WPP #7: Unit K Concept 11

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Student Problem #7 : Unit K Concept 10

• What is this problem about?

This picture covers a problem from Unit K Concept 10. This concept deals with writing repeating decimals as a rational number using geometric series. In this type of problem what you are basically trying to do is break down the decimal to discover the rational number or the sum of the decimal. After breaking down the decimal into repeating units you then are able to figure out the first term of the series and then the common ratio of the series which allows us to then plug it into the equation that has the sigma with the infinity sign. Then, you plug in a sub 1 and r into the summation notation formula in order to simplify and figure out the rational number. 

• What does the viewer need to pay special attention to in order to understand the concept?

In order to understand the concept the viewer needs to pay special attention to how the decimal is broken down. What we do is basically take the repeating decimal and set it as its own. Then we out an addition sign which then allows us to break down the decimal by putting zeroes in front of the repeating decimal. The point of this is to make sure that you get the correct value for a sub 1. Also, when you have wrote out the series it is important that you write the broken down decimal correctly so that when we divide one term to the other, we and up with the correct common ratio (r).

Fibonacci Haiku

Fibonacci Haiku

Family

Love

My Foundation

My Support System 

I will always love them 

They are my motivation to do better everyday. 

Fibonacci Haiku 

Basketball

Perseverance

Hard Work 

Passion to play 

It is apart of me 

Helps maintain the balance I need in life.  

Student Problem #6 Unit J Concept 6

Student Problem #6 Unit J Concept 6

• What is this problem about?

This problem covers an example from Unit J Concept 6. This concept is very similar to Concept 5 except now we are dealing with Partial Fraction Decomposition with repeated factors. In this type of problem when you try in factor the denominator out you will find that one of the factors is repeated. Meaning that now when you separate the factor into separate equations for the repeated factor you must include the factor as a denominator as many times as the exponent. For example if the denominator as shown is (x-1)^3 you must have one fraction be A/(x-1), the nest one be B/(x-1)^2, and the last one be C/(x-1)^3. This is the only difference, then you would just solve as you did in concept 5. 

• What does the viewer need to pay special attention to in order to understand the concept?

In this concept the viewer must pay special attention to the common denominator so that when multiplying the numerator by what a part of the fraction is missing then your system comes out to being correct. Also, you must pay attention to how to right the denominators when separating the fractions. You must also pay close attention making sure your answers are plugged in correctly in the end. 

Student Problem #5 Unit J Concept 5

Unit J Concept 5

• What is this problem about?

This problem goes over a problem from Unit J Concept 5. Unit J Concept 5 covers a lesson on Partial Fraction decomposition with distinct factors. This concept is much easier than it seems. There are 7 steps in which you must take to complete this problem and they are as follows: Factor out the denominator, separate each of the factors into their own fractions and put the letters A,B,C, etc. on top, get a least common denominator for the factors by multiplying it by what its missing, combine like terms, set the coefficients of the numerator equal to like term letters on the right, set up the system and solve, and finally put A, B,C, ect. back to where there variable is at in the spit up fractions in the beginning. 

• What does the viewer need to pay special attention to in order to understand the concept?

The viewer needs to pay special attention not to forget to put zeroes in the numerator if there is just an x, or if something is missing. This is important because when setting up your system of equations you may forget and get confused of what number goes on the other side of the equal sign. Also, you must pay attention to how you take out the x's once writing your system. You need to be sure to take the x's out so that you can combine terms an solve for A or B, it is not necessary to keep those x's in the equations at this point.