Unit 4

  • Evaluating Expressions

    We have learned that, in in an algebraic expression, letters can stand for numbers. When we substitute a specific value for each variable, and then perform the operations, it's called EVALUATING THE EXPRESSION.   To evaluate an expression, first replace each letter in the expression with the assigned value, then perform the operations in the expression using the order of operations.  See the quick video on the right for an example.  Here's a link to practice evaluating expressions: https://www.khanacademy.org/math/algebra-home/alg-intro-to-algebra/alg-intro-to-variables/e/evaluating_expressions_1

  • Prime Factorization

    The prime factorization of a number is when a composite number is written as the product of prime numbers.  Every number has its own unique prime factorization (like a fingerprint).  
    Example:  The prime factorization of 56 = 2 x 2 x 2 x 7.

    We can write the prime factorization with exponents.  (EX: 56= 23 x 7)          
    2 x 3 x 9 is NOT the prime factorization of 54 because 9 is not a prime number.    We use FACTOR TREES as a tool to find the prime factorization of numbers.  

    Games and practice for Prime Factorization:  http://www.mathplayground.com/factortrees.html   and   http://www.transum.org/Maths/Activity/Prime/

  • Combining Like Terms]

    "Like terms" are terms whose variables (and their exponents such as the 2 in x2) are the same, but the coefficients (the numbers you multiply by, such as "5" in 5x) can be different.  

    EX:  7x,  -5x,  and x are like terms but  7y  and 8x2  are not because the variables are different or the exponents are different.

    We can combine like terms simply by adding the coefficients.  Remember x by itself has an invisible 1 for a coefficient.  

    EX:    3x2 - 7 + 4x3 - x2 + 2  =  (3x2 - x2) + (4x3) + (2 - 7)  =  2x2 + 4x3 - 5