mat 117 week 3 DQ's 4 different explanation
mat 117 week 3 DQ's 4 different explanation
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Date Created: 11/16/15
Week 3 DQ 1 – Due Day 2 Please post a 150 300 word response to the following discussion question by clicking on Reply. Take any number (except for 1). Square that number and then subtract one. Divide by one less than your original number. Now subtract your original number. Did you reached 1 for an answer? You should have. How does this number game work? Hint: Redo the number game using a variable instead of an actual number and rewrite the problem as one rational expression. How did the number game use the skill of simplifying rational expressions? Create your own number game using the rules of algebra and post it for your classmates to solve. Think about values that may not work. State whether your number game uses the skill of simplifying rational expressions. Consider responding to your classmates by solving their number games or expanding on their games to create an even more challenging one. You may want to review responses to your number game in case you need to make changes or help another student. Explanation 1 Take any number (except for 1). 2 Square that number and then subtract one. 2^21=41=3 Divide by one less than your original number. Now subtract your original number. 3/1=32=1 It worked! I reached number 1. Let the unknown number = A Square that number and then subtract one. A^21 Divide by one less than your original number. Now subtract your original number. A^21/ a1 a (A1)(A+1)/A1 A Cancel like terms A+1A = AA+1= 1 I reached 1 again! Now here is my number game.... Take any number, square it, and add 6 multiplied by the original number. After that add 5. Now divide this by the original number plus one. Now subtract your original number to get 5. You can also replace the number with a variable and get the number 5 Explanation 2 Original #: 10 10² = 100 100 – 1 = 99 99 / 9 = 11 11 – 10 = 1 With Variable A A² 1 / (A – 1) – A (A+1)(A1) / (A1) A1 Cancels out (A+1) A = 1 Choose any number for this game. Square the number and then add 6 multiplied by your original number. Now add 5. Divide the answer you get by the original number plus one. Now subtract your original number. For any number you choose your final answer should be 5. 8² = 64 64 + 6(8) = 112 112 + 5 = 117 117 / (8+1) = 13 13 – 8 = 5 I am pretty sure that all number will work for this game. This number game does not really deal with simplifying rational expressions. Explanation 3 Explanation 3 The number that I used was 4 and this is what I came up with: 4^4=161=15/3=54=1 The number that I came out with is 1 which was what I was suppose to come out with, amazing! This number game works by letting the number needing to be reached or the unknown number = x. The equation would look like this x^21, then you would divide it by one less than x and then subtract the equation by x. In order to get to one for the answer you would have to cancel out all of the like terms and you would be able to reach the same answer as the original problem given above which is 1. The number game that I have in mind is: Choose a number between 0 and 49 and then add 50, multiply the number you have chosen by 2 then subtract it by your original number and then subtract it by 100. Did you get the number you choose between 0 and 49? Explanation 4 Number: 4 Square: 4^2 = 16 Subtract: 4^2-1 = 15 Divide by one less:4^2-1/3 = 5 Subtract: 4^2-1/3-4 = 1 Yes the answer ended up being 1. I do not know how this works. A A^2 A^2-1 A^2-1/B A^2-1/B - A I dont think the B is suppose to be there. Im Confused. I can see how the expression resembles like expressions we have been learning. Using the methods of math and simple adding subtracting and dividing can bring you back to your starting point more simplified. My example for the class: Im not much on Algebraic Teasers but here is one: 100 What is the remainder when you divide 100 by 11? Week 3 DQ 2 – Due Day 4 Please post a 150 300 word response to the following discussion question by clicking on Reply. How is doing operations—adding, subtracting, multiplying, and dividing— with rational expressions similar to or different from doing operations with fractions? Can understanding how to work with one kind of problem help understand how to work another type? When might you use this skill in real life? Explanation 1 Doing operations with rational expressions and fractions are the same because you have to do the same steps in order to achieve the answer. Both require a common denominator to add or subtract. When dealing with multiplication you multiply the numerators and denominators. Understanding how to do one type can help with the other because you can reference the steps with one problem when dealing with common denominators. If you forget how to multiply a fraction but know how to multiply a rational expression chances are they are done the same way. As always, any math skill increases the sharpness of your critical thinking skills and problem solving skills. But knowing how to do this particular method can help you when you need to divide long problems or when you are creating a budget for yourself. Knowing harder math problems help simple ones that we use in every day life. Explanation 2 When working with rational expressions the methods used in simplifying and solving them are very similar to working with fractions. This is because you can find the factors of one by using fractions. You have to look for common denominators in order to factor and the techniques for working with the fractions in rational expressions are the same as working with regular fractions. This includes reducing one down to its lowest form which with rational expressions helps to identify the similar terms of the expression, using the reciprocal to come up with a factor of one, and adding or subtracting common terms. I think that understanding how fractions work is very helpful when working with rational expressions. If you are having problems with one, the odds are you will have problems with the other. You might need this information when trying to calculate something or a group of things that are not whole. Maybe in trying to only pay a percentage of all or some of your monthly bills, trying to save a certain percentage or something, or creating a budget for your home. I am sure that there are many other ways to use this information but most people have to deal with weekly or monthly budgets and this could apply to all of them. Explanation 3 Doing operations—adding, subtracting, multiplying, and dividing—with rational expressions is similar to doing operations with fractions in that you have to set the problem up correctly for it to be correct. The single most important similarity in both of these operations, when adding and subtracting, is finding a common denominator from which you will properly continue on to solve the rest of the operation. The only time that this can get a little challenging or different from each other is when variables are involved. Variables force us evaluate the problem a little differently before proceeding. But, in the end, it is just like an operation with just number. You must find a common denominator with or without variables. Dividing and multiplying operation are set up a little different than adding and subtracting in that a common denominator is not needed. Having a good understanding of one type of operation will absolutely help you with other types of operations. These types of operations are applicable in everyday life from estimating material needs for landscaping or building. Basically, you can use these operations when trying to figure out unknowns from some information that is already known. Explanation 4 Doing operations such as adding, subtracting, multiplying, and dividing with rational expressions are similar to doing operations with fractions. So far from what I have learned in this class and my class before the same rules are applying when it comes to what to follow. I find it easier to deal with the addition and the subtraction problems because I tend to struggle when it comes to multiplying fraction and dividing fractions. Another similarity that I see is when adding and subtracting it requires the lowest common denominator and multiplication and division works the same. These skills can be used in a real life setting but I always find myself figuring things out with simpler forms of math. I know that it may end up being a longer process but I feel more comfortable that I have come out with the correct answer. For instance, instead of me trying to figure out precisely how to evenly divide amounts of food between my children I give the same size scoop and measure that way. I may be way off here but I just do not use measurements such as fractions in everyday life.
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