoned out your result.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: (type in your solution starting in the next line)
The answer is 9 hours. One can find this by already knowing that 8*9= 72 or one can use the method of division used in question 2 to determine that 72 divided equally into 8 parts equals 9.
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self-Critique: OK. I had a slight hesitation when remembering my basic multiplication, but remembering that 8*10 is 80 helped me reassure myself that 8*9 is definitely 72
------------------------------------------------
Self-Critique Rating: OK
*********************************************
Question: `q004. Calculate (8 + 3) * 5 and 8 + 3 * 5, indicating the order of your steps. Explain, as best you can, the reasons for the difference in your results.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: (type in your solution starting in the next line)
(8+3)*5=55 and 8+3*5=23. The reason we get two different answers is because of the proper order of operation which proceeds as follows: parentheses, multiplication and division from left to right, and the addition and subtraction from left to right. Because the parentheses is not a part of the second problem a different order of operations is used to solve it, and a different sum is acquired. Therefore after applying the addition in the parentheses for (8+3)=11 the simplified form of the first problem becomes 11*5=55. The second multiplies 5*3 first, and then that makes the equation 8+15=23.
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self-Critique: OK
*********************************************
Question: `q005. Calculate (2^4) * 3 and 2^(4 * 3), indicating the order of your steps. Explain, as best you can, the reasons for the difference in your results. Note that the symbol '^' indicates raising to a power. For example, 4^3 means 4 raised to the third power, which is the same as 4 * 4 * 4 = 64.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: (2^4)*3= 48 Again we begin by organizing our thought through the order of operations and simplify (2^4) to 2*2*2*2 and see that 2 cubed equals 16. From there, a simple solution is found once 16 is multiplied by 3 making the simplified form of the problem 16*3=48
2^(4*3)=4,096 By order of operations we must take care of what is inside the parenthases first, thus making the problem stand as 2^12. From here we multiply 2*2*2*2*2*2*2*2*2*2*2*2 and come to the solution of 4,096
confidence rating #$&*:because I’m hoping I counted enough two’s in my equation.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self-Critique: 3, I was unsure if I had counted the proper number of 2’s in my equation when determining a solution, but that was my only uncertainty.
*********************************************
Question: `q006. Calculate 3 * 5 - 4 * 3 ^ 2 and 3 * 5 - (4 * 3)^2 according to the standard order of operations, indicating the order of your steps. Explain, as best you can, the reasons for the difference in your results.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: 3*5-4*3^2=-21 First we recognize the squared variable, making the equation 3*5-4*9. The by order of operations we multiply first, making the equation now to be seen as 15-36, which we can then easily determine equals -21.
3*5-(4*3)^2=-129. This equation includes parentheses so we work on those first by multiplying 4*3 which equals 12. That makes the equation 3*5-(12)^2. 12 squared equals 144 and 3*5 equals 15 and that makes the equation 15-144, which using simple subtraction gives us a sum of -129
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
------------------------------------------------
Self-Critique Rating: 3, I was shaky on remembering whether or not the “^2” belonged to the 12 or to the entire equation, but I felt pretty sure it remained only with what was in the parentheses.
*********************************************
Question: `q010. If you divide a certain positive number by 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: Equal. A positive number divided by 1 keeps the number in tact.
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self-Critique: OK
*********************************************
Question: `q011. If you divide a certain positive number by a number greater than 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: The result is a number less than the certain positive number. A number divided between two or more things becomes less than the original quantity. For Example, 8/2=4. 4 is less than the original number of 8.
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self-Critique: OK
*********************************************
Question: `q012. If you divide a certain positive number by a positive number less than 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: Trick question. There is no positive number less than 1. Some may say zero is, but it is actually neither positive or negative.
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self-Critique: 1. This is not the solution given on the worksheet, however I do not agree with the given answer as I cannot think of a positive number that is less than 1. Perhaps I do not understand this area of math.
*********************************************
Question: `q013. Students often get the basic answers to nearly all, or even all these questions, correct. Your instructor has however never seen anyone who addressed all the subtleties in the given solutions in their self-critiques, and it is very common for a student to have given no self-critiques. It is very likely that there is something in the given solutions that is not expressed in your solution.
This doesn't mean that you did a bad job. If you got most of the 'answers' right, you did fine.
However, in order to better understand the process, you are asked here to go back and find something in one of the given solutions that you did not address in your solution, and insert a self-critique. You should choose something that isn't trivial to you--something you're not 100% sure you understand.
If you can't find anything, you can indicate this below, and the instructor will point out something and request a response (the instructor will select something reasonable, but will then expect a very good and complete response). However it will probably be less work for you if you find something yourself.
Your response should be inserted at the appropriate place in this document, and should be indicated by preceding it with ####.
As an answer to this question, include a copy of whatever you inserted above, or an indication that you can't find anything.
your answer: vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv While working through this I paused for hesitation in remembering some skills such as expressed in questions 3, 5, 6, and 12. I have always had trouble in the small things of math. For example, I may get a formula correct for a certain equation but I would forget to carry the one or to divide at the end or something very simple like that to cause my solutions to be wrong. Because of this I tend to hesitate on what I know and go back and double check a few times before moving on.