Expressions

When you multiply a factor by itself, you can write a numerical expression using exponents .   The number 23  is written in exponential form, where 2 is the base and 3 is the exponent.   An  exponent , or power, tells how many times the base is used as a factor.

Order of operations:

  1. Perform operations in  parentheses.
  2. Find the values of numbers with  exponents.
  3. Multiply  or  divide  from left to right in the order it appears in the problem.
  4. Add  or  subtract  from left to right in the order it appears in the problem.

A fun way to remember the  order of operations  is the phrase ”  Please  Excuse My  Dear  Aunt  Sally.” The first letter in each word can help you remember the order of operations.

The commutative property states that you can add or multiply numbers in any order.

The associative property says when you are only adding or multiplying, you can group any of the numbers together.

A  variable  is a letter or symbol that represents a quantity that can change.   A constant  is a quantity that doesn’t change.   An  algebraic expression  is a variable  or combination of variables, numbers, and operations.

When you evaluate an  algebraic expression , you substitute a number in for the variable and find the value.

Like terms  are terms that contain the same variable, with corresponding variables having the same power.  Simplify expressions by combining like terms.

Practice

1) Evaluate.  12 + 7 + 18 + 23

2) Evaluate.  7 + 21 + 13 + 9

3) Evaluate:  2 x 27 x 10

4) Evaluate:  5 x 17 x 2

5) Write as an expression with an exponent.  3 x 3 x 3 x 3 x 3

6)  Write as an expression with an exponent.  7 x 7 x 7

7)  Write as an expression with an exponent.  8 x 8 x 8 x 8 x 8 x 8

8)  Write as an expression with an exponent.  1 x 1 x 1 x 1

9)  Evaluate: 92

10) Evaluate: 53

11) Evaluate: 4x + 7 when x = 11

12) Evaluate 24 – b when b = 30

13) Combine like terms: 4x – 3y + 3x + 5y – 4

14) Combine like terms: 12 – 2y + 5x + 4y – 7x – 8

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