Introduction to Algebra Homework

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Evaluating Algebraic Expressions

Read the following instructions in order to complete this discussion, and review the example of how to complete the math required for this assignment BELOW..

 

  1. Write your birth date or the birth date of someone in your family as mm/dd/yy. (Example: March 13, 1981 is written 3/13/81, and November 7, 1967 is written 11/7/67).   

    • Now let a = the one- or two-digit month number, 

    • b = the negative of the one- or two-digit day number, and 

    • c = the two-digit year number.
      (Our example:  a = 3, b = -13, and c = 81 or a = 11, b = -7, and c = 67) 
        
  2. Use the following algebraic expressions for parts 3-5 of the discussion: 

    •   

    •    

    •  
        
  3. Evaluate the three given expressions using the a, b, and c from your birth date.  Make sure that b is negative when you plug in the values
      
  4. After you have your math worked out on scratch paper, go back and verbally describe the steps you took to evaluate the expressions. Make sure to use each of the vocabulary words at least once in your writing.
    • Did you notice anything interesting about the results of  and ? Was this coincidence or do you think there is a reason for this?
        
  5. Incorporate the following five math vocabulary words into your discussion. Use bold font to emphasize the words in your writing (Do not write definitions for the words; use them appropriately in sentences describing your math work.): 

    • Exponent 

    • Integer 

    • Variable 

    • Lowest terms 

    • Divisor 
 
 

INSTRUCTOR GUIDANCE EXAMPLE: Week One Discussion

1. I will use the following five vocabulary words in my discussion demonstrating my understanding of their meaning as relating to the math work.

exponent integer variable lowest terms divisor

2. I will be using my sister’s birth date for this exercise, and it is 21 October 1961. This means I have the following integers to work with:
Let a = 10

b = 21 (notice I made the day number negative) c = 61 

 

I will be using the algebraic expressions in A – C given in the assignment for parts 3 – 5 of the discussion.

A) a– b3

10– (-21)1000 – (-9261) 1000 + 9261 10,261

This is the given expression with variables a and b and exponents of 3 on each of them
I have plugged in 10 for 
variable a and -21 for variable b. The integers were raised to the given exponents.
Minus a negative becomes a plus.
Here is the final answer.

B) (a – b)(a+ ab + b2)
[10 
– (-21)][10+ 10(-21) + (-21)2]

31(100 – 210 + 441) 31(331)
10,261

C) bc 2b – a

2161 2(-21) – 10

– 82 – 52 41 26

In the first part the two negatives became a plus, and in the second part the squaring and the multiplication was done. The first addition was done and the signs were simplified. The second quantity was simplified.

Here is the final answer.

This expression uses all three variables: a, b, and c. It is a rational expression with a divisor of 2b – a. The integers have been plugged in for the variables.

Both numerator and denominator have been evaluated. Both are negative which means the answer will be positive. This is our answer in lowest terms, and I will leave the answer as an improper fraction.

This is the given express which also uses variables a and b.

I have plugged in 10 for a and -21 for b in each case. [10 + 21][100 + (-210) + 441]

6. [Student answers will vary on this question depending upon math background and memory.] 

 

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