01+Order+of+Operations,+Properties,+Variables+and+Expressions

Sections 1-1, 1-2, 1-4, 1-5, 1-6

PEMDAS- Hunter Helfenbein

COMMUTATIVE, ASSOCIATIVE, DISTRIBUTIVE- Melissa Ashkinaze- Commutative and Distributive Properties [] []

 //**#1. Commutative properties**// The commutative property of addition says that we can add numbers in any order. The commutative property of multiplication is very similar. It says that we can multiply numbers in any order we want without changing the result. **Addition**  **3** x **8** x **5b = 5b** x **3** x **8**  //**#2.Distributive property**// The distributive property comes into play when an expression involves both addition and multiplication. A longer name for it is, "the distributive property of multiplication over addition." It tells us that if a term is multiplied by terms in parenthesis, we need to " **distribute** " the multiplication over all the terms inside. **2x(5 + y) = 10x + 2xy** //**Example 1 Distribute Over Addition**// (3 + 11)5 = 3 ⋅ 5 + 11 ⋅ 5 Distributive Property = 15 + 55 Multiply. = 70 Add. **Example 2 Distribute Over Subtraction** **a) Rewrite 2(13 - 7) using the Distributive Property. Then evaluate.**  2(13 - 7) = 2(13) - 2(7) Distributive Property  = 26 - 14 Multiply.  = 12 Subtract.   **Example 3**
 * 5a + 4 = 4 + 5a**
 * Multiplication**
 * a) Rewrite (3+11)5 using the Distributive Property. Then evaluate.**


 * a) You can swap when you add: || **3 + 6 = 6 + 3** ||


 * b) You can swap when you multiply: || **2 × 4 = 4 × 2** ||


 * COMBINING LIKE TERMS-**

The following are like terms because each term consists of a single variable (x) and a numeric coefficient. 2x, 13x, x, -29x
 * What are like terms?**

Each of the following are like terms because they all consist of xy and a coefficient. 13xy, -1/2xy, 8xy, 9.2xy

Each of the following are not like terms because they each consist of a different variable. 15y, 2x, q, 91m
 * What are NOT like terms?**

Each of the following are not like terms because they have a different exponent and therefore cannot be combined 15y, 76x2, 58y4

ex1: 5x2 + 7x + 2 - 2x2 + 7 + x2 you can only combine the like terms that have the same exponent and variable in this example you can combine 5x2+2x2+x2 and 2+7 8x2+9+7x
 * How do you combine like terms?

** The Associative Property

Addition Form: In the addition form, the sum of the equation is the same no matter what way you group the addends on each side.

The General addition form of the Associative Property is: (a + b) + c = a + (b + c) The Order of this equation can be changed as to what numbers are in the parentheses.

Multiplication Form: The product is the same no matter what way you group the factors. (ab) c = a (bc)

For example, this can be changed to: a (bc) = (ab) c

Example: Solve using the addition form of the Associative Property (1 + 2) + 3 = 1 + (2 + 3) 3 + 3 = 1 + 5 6 = 6

Example 2: Solve using the multiplication form of the Associative Property (2 x 3) x 4 = 2(3 x 4) 6 x 4 = 2 x 12 24 = 24

Helpful links for the Associative Property: []

[[http://www.icoachmath.com/sitemap/AssociativeProperty.html|http://www.icoachmath.com/sitemap/AssociativeProperty.html

]]Mike Vercellone