MTE 494 10 07 09 Midterm Test 1 Instructions This test contains 4 questions most of which entail multiple parts You must complete the test individually and may not consult classmates or anyone else other than the instructor You may draw on the course materials and resources but not in a copy and paste manner Instead paraphrase textual statements and descriptions in your own words in a manner that does not distort or misrepresent their intended meanings Your exam paper must be composed in a self contained MS Word file with any diagrams or drawings embedded in the appropriate places within your narrative Use this file name convention MTE494 Midterm1 XYZ where X Y Z are you first middle and last initials respectively Submit your file to me as an email attachment no later than 10 00 a m on October 12 2009 Send me a follow up message asking for confirmation of receipt to verify that what you sent out was actually submitted to me If you do not receive a confirmation from me then try sending via another email account or program Question 1 SoloClearing is a one man owned and operated landscaping company that specializes in weed clearing The company uses a high power weed trimmer that consistently clears the same area of weedy land in a given unit of time One day the company spent a total of 2 5 hours on one job clearing weeds and 3 75 hours on a second job doing the same thing Suppose the expression 37 2 5 3 75 represents the total area in square yards of land cleared with the weed trimmer on that day a The weed trimmer clears 37 square yards of land per hour If 37 2 5 3 75 represents the total area and 2 5 3 75 represents the total number of hours spent clearing that area then 37 must represent the rate at which area is cleared per hour b Based on order of operations we perform the operations in the expression in a specific order to calculate the total area of land cleared In what order do we perform the calculations First Add together the number of hours it took to do each job 2 5 3 75 This calculates the total number of hours it took to do both jobs Second Multiply 37 by the value obtained above 37 2 5 3 75 This calculates the total amount of area cleared in that number of hours worked Note It will be helpful for part c to use commutativity of and think of this value as 2 5 3 75 37 c Explain how to interpret the expression in terms of the making copies meaning of multiplication identify which amount is being copied and how many copies of it are 1 MTE 494 10 07 09 made so that it makes sense that the expression represents an amount of area and that it is calculated using the order you specified in part b In the making copies meaning the expression 37 2 5 3 75 would denote the amount made by making 37 copies of 2 5 3 75 Since 2 5 3 75 represents a number of hours then 37 2 5 3 75 represents 37 copies of that number of hours This means that the resulting value will be a number of hours But this doesn t make sense in the given situation because we are told that the expression 37 2 5 3 75 represents a total area We seem to have a quandary here We need a way to think about the given expression that both fits the making copies meaning of multiplication AND respects that the expression represents an amount of area We can use the fact that multiplication is a commutative operation the value of 37 2 5 3 75 is the same as the value of 2 5 3 75 37 and this latter expression represents the amount made by making 2 5 3 75 copies of 37 So we can think of the original expression as the value of the expression 2 5 3 75 37 which according to our meaning represents the amount made by making 2 5 3 75 copies of 37 yards the amount of area cleared in each hour In calculating the value of 2 5 3 75 first in part b we are essentially calculating how many copies of 37 yds to make Answering this question coherently rests on the subtle yet important fact that the making copies conception of multiplication entails two aspects that must be kept in mind the expression a b denotes 1 imagining making a copies of b and 2 the value obtained by making a copies of b The commutativity of the operation in this meaning has to do with aspect 2 and the method of calculating this value not with aspect 1 Note Your explanation must describe the meaning of the expression each of its components and the operations used to calculate its value explicitly in terms of this model of multiplication 2 MTE 494 10 07 09 Question 2 Suppose that two students CJ and Julie walk the same distance The figure below shows the relationship between the size of CJ s step and the size of Julie s step Use our meanings of fraction measure and multiplication the ones developed in the course to reason through this scenario and answer this question How many steps did CJ take in relation to the number of steps Julie took Write your reasoning in a way that makes clear to the reader the relevant quantities and relationships involved in the scenario and your solution 1 The figure shows that 1 13th of a CJ step is the same size as 1 8th of a Julie step 2 1 CJ step is 13 times as much as 1 13th of a CJ step 3 1 CJ step is 13 times as much as 1 8th of a Julie step 4 1 CJ step is 13 one eighths 13 8 Julie steps by 2 3 5 If CJ takes 1 step then Julie will take 13 8ths Julie steps to cover the same distance 6 If CJ takes 2 steps then Julie will take 13 8ths of her steps twice she will take 2x13 8 Julie steps 7 If CJ takes 3 steps then Julie will take 13 8ths of her steps three times she will take 3x13 8 Julie steps In general if CJ takes n steps then Julie takes 13 8 times as many steps she takes n x 13 8 steps 3 MTE 494 10 07 09 Question 3 Consider this scenario It is 1873 in Territorial New Mexico The Lone Ranger is chasing a desperate bank robber over the desert Both are on horseback and the bank robber got an 11 mile head start The bank robber s horse can run steadily at 16 miles per hour The Lone Ranger s horse can run steadily at 19 miles per hour The bank robber is heading for the Mexican border for if he can cross the border he will be safe The …