Evaluate variable expressions involving integers

key notes :

Understanding Variable Expressions

Definition:

• A variable expression (or algebraic expression) is a mathematical phrase that includes numbers, variables (letters representing unknown values), and operations.

Variables:

• Variables are symbols (usually letters) that stand for unknown or changeable values.
• Example: In the expression 3x+4, x is the variable.

Evaluating Variable Expressions

Substitution:

To evaluate a variable expression, substitute the given value(s) of the variable(s) into the expression and perform the arithmetic operations.

Example: Evaluate 3x+4 for x=2.

• Substitute x=: 3(2)+4
• Perform the operations: 6+4=10

Order of Operations (PEMDAS):

When evaluating expressions, always follow the order of operations:

• Parentheses
• Exponents (not typically covered in 6th grade, but good to be aware)
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

Steps to Evaluate Variable Expressions

Step 1: Substitute the Values:

• Replace the variables in the expression with their given values.
• Example: For x=3, y=4, evaluate 2x+3y.
• Substitute: 2(3)+3(4)

Step 2: Follow the Order of Operations:

• Perform any calculations inside parentheses first.
• Then, perform multiplication and division from left to right.
• Finally, perform addition and subtraction from left to right.
• Example: 2(3)+3(4)
• Multiply: 6+12
• Add: 18

Examples

Single Variable:

Evaluate 5x−7 for x=2

• Substitute: 5(2)−7)
• Calculate: 10−7=3

Multiple Variables:

Evaluate 3x+4y for x=1 and y=2

• Substitute: 3(1)+4(2)
• Calculate: 3+8=11

With Parentheses:

Evaluate 2(x+y) for x=3 and y=5

• Substitute: 2(3+5)
• Calculate inside parentheses: 2(8)=16

Tips for Students

Substitute Carefully:

• Ensure you replace each variable with the correct value.

Follow Order of Operations:

• Always use PEMDAS to avoid mistakes.

Show Your Work:

• Write each step to make your calculations clear and to check for errors.

Practice Regularly:

• Consistent practice with different types of expressions helps solidify understanding.

Learn with an example

Let’s Practice!