**Unit 5: Expressions & Equations**

**Independent and Dependent Variables**The independent variable is found on the x-axis of a graph.

The dependent variable is found on the y-axis of a graph.

The dependent variable changes based on the independent variable.

When looking at a data table, if you are trying to decide which is independent and which is dependent ask yourself, "Which of these two things changes based on the other?"

Identifying Independent and Dependent Variables: Online Practice

Identifying the Independent and Dependent Variables Video

**Translating Expressions****Translating a written expression to an algebraic expression**

**If you are given a written expression you must identify…**

**The numbers present in the expression; they may be written as numbers: 5, 62, 108 OR written as words: five, sixty-two, one hundred and eight**

**The necessary operation or operations**

**The order of the operations; the Order of Operations must be followed when creating and evaluating expressions, if an operation MUST come first, then you must included parenthese**

**EX) three less than the product of 5 and z is translated to: 5z – 3**

**EX) forty increased by the difference of y and 8 is translated to: 40 + (y – 8)**

Translating Expressions: Video

**Equivalent Expressions**We can use the distributive property to create equivalent expressions. The distributive property tells us to multiply the outside number or term by both terms inside the parentheses.

What is the Distributive Property? Video

The distributive property can be used to show the area of a rectangle. The area of a rectangle is equal to length times width.

A = lw

A = lw

**Algebraic Expressions**

**Translating Expressions:**When translating expressions, you must create an expression using numbers, variables and operations to represent what the words or situation is telling you.

Order matters in subtraction and division, so it is very important when translating expressions involving subtraction and division that the order of the numbers is correct.

**Evaluating Expressions**When given a value to substitute for the variable, you must then evaluate the expression according to the order of operations.

The order of operations can be remembered through PEMDAS.

Anything found inside the parentheses must be completed FIRST.

Any exponents must be evaluated SECOND.

Next, you complete multiplication and division as you see it from left to right.

Finally, you complete any addition and subtraction from left to right.

What are numerical and algebraic expressions? Video

Simplifying Numerical Expressions Video

**Solving Algebraic Equations**In order to solve for a variable in an algebraic equation you must work backwards to get the variable all by itself.

You must use inverse or opposite operations to isolate the variable.